Evaluation of 3D Spatializations

Department of Geography Geographic Information Visualization and Analysis University of Zurich - Irchel Winterthurerstrasse 190 CH-8057 Zurich

Evaluation of 3D Spatializations

Master Thesis

Sara Maggi 6654 Cavigliano Tel: +41 (0)79 262 58 89 E-Mail: [email protected]

Supervisors: Prof. Dr. Sara I. Fabrikant, Dr. Arzu Cöltekin

Zurich, October 2009

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Acknowledgements I would like to thank everyone who support me and made this thesis possible. First of all, I am particularly grateful to Dr. Sara I. Fabrikant for her supervision, her valuable and well-timed guidance throughout my work. I would like to thanks Dr. Arzu Cöltekin for her numerous advises and support of technical problems. I’m heartily thankful to all people who participated to the experiment with 3D network spatializations. They enabled me to statistically evaluate the results and thus to realize this work. Many thanks are going in particular to Jessica and Jonathan who read through my work and corrected the English. Special thanks to all my friends, in particular Maria, Miriam, Veronica and Mirjam for their presence during the good and bad times. Finally, I would like to heartily thank Michael and my family, Manuela, Marco and Stefano, for their interest to my work and the unconditional support in everyday life.

Zurich, October 2009 Sara Maggi

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Abstract Spatializations are techniques aimed to graphical depict non-spatial data in very large databases. To realize this purpose they used geographical metaphors as location, distance or direction for the knowledge discovery as well as the information exploration. This master thesis proposes an evaluation of 3D network spatializations through an experiment with participants. In particularly, it was investigated how non-expert people interpreted the concepts of proximity and similarity in information spaces. Moreover, three non-spatial visual variables defined by Bertin were analysed in order to understand how they influenced the perception of the distance-similarity metaphor in 3D spatializations. This work is based on theories of the GIScience, of the information visualisation and of the cognitive science. As methodological procedure for evaluating 3D spatializations it was conducted an experiment with participants according to a mixed factorial design. Participants were compared with different dynamic and interactive 3D network representations. To visualize the 3D images it was used an immersive virtual reality system called Geowall. As a result, participants interpreted the network displays according to the "First Law of the Cognitive Geography". It affirms that people believed closer things were more similar to each other than distant one (Montello, Fabrikant et al. 2003:2). The number of intervening nodes between documents as well as the non-spatial visual variables width, color value and color hue moderated significantly the perception of the distance-similarity metaphor. The size of the links connecting documents in a network spatialization resulted to be the most relevant and strong visual variable in depicting relatedness between documents. In addition, the homogeneity of the line color value, hue and width, as well as the context and complexity of the information space had an influence on the similarity judgement. Furthermore, the results of this experiment were compared with the results of a previous study with 2D network spatializations conducted by S.I. Fabrikant, D.R. Montello et al.(2004). The conclusion was that the addition of a third dimension in spatialized network displays can allow to depict more information as two-dimensional representations. But this is not enough to justify the use of 3D representation in designing cognitively adequate spatializations because participants requires more cognitive efforts to interact with them. iii

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Finally, it was compared stereoscopic 3D spatialized network representations with monoscopic one, but no significantly differences in perception among the participants were found.

Contents Acknowledgements

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Abstract 1

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1 1 2 3 4 4 4 5 5 6

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Visualization in 3D 3.1 Space perception and depth cues . . . . . . . . . . . . . . . . 3.2 Methods for 3D visualization . . . . . . . . . . . . . . . . . . 3.3 Problems with 3D visualization . . . . . . . . . . . . . . . . .

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Information spaces and their semantics 4.1 Information space . . . . . . . . . . . . . . . . . . . . . . . . . 4.2 Semantics of information spaces . . . . . . . . . . . . . . . .

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The map representation: cartography and visual variables

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Spatialization 6.1 Definition . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2 Data types in spatialization . . . . . . . . . . . . . . . . 6.3 Spatialization framework . . . . . . . . . . . . . . . . . 6.4 The concept of similarity and spatializations techniques 6.4.1 The concept of similarity in a document space . 6.4.2 Spatializations techniques . . . . . . . . . . . . .

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Introduction 1.1 Introduction to the topic . . . . . . . . 1.2 Motivation . . . . . . . . . . . . . . . . 1.3 State of the research in GIScience . . . 1.4 Statement of purpose . . . . . . . . . . 1.4.1 Research objectives . . . . . . . 1.4.2 Research questions . . . . . . . 1.4.3 Formulation of the hypotheses 1.5 Literature review . . . . . . . . . . . . 1.6 Outline of the thesis . . . . . . . . . . .

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Information visualization 2.1 Definition . . . . . . . . . . . . . . . . . . . . . . . . 2.2 The process of visualization . . . . . . . . . . . . . . 2.3 The process of visual perception and visual thinking 2.4 Data types in information visualization . . . . . . . 2.5 Network displays in a 2D and 3D space . . . . . . .

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Relevance of GIScience for spatialization . . . . . . . . . . . Spatialization examples . . . . . . . . . . . . . . . . . . . . . Related project . . . . . . . . . . . . . . . . . . . . . . . . . . .

Method 7.1 Participants . . . . . . . . . . . . . . . . . . . . . . 7.2 Apparatus . . . . . . . . . . . . . . . . . . . . . . . 7.3 Design . . . . . . . . . . . . . . . . . . . . . . . . . 7.3.1 The independent variables . . . . . . . . . 7.3.2 The mixed factorial design . . . . . . . . . 7.3.3 The dependent variables . . . . . . . . . . . 7.3.4 The control variables . . . . . . . . . . . . . 7.3.5 The between-subjects experimental design 7.3.6 The within-subject experimental design . . 7.3.7 The post-test questionnaire . . . . . . . . . 7.3.8 Hypotheses . . . . . . . . . . . . . . . . . . 7.4 Materials . . . . . . . . . . . . . . . . . . . . . . . . 7.5 Procedure . . . . . . . . . . . . . . . . . . . . . . . 7.5.1 Pilot test . . . . . . . . . . . . . . . . . . . . 7.5.2 Main experiment . . . . . . . . . . . . . . .

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Results and analysis 67 8.1 Descriptive statistics . . . . . . . . . . . . . . . . . . . . . . . 68 8.1.1 The one-sample Kolmogorov-Smirnov test . . . . . . 69 8.2 Histograms of the similarity ratings for each display . . . . . 69 8.3 The One-sample t-test . . . . . . . . . . . . . . . . . . . . . . 69 8.3.1 Aggregation of mean similarity judgements for each independent variable . . . . . . . . . . . . . . . . . . . 71 8.4 Pearson’s correlations . . . . . . . . . . . . . . . . . . . . . . . 76 8.5 GLM test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86 8.6 Repeated Measures ANOVA . . . . . . . . . . . . . . . . . . . 88 8.7 The fronto-parallel orientation of the displays . . . . . . . . . 90 8.8 Response time . . . . . . . . . . . . . . . . . . . . . . . . . . . 97 8.9 Responses of the post-test questionnaires . . . . . . . . . . . 100 8.10 Comparison between the 2D and the 3D experiment results . 111

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Discussion

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10 Conclusion and future directions for research

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A Consent Form and Questionnaire

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B Descriptive Statistics

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C Vizard Script: 3D Stimuli

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D SAS Script: Pearson’s Correlation

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Bibliography

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List of Tables 5.1 7.1 7.2 7.3 7.5

Levels of organization of the seven visual variables by Bertin (1983:69). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Summary of the professional experience, training or college classes that participants have. . . . . . . . . . . . . . . . . . . Geowall’s components . . . . . . . . . . . . . . . . . . . . . . Geowall’s components . . . . . . . . . . . . . . . . . . . . . . Matrix of the experiment outlined according to a factorial experimental design: a (3 X 21) + 2 design. One factor, the network distance, had 3 (+ 2) levels. The other factors, namely, hue, value, topology and width, had each 5 or 6 levels (6 + 5 + 5 + 5 = 21). . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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8.1

Mean similarity ratings of the 17 topology displays in which the Network and the Node distances between A:2 could be equal or greater the ditances between A:1. . . . . . . . . . . . 71 8.2 Mean similarity ratings of the 15 width displays in which the Network distance between A:2 could be equal or greater the distance between A:1. . . . . . . . . . . . . . . . . . . . . . . . 73 8.3 Mean similarity ratings of the 15 value displays in which the Network distance between A:2 could be equal or greater the ditance between A:1. . . . . . . . . . . . . . . . . . . . . . . . 74 8.4 Mean similarity ratings of the 18 hue displays in which the Network distance between A:2 could be equal or greater the ditance between A:1. . . . . . . . . . . . . . . . . . . . . . . . 75 8.5 Summary of the FPP statistics. . . . . . . . . . . . . . . . . . . 92 8.6 Summary of the FPP statistics pro participants: number of FPPs which participants saw, number of FPPs they saw just before responding, time and percentage of the time in which they saw FPPs. . . . . . . . . . . . . . . . . . . . . . . . . . . . 93 8.7 Summary of the amount of FPP pro participants in average and FPP time pro variable. . . . . . . . . . . . . . . . . . . . . 94 8.8 Summary of the amount of FPP pro participants in average and FPP time pro variable. . . . . . . . . . . . . . . . . . . . . 94 8.9 Summary of response times of the 2D and 3D experiments. . 97 8.10 Histograms of the displays hue_BBB_2X, t1_top41_2X and value_222_2X. . . . . . . . . . . . . . . . . . . . . . . . . . . . 111 B.1 Descriptive Statistic of the 3D Experiment. . . . . . . . . . . 141 B.2 One-Sample Kolmogorov-Smirnov test. . . . . . . . . . . . . 146 vii

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LIST OF TABLES

B.3 Histograms of the similarity rating pro display. . . . . . . . . 160

List of Figures 2.1

Schema of the visualization process (Ware 2004:4, figure 1.2).

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Model of the human visual perception processes (Ware 2004:21, figure 1.11). . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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2.3

3.1 3.2

Example of an Entity-Relationship diagram (ConceptDraw 2009. Access:09.09.2009. . . . . . . . . . . . . . . . . . . . . .

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Monocular static cues: size gradient, interposition and linear perspective. . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Monocular dynamic cues: motion parallax and kinetic depth effect (Ware 2004:270, figure 8.13). . . . . . . . . . . . . . . . .

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Binocular cues: eye convergence and stereoscopic depth. (HowStuffWorks 2009. Access: 09.09.2009) . . . . . . . . . . . . . . 15

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Spatial metaphors that underlie representations in the three semantic spaces types. (Fabrikant and Butterfield, 2001:271, table 2) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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The three degree of effectiveness of the Bertin visual variables in signifying geometric primitives (Bertin 1983; in: DiBiase et al. 1992:204). . . . . . . . . . . . . . . . . . . . . . . . .

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Ontological design for the semantic generalization process (Fabrikant and Skupin 2005:671). . . . . . . . . . . . . . . . .

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Source domains for the semantic generalization process in which semantic primitives are combined with geographic perspectives (Fabrikant and Skupin 2005:672, table 35.1). . .

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6.1 6.2

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Geometric generalization process (Fabrikant and Skupin 2005:674, figure 35.2). . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

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Multidimensional scaling example (Mark 2001; in: Skupin and Fabrikant 2003:98). . . . . . . . . . . . . . . . . . . . . . .

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Example of principal components analysis technique (Center for Machine Perception 2009). . . . . . . . . . . . . . . . . . .

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GnuMap: representations of gnutella P2P network by Spring algorithms (aiSee 2005). . . . . . . . . . . . . . . . . . . . . .

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Author co-citation analysis example (Society and Decision Making 2008. Access: 08.07.2009.) . . . . . . . . . . . . . . . .

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6.5 6.6 6.7

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LIST OF FIGURES

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6.10 6.11 6.12 6.13 6.14 6.15 6.16 7.1 7.2 7.3 7.4 7.5 7.6 8.1 8.2 8.3

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A self-organizing map which depict countries on the base of poverty indicators. The figure on the right is a world map in which countries have been coloured with the same color of the figure’s links (Laboratory and Computer and Information Science 2009). . . . . . . . . . . . . . . . . . . . . . . . . . Examples of a Tree map construction and an interactive Tree map of the market which shows the stock market grouped by sectors. The size of the nodes corresponds to the company’s market capitalization and the color indicates the difference of the current price from the closing price of the day before (green is up, red is down).(eagereyes 2009) . . . . . . Reuters news stories are represented as a 2D point configuration (Spacecast 2002). . . . . . . . . . . . . . . . . . . . . . . The desktop metaphor. . . . . . . . . . . . . . . . . . . . . . . The "semantic constellation" of an information space produced by Chaomei Chen (Chen 1999) . . . . . . . . . . . . . Network of connectivity between websites (created with the TouchGraph Browser). . . . . . . . . . . . . . . . . . . . . . . WebTracer (Nullpointer 2009) . . . . . . . . . . . . . . . . . . The Nicheworks tool (An Atlas of Cyberspaces 2007). . . . . 3D landscape: topic density surface (Spacecast 2002). . . . . Histograms of the participant’s age. . . . . . . . . . . . . . . Histograms of participant’s number that wear glasses and have lack of depth perception. . . . . . . . . . . . . . . . . . . Histograms of participant’s ability to read maps and frequency of recreational activities. . . . . . . . . . . . . . . . . . . . . . Professional experience, training or college classes that participants had. . . . . . . . . . . . . . . . . . . . . . . . . . . . Geowall in the 3D Visualization Lab of the geographic Institute, e University of Zurich . . . . . . . . . . . . . . . . . . . Experiment’s question for each stimulus. . . . . . . . . . . .

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Histograms of the displays in which the similarity ratings were not normally distributed. . . . . . . . . . . . . . . . . . 70 Example of displays: hue_BBB_2X, value_222_1X and width_123_3X. 71 SAS output of the Pearson’s correlations between Network distance ratios and the similarity ratings of the four visual variables pro participant (CORRHUE, CORRTOPO, CORRVALUE, CORRWIDTH) and the z-scores of the Fisher’s tranformation (zCORRHUE, zCORRTOPO, zCORRVALUE, zCORRWIDTH). 76 Pearson’s mean correlations between the Network distance ratios and the similarity ratings among the four variables hue, topology, value and width. . . . . . . . . . . . . . . . . . 77 SAS output of the Pearson’s correlations between the Node distance ratios and the similarity ratings of the topology displays and pro participant (CORRNODE, zCORRNODE). . . 77 Pearson’s mean correlations between the Node distance ratios and the similarity ratings. . . . . . . . . . . . . . . . . . . 77

LIST OF FIGURES

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One-sample statistics and t-test based on the z-scores of the Pearson’s correlations (test value=0). . . . . . . . . . . . . . . Table: GLM multivariate analysis of variance. Test of the between-subject effects between the correlation’s z-scores and the fixed factors gender and academical background. . . . . Scatter-plots of the correlations between the mean similarity ratings and the Network distance ratios of the topology and the hue displays. . . . . . . . . . . . . . . . . . . . . . . . . . Scatter-plots of the correlations between the mean similarity ratings and the Network distance ratios of the value and the width displays. . . . . . . . . . . . . . . . . . . . . . . . . . . Scatter-plots of the correlations between the mean similarity ratings (y-axis) and the Network distance ratios (x-axis). . . Scatter-plots of the correlations between the mean similarity ratings and the Node distance ratios. . . . . . . . . . . . . . . Scatter-plots of the correlations between the mean similarity ratings in function of the Network distance ratios and the Node distance ratios. . . . . . . . . . . . . . . . . . . . . . . . Output of the Repeated-Measures ANOVA. . . . . . . . . . . GLM univariate analysis of variance between the mean similarity ratings of each participant with the follow fixed factors: gender, academical background, age, ability on reading maps and frequency in recreational activities related with map’s reading. . . . . . . . . . . . . . . . . . . . . . . . . . . . Output of the Repeated-Measures ANOVA. . . . . . . . . . . Repeated-Measures ANOVA: pairwise comparisons of the similarity ratings between the four display types. 1=hue, 2=topology, 3=value, 4=width. . . . . . . . . . . . . . . . . . Multivariate effects of the similarity ratings. . . . . . . . . . . MANOVA test: within-subject effects of the number of FPP participants saw during the entire experiment among the dependent variables. . . . . . . . . . . . . . . . . . . . . . . . . . MANOVA test: within-subject effects of the number of FPP participants saw just before responding among the dependent variables. . . . . . . . . . . . . . . . . . . . . . . . . . . MANOVA test: within-subject effects of the FPP time among the dependent variables. . . . . . . . . . . . . . . . . . . . . . GLM multivariate analysis of variance: tests of between-subject effects. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . GLM univariate analysis of variance: tests of between-subject effects. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . GLM Repeated Measures ANOVA: tests of within-subject effects among the independent variables hue, topology, value and width. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Univariate analysis of variance, test of between-subject effects of the response time compared with the following factors: gender, age, ability in map reading, frequency in recreational activities with maps and academical background. . .

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8.26 GLM Repeated-Measures ANOVA: tests of within-subject effects of the response times between 2D and 3D displays. . . 8.27 Distance types which participants had used to judge the similarity between the documents. . . . . . . . . . . . . . . . . . 8.28 Consideration of the color value to judge similarities between documents. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.29 Consideration of the link’s darker shading to judge similarities between documents. . . . . . . . . . . . . . . . . . . . . . 8.30 Consideration of the link width to judge similarities between documents. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.31 Interpretation of thicker lines as indicating a greater similarity between documents. . . . . . . . . . . . . . . . . . . . . . 8.32 Consideration of line’s hue in judging similarity between documents. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.33 Interpretation of green lines as indicating a greater or a lesser similarity between documents. . . . . . . . . . . . . . . . . . 8.34 Facility to make a decision about similarity between documents with the four different display types. . . . . . . . . . . 8.35 Utility to make a decision about similarity between documents with the four different display types. . . . . . . . . . .

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Chapter 1

Introduction 1.1

Introduction to the topic

«...information visualization focuses on information, which is often abstract. In many cases information is not automatically mapped to the physical world (e.g. geographical space). This fundamental difference means that many interesting classes of information have no natural and obvious physical representation. A Key research problem is to discover new visual metaphors for representing information and to understand what analytical tasks they support.» (Gershon et al. 1998:10). Information visualisation has the purpose to represent abstract data visually in order to enhance the cognitive capabilities of the mind but also to aid thinking. In 1990s GIScientists and researchers in other fields began to reserve a particular attention to this research area. Indeed they contributed to extend typical geographical principles and cartographic methods to the visualization of non-spatial information. Today, the research area in the visualization of non-spatial data emerges within the field of Human Computer Interaction (HCI) which has the aim to make accessible information contained in very large databases (Fabrikant and Buttenfield 2001:263). It concerns different computational techniques able to transform high-dimensional data into low-dimensional data. These techniques are called spatializations and intend to facilitate the exploration of information contained in very large databases and the discovery of new knowledge in an intuitively manner. Commonly, information is portrayed using spatial metaphors and the cognitively knowledge of the environment that people gained in their everyday life.

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CHAPTER 1. INTRODUCTION

The database content, or semantic, is represented in so-called information spaces and could be visualized in very different manner, e.g. as 2D or 3D simple point maps, network maps or landscape maps. Spatializations of semantic information and their relationships in low-dimensional 3D spaces are the theme of this master thesis. Moreover, an empirical test with participants was accomplished in order to evaluate different 3D network spatialized displays with statistical methods. The objective is to understand in which way cartographic and geographic principles might enhance the representation of non-geographic information. In addition, this master thesis will give a better understanding of how people interpret spatialized representations. Consequently, it will be a contribution to the research fields of information visualization and GIScience but also it will help researchers developing cognitively adequate spatializations.

1.2

Motivation

Today, the complexity of information and the exponential growth of data, which have to be stored and processed, require new methods able to extract information from large databases more efficiently (Fabrikant 2000:65). For this reason, the research in the fields of GISience and information visualization focuses in depicting efficiently abstract data in very large databases by means of geographic principles and cartographic techniques. Both have the purpose to facilitate the cognition and the knowledge discovery of information. In this context, the rise of the term "spatialization" refers to all the techniques aimed to graphical depict information with spatial metaphors. All that in a efficiently and effective manner for the knowledge discovery but also the information exploration. Data are often represented as points and the spatial arrangement of these points represent the degree of semantic relatedness that these data have to each other. This graphical representation is inspired by the first law of cognitive geography. It affirms that people believe closer things are more similar to each other then distant one (Montello and Fabrikant 2003:2). This statement derives from the Tobler’s first law of geography which says «Everything is related to everything else, but near things (can be places, landforms, language, ect.) are more related than distant things» (Tobler 1970:236) and it is used in spatializations as basic principle also called distance-similarity metaphor.

1.3. STATE OF THE RESEARCH IN GISCIENCE

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The main research issue is how non-expert people perceives this principle of spatialized displays. The best approach to answer to this research question is to conduct an empirical evaluation with participants with different academical background, age, gender and spatial abilities.

1.3

State of the research in GIScience

The challenge today is to consolidate design guidelines for cognitively adequate 2D and 3D information spatializations. To reach this goal, empirical evaluations are needed which will allow GIScientists and researchers to formalize the concept of proximity in relation with the concept of relatedness. In other words, research focuses on which proximity measure or spatial distance is the more effective and efficient to quantify the relatedness or semantic similarity between documents in very large databases (Montello and Fabrikant 2003:1-2). Types of proximity can be for example: number of nodes between source and destination (network topology), metric distance along links in network displays or metric direct distance between items. Another important research field in GIScience investigated in what manner non-spatial visual variables may influence the perception of the distancesimilarity metaphor in spatializations. Links that connect entities in network displays can vary in width, color hue and color value. The problem is how and in which magnitude these visual variables determine the judgement of similarity between items in network spatializations. As yet there are carried out various empiric experiments with different spatializations types, particularly with 2D point-display spatializations, 2D network-display spatializations and finally 3D point-display spatializations (see section 1.5 "Literature review"). The results of these tests emphasize how distance in spatializations is perceived and how non-spatial visual variables are interpreted in network-display spatializations by participants. Other tests highlight how instructions can influence the use of proximity measures in order to judge similarities between items in spatialized displays (Fabrikant and Montello, 2008). This work will be a continuation of these studies and will propose an evaluation of 3D network-display spatializations. So, it will contribute to the development of design guidelines for plausible cognitively spatializations.

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1.4 1.4.1

Statement of purpose Research objectives

The objective of this thesis is focused on the graphical visualization of 3D network-display spatializations. Particularly, there are analysed in which measure topological proximity and cartographic non-spatial visual variables can influence the perception of the distance-similarity metaphor in 3D spatialized network representations of documents contained in large databases. Namely, the objectives of this work are firstly to understand how and which strategy users use to judge the similarity between documents when there are contradictory notions of distances (network metric vs. topological proximity). Secondly how non-spatial visual variables (color hue, color value and line size) influence their similarity judgements, and thirdly if it exist a difference in perception between stereoscopic and monoscopic 3D spatialized network representations. Moreover this work have as purpose to compare 2D and 3D spatialized network representations in order to show their advantages and disadvantages.

1.4.2

Research questions

In order to realize the above-mentioned research objectives, this work aims to respond to the following research questions: 1. How and which strategy use users to judge the similarity between documents of large databases in 3D spatialized network representations, when there are contradictory type of distances, particularly by changing network and node distance in oppositely manner? 2. How influence non-spatial visual variables the judgement of similarity between documents of large databases in 3D spatialized network representations? Then which non-spatial visual variable is the most suitable to quantify the similarity between documents of large databases in 3D spatialized network representations? 3. Depends the judgement in similarity between documents on the cognitive abilities of people? 4. Influences the orientation of the displays the perception of the distancesimilarity metaphor? 5. Are there differences in the perception between stereoscopic and monoscopic 3D spatialized network representations?

1.5. LITERATURE REVIEW

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6. According to empiric evidences, are there differences in the perception between 2D and 3D network spatializations? Which are their advantages and disadvantages?

1.4.3

Formulation of the hypotheses

The above-mentioned research issues (see section 1.4.2) have been derived the following null-hypotheses (see also section 7.3.8 "Hypotheses") that were used for the final statistical analyse (chapter 8 "Results and analysis"): 1. Changes in topology do not influence the similarity judgement between documents of large databases in 3D spatialized network representations. 2. Changes in visual variables (color hue, color value and width) do not influence the similarity judgement between documents of large databases in 3D spatialized network representations. 3. Similarity ratings do not depends on the cognitive abilities of participants. 4. The orientation of the displays does not influence the perception of the distance-similarity metaphor. 5. There are no difference in perception between stereoscopic and monoscopic 3D spatialized network representations. 6. There are no difference in perception between 2D and 3D spatialized network representations.

1.5

Literature review

This work based primarily on previous studies of S.I. Fabrikant and D.R. Montello. Particularly, the studies of point-display spatializations in 2D and 3D, and 2D network-display spatializations: • FABRIKANT, S I, MONTELLO, D.R., NEUN, M. (2008): Evaluating 3D point-display spatializations. In: GIScience 2008-Fifth International Conference on Geographic Information Science, Park City, Utah, 23 September 2008-25 September 2008, 66-69. • FABRIKANT, S.I., MONTELLO, D.R., RUOCCO, M., MIDDLETON, R.S. (2004): The Distance-Similarity Metaphor in Network-Display Spatializations. In: Cartography and Geographic Information Science, vol. 31, no. 4, 237-252.

6


• MONTELLO, D. R., FABRIKANT, S. I., RUOCCO, M., MIDDLETON, R. S. (2003): Testing the First Law of Cognitive Geography on Point-Display Spatializations. In: Spatial Information Theory: Foundations of Geographic Information Science (COSIT 2003), Lecture Notes in Computer Science 2825. Kuhn, W., Worboys, M., and Timpf, S. (Eds.) Springer Verlag, Berlin, Germany: 316-331.

1.6

Outline of the thesis

This thesis is subdivided in ten chapters. The next chapter broadly explains what the information visualization science are and the process of visualization. The third chapter describes the three-dimensional visualization, its relative methods and the problems that may arise in visualizing 3D displays. The fourth chapter introduces the concept of information space and its semantics. Cartographic principles for the map representation are presented in the fifth chapter. The fifth chapter defines the concept of spatialization, and the relative framework. Furthermore, there are presented the main techniques for the generation of spatializations and the concept of similarity in document spaces. The relevance of spatialization in GIScience are also highlighted with some examples. In the seventh chapter is described the method used in this thesis to conduct an experiment with participants. The purpose of this is to evaluate various 3D spatialized displays. The following chapter presents the results of the experiment and their evaluation with statistical methods. In the last two chapters are discussed the results in relationship with the stated purpose listed in the section 1.4.2. Then theoretical and methodological contribution in the future research direction. In the conclusion part the main results are summarized which lead to propose some new research directions.

Chapter 2

Information visualization 2.1

Definition

C. Ware, in his book "Information Visualization: Perception for Design", sustains that information visualization «is the use of interactive visual representations of abstract data with the purpose to amplify cognition» (Ware 2004:xvii). Thus, visual abstractions have been developed to aid thinking. In fact, they allow users to access rapidly a large amounts of data and detect relationships with a reduced efforts of the working memory. Moreover, they can be dynamic and interactive. So users can change the visualization in according to their preference during a task. C. Ware adds «the potential for information visualization is vast and enable to build systems that give rapid insight into information-intensive problems in many fields, but the design of information visualization systems is also very subtle, there needs to be a supporting science for how to do it». (Ware 2004:xvii). As a result, many disciplines have been developed around this area: cartographers, information design, statistical data graphics, et. C. Chen also affirms that information visualization can help people to find information they need in an effectively and intuitively manner (Chen 2006:27). Information visualization is divided in two main aspects: the structural modelling and the graphical representation. The first one refers to the process of extraction and generalization of relationships between documents or other abstract data. Information are thus defined in a given structure that reflect their relationships. The second aspect concerns the transformation of a structure representation into a graphical representation (Chen 2006:27). These two different aspects are treated more in detail in chapter 6 "Spatialization".

7

8

CHAPTER 2. INFORMATION VISUALIZATION

2.2

The process of visualization

According to C. Ware (Ware 2004:4), the process of information visualization is subdivided in four phases. First, data are collected and saved. Then, data are transformed in a design or structure that are easily understandable (structural modelling). Successively, graphical representations that can be visualized on the screen by means of graphics algorithms and display hardware are produced. Finally, data are published and then perceived from users: the visual perception and cognitive process start (see section 2.3 "The process of visual perception and visual thinking").

Figure 2.1: Schema of the visualization process (Ware 2004:4, figure 1.2).

2.3

The process of visual perception and visual thinking

In his book, C. Ware (Ware 2004:20-22) describes broadly how humans process visual information. He identifies three phases of the perceptual processing that take place in different subsystems of the human brain. The first step of the visual perception occurs in eye neurons and in the primary visual cortex. Here, the basic properties of the graphical representation (features, orientation, color, texture and movement) that the user is gazing are extracted. In the next stage, the visual field is divided into more simple regions which present the same characteristic (regions with the same color or the same texture or motion patterns). The last step involves the active attention of the user on few objects. These objects are selected actively by the user through visual search strategies and held in visual working memory for ulterior cognitively processing. This process is the visual thinking

2.4. DATA TYPES IN INFORMATION VISUALIZATION

9

and comprehends the object identification. In addition, it is connected with the motor system for the muscle movement.

Figure 2.2: Model of the human visual perception processes (Ware 2004:21, figure 1.11).

2.4

Data types in information visualization

Information visualization aims to depict data into an efficient visual representation. In essence, so C. Ware (Ware 2004:23), data can be classified in two types: entities and relationships. Entities are the objects that have to be depicted in a semantic space, while relationships are the structures and patterns that link entities to each other. This last concept can be of various nature: structural, physical, conceptual or casual. The Entity-Relationship diagram is an example of graphic that illustrates the connections between entities (abstract or spatial data) in a database according to their semantic and conceptual relationships. Database designers are using for a long time this graphical model. Recently it has been accepted and adapted as well as in information visualization for more complex representations (Ware 2004:23). In the next section are introduced the concepts of node-link diagram and network display, graphics that are commonly used to depict information contained in very large databases.

10


Figure 2.3: Example of an Entity-Relationship diagram (ConceptDraw 2009. Access:09.09.2009.

2.5. NETWORK DISPLAYS IN A 2D AND 3D SPACE

2.5

11

Network displays in a 2D and 3D space

There is a lot of layout algorithms to graphically represent information contained in very large databases. These arrange entities in according to aesthetic and cognitive rules: minimization of link crossings, displaying symmetry of structure or minimizing bends in links (Di Battista et al. 1998, in: Ware 2004:210). Commonly, abstract data are illustrated by means of nodelink diagrams, in which nodes represent the entities and links represent the relationships that exist between these entities. This information structure can be also called network. J. Bertin defines 2D networks as graphics, in which «the correspondences on the plane can be established among all the elements of the same component» (Bertin, 1983:271). Thus, a network is efficiently represented, when the nodes are connected to each other in a manner that a minimal number of intersections arises. Three-dimensional networks can be depicted as well, but there are more necessary for perceptual variables and for more complex representation structures. The advantage of 3D graphs is the lack of any intersection. J. Bertin affirms that by monoscopic graphs the addition of a third dimension «creates a sense of volume and it also suggest that the lines do not cut across each other» (Bertin 1983:271). To represent monoscopic 3D network, he suggests to change the thickness of the links in according to the distance, so it will produce the impression of depth (Bertin 1983:378). By stereoscopic representations, instead, depth is perceived through binocular cues, which are explained in details in the next chapter.

12


Chapter 3

Visualization in 3D 3.1

Space perception and depth cues

We live in a three-dimensional world and for this reason many information visualization designers sustain that 3D representations are detaining more advantages as 2D ones. In fact they can revel more information, because they are organized in a vaster structure and thus have an additional degree of freedom (Fabrikant et al. 2008:1). In order to provide perception of depth (the visual ability to see in a three-dimensional space), visualization designers supply 3D representations with different depth cues accordingly to the display type: monocular static, monocular dynamic and binocular, or stereoscopic (Ware 2004:259260). Monocular static cues of depth are for examples size gradient, interposition and linear perspective. On the basis of a different size gradient, two objects can be perceived as being as far away to each other. If we assume that they have the same size, the object with a smaller size is perceived as farther away compared to the larger one. Interposition, or overlap, is the strongest depth cue and occurs only when the objects are overlapped, the object that cover the other ones is perceived as being closer to us. At last, the linear perspective refers to the geometric convergence of lines to a single point in function of the distance such as road tracks. In fact, they appear to converge within distance and thus more the lines converge, more they appear further. Monocular dynamic cues of depth are kinetic depth and motion parallax (animated displays). The motion parallax occurs when a person in movement looks at objects placed at different distances. They appear to move at 13

14

CHAPTER 3. VISUALIZATION IN 3D

different rates and more distant they are, more it appears that they move slowly (different velocity gradients). The kinetic depth effect, instead, is produced in rotating an object projected onto a screen. As a result, 3D shape can be perceived. Finally, binocular cues of depth are eye convergence or stereoscopic depth. Stereoscopic disparity is the most important depth cue used from the brain to analyse the 3D space. It refers to the fact that the two eyes receive the image of an object of the 3D space from two different viewpoints which the brain integrates into a single 3D image. This process allows people to perceive the depth and the distance existent between objects of the threedimensional world. This is an important task for the movement and the orientation in space (encyclopaedia britannica 2008. Access:18.06.2009).

Figure 3.1: Monocular static cues: size gradient, interposition and linear perspective.

Figure 3.2: Monocular dynamic cues: motion parallax and kinetic depth effect (Ware 2004:270, figure 8.13).

3.1. SPACE PERCEPTION AND DEPTH CUES

15

Figure 3.3: Binocular cues: eye convergence and stereoscopic depth. (HowStuffWorks 2009. Access: 09.09.2009)

16


3.2

Methods for 3D visualization

Representations in 2D have been studied for a long time. This permitted to elaborate a consistent guideline design framework. Recently there are ascertained an increaser interest for 3D representation which are as well motivated by more and more low-cost technologies and improvements in 3D computer graphics. Guidelines for efficiently 3D representations gain ground within the visualization science, but much have to be made yet. To draw up a suited guideline for designing it is necessary first to have a good understanding in how people perceive space (Ware 2004:259). As mentioned in section 2.3.1, there are many possibilities to represent images projected onto a 2D screen with the illusion of depth perception. These possibilities are monocular displays provided with static or interactive dynamic 3D representations and stereoscopic displays based on binocular cues. These last display types can allow users to see representations in "truly" 3D. 3D visualizations in stereo are produced through various methods. The stereo effect occurs when two different images are projected to each eye. Then, the brain elaborates the two overlaid images fusing them into a threedimensional one. The following presents the three dominant techniques to visualize 3D images in stereo (Space Science Visualization 2006. Access: 23.06.2009): • Anaglyph: With this technique images are produced with two colors. Indeed those two different images can be seen by means of glasses with coloured lenses (red and blue). This allows to perceive stereo, because eyes see two images due to the difference in color. This method is not as efficient as the next two one, but the advantage is that only one projector is needed with very cheap glasses. • Active: Active stereo systems use very expensive projectors which send alternating images to the right-eye and left-eye in a very rapid succession. This technique requires a very expensive set of active liquid crystal glasses. • Passive: Passive stereo techniques use two low-cost projectors which send overlapping images to the screen. The images are polarized using special filters and viewed with a pair of cheap polarizing glasses. The most stereoscopic images are produced through passive methods because of the infrastructure law costs. The only problem with that last

3.3. PROBLEMS WITH 3D VISUALIZATION

17

method is that the perceived 3D image can be compromised by head movement. Users have to keep their head horizontally to the screen (Space Science Visualization 2006. Access: 23.06.2009).

3.3

Problems with 3D visualization

Problems with 3D stereoscopic displays could be (Ware 2004:271-275): • Stereo-blindness: 20% of the population is stereo-blind and cannot perceive depth cues in 3D stereoscopic images. • Diplopia: This phenomenon occurs when the disparity between the two images is too big. Consequently, the two images cannot be perceived as a whole and it cause a double vision of the stereo image. According to empiric studies, to solve this problem the screen disparity do not have to overcome the 1.6 degrees and it should be less then 0.03 times the distance to the screen (Valyus 1966; in: Ware 2004:275). • The frame cancellation: This phenomenon occurs when an object in 3D displays is at the edges of the screen. It appears to be occluded by the screen and the depth effect is thus overrode. • The Vergence-Focus problem: On the computer screen all objects lie in the same focal plane, despite they possess a different depth. Consequently, the coupled vergence-focus mechanism1 cannot function correctly. This problem cause eye-strain during the navigation within dynamic and interactive stereoscopic displays. • Distant objects: In order that the stereoscopic depth cues can be optimal perceived, viewer have to be within a distance of 10 meters or less. Anyway, beyond 30 meters disparities cannot be resolved because they are to small. Furthermore, researchers have detected two common optical illusions which could modify the perception of distance among entities as well as the perception of line segment length in spatializations, so Montello et. al. (2003:318) and Wolfe and Maloney (2005:967): • The filled-space illusion (Oppel-Kundt illusion): It occurs when two equally long horizontal distances, in this case AB and BC, are perceived differently because of the unlike number of intervening elements between them. Consequently, the distance AB containing many intervening entities appears longer compared to the empty distance BC.

18


• The horizontal-vertical illusion: It occurs when two equally long lines, one horizontal and one vertical are perceived differently. Indeed, previous studies have demonstrated that vertical lines appear longer as horizontal lines (Wolfe and Maloney, 2005:967).

Finally, Herman et al. (2000:7-8) point out that the addition of an extra dimension can, on the one hand favour the representation of large data structure but on the other hand, it is difficult to find the most appropriate layout. In fact, a new problem could arise when users have the possibility to interactively change the perspective of dynamic three-dimensional displays. Indeed, they can manipulate the displays until they find the best view with the less number of occlusions among those entities. As a result this involves more cognitive and time costs. The main challenge is thus in the employment of appropriate 3D graph layout techniques as well as the additional visual cues, like for example transparency and depth queuing. This way, the navigation through information in 3D representations can be simplify maintaining however intact the layout aesthetic and without compromising to much the cognitive effort in doing it.

Chapter 4

Information spaces and their semantics 4.1

Information space

Information are defined in Computer Science as processed, stored, or transmitted data (the free dictionary). Information can be reorganized in a specific structure and then graphical depicted in an so called information space. This structure can be logical, metrical, non-metrical or mnemonics with the purpose to allow users to extract or process information easily. Information spaces are introduced in late 20th century and are subdivided in many categories according to their information structure. Information is organized into a specific physical and conceptual order. Skupin and Buttenfield (1997:117) make the example of newspapers: information are conceptually organized into articles that are in turn physically placed in well-defined locations on pages. This is a conventional and familial organizational structure. People reading newspapers can also navigate easily to the interested articles. Information spaces can be more complex as large hypermedia spaces such the World Wide Web or large structured databases (Skupin and Buttenfield 1997:117).

4.2

Semantics of information spaces

Three different spatial structures are distinguished to represent semantic content of large information spaces based on spatial metaphors: geographic space, cognitive space, and Benediktine space (Fabrikant and Butterfield 2001:267). 19

20

CHAPTER 4. INFORMATION SPACES AND THEIR SEMANTICS

The first approach, the geographic space, represents an item in a semantic structure with a metaphor that is based on people experience with realworld spatial concepts, such as location, distance or direction. It formalizes an information space according to the location of objects and its relationships with other objects in a specific geographical space and time. An object can be defined according to its position in a determinate moment. R.G. Golledge (1995; in: Fabrikant and Butterfield 2001) affirms that additional spatial concepts can be derived from simple primitive concepts of objects, as identity, location, direction, distance, magnitude and scale. Two important concepts are, in this work, location and distance. Location is the spatial and temporal component of an object Distance is also a concept that depends on its reference system. It can be based on Cartesian measurements or as "proximity" or "similarity". Combing this two concepts in spatialized displays, the content of an information space can be interpreted as following: the concept of location is linked to the existence of a specific item and it can be represented through a point. The concept of distance between items is linked with the relatedness and similarity which they have to each other. If entities are placed within a given radial distance of a central location it means that they are all related within each other. They forms thus a clusters of related information. Moreover, the relationship or similarities that data points have among each other in information spaces can be represented through 2D and 3D linear connections, for example spatial networks, or through 2D and 3D surfaces (Fabrikant and Butterfield 2001:268-269). The second framework, the cognitive space, aims to create a semantic spatialized representation based on the knowledge that people have acquired about space but less based on geographic properties as location, distance and direction. The cognitive space is related with the «respecting, valuing and working with the different intelligences, learning styles and cultural and cognitive diversity» (Learning space 2005): it is focused on the individually knowledge acquisition of the environment through the interaction with space. Each individual interacts with the external stimuli in a unique way. This framework type is related to the concept of "naive geography" proposed by Egenhofer and Mark who defines it as «the body of knowledge that people have about the surrounding geographic world» (Egenhofer and Mark 1995:4). This approach is important for the usability and designing of an information space to translate the information needed by the user. Then the preferences into predefined system’s representation schemes, such as multiple conceptualizations, multiple levels of details of space, asymmetric dis-

4.2. SEMANTICS OF INFORMATION SPACES

21

tances between objects (conceptual closeness), local and relative distance inferences (Egenhofer and Mark 1995:7-11). It aims to formalize information representations that are intuitively understood and make them easily accessible to a large portion of the population (Egenhofer and Mark 1995:1). The last framework, the Benediktine space, aims to formalize the structure of Cyberspace by means of four principles (Benedikt 1991; in: Fabrikant and Butterfield 2001:270-271): exclusion, maximal exclusion, scale and transit. These principles refer to the fact that two objects cannot be placed in the same location at the same time. Instead, the use of the second principle helps to decide the dimensional partition of the data according to the first principle. That is why the dimensionality of the information should minimize the violation of the exclusion’s principle. Ordinarily, x, y, z coordinates in the Cartesian space and time are chosen. Then, the third principle refers to the detail’s level of an information space: more dense it is, more slowly the user moves through an information space. The last principle refers to the cost that users spend to move from a point to another in an information space. This is in relation with the distance between the considerate points. It is also possible to visualise more than three dimensions in an information space depending of the number of element’s variables. Moreover, in the representation and semantic transformation of information into a Benediktine space, the entity’s properties and their functional relationships in an information space are preserved. The ontological perspective useful in designing an information space, which was introduced in the section 4.2, can be summarize as following: basic geographic concepts are used in order to conduct a geometric reduction of information complexity, or geometric generalization. High dimensional data are transformed into a low dimensional geographic representation (lower level of semantic details). It refers to the environmental structures which can be formalized by means of geometric, topological or dimensional measures. Then, cognitive perspectives are used to formalize user-centred views. Information space are depicted according to the learning process, the spatial knowledge acquisition and the social constructed meanings. Finally, the Benediktine spaces are used to conduct the semantic generalization by which multidimensional structures are transformed into lower dimensional representations preserving their semantics, namely preserving their entity’s properties and functional relationships. Those three approaches can be also distinguished in terms of spatial

22

CHAPTER 4. INFORMATION SPACES AND THEIR SEMANTICS

metaphors which are used to represent information spaces. In geographic spaces objects are represented in a Cartesian coordinate system according to spatial metaphors as distance, direction and hight. Representations based on cognitive spaces are depicted through user’s expectations about spatial relationships in geographic space. Finally, transformation in Benediktine spaces are conducted preserving five topological measures of the physical space which are dimensionality, continuity, curvature, density and limits.

Figure 4.1: Spatial metaphors that underlie representations in the three semantic spaces types. (Fabrikant and Butterfield, 2001:271, table 2)

Chapter 5

The map representation: cartography and visual variables Maps are developed by cartographers in order to depict geographic features and abstract data. This graphical representation is a visual communication and visual thinking tools (DiBiase et al. 1992:203). MacEachren et al. (1992) define map representations as «an act of cognition, a human ability to develop mental representations that allow us to identify patterns and create or impose order» (MacEachren et al. 1992; in: DiBiase et al. 1992:203). The first set of map signs to be developed were introduced by the French cartographer J. Bertin, who was famous for his book Semiology of Graphics edited in 1967. According to Blok (Blok 2007), Bertin’s theories has been extended and adapted for other map uses, such as 3D visualizations, animation or for other senses as well (touch, hearing and smell). However the visualization of maps is continuously developing influenced by technology and by conceptual and user-oriented improvements (Blok 2007). The long tradition of cartography is very important for the information visualization in order to generate effective graphic representations: DiBiase et al. point out that cartographic symbolization is, in essence, a problem of appropriately and creatively signifying geographic (and abstract) data with Bertin’s visual variables (DiBiase et al. 1992:203). Visual variables are used with the purpose to represent variations in data on a map: it is essential to match these variations in an intuitive way (Fabrikant and Skupin 2005: 674). Bertin formalized geographic spatial information into graphic variables which was mainly used for 2D, static maps. His framework is still recognized today (Blok 2007). He defined seven fundamental visual variables: 23

24CHAPTER 5. THE MAP REPRESENTATION: CARTOGRAPHY AND VISUAL VARIABLES

location, size, color value, texture, color hue, orientation and shape (Bertin 1983). They are used to depict data in different ways by means of marks positioned on a plan. Those marks are depicted according to their level of measurement and dimensional characteristics. The spatial dimensionality of geographic features is expressed trough points, lines and areas called also elementary primitives. This dimensionality depend on the scale of visualization. Moreover, data can be divided in four different levels of measurement according to their scale type, for instance nominal, ordinal, interval and ratio scaling levels. J. Bertin (1984) also defines how geometric primitives can be effectively and efficiently represented with visual variables according to their level of measurement. This is outlined in the figure 5.1. Other famous authors as McCleary (1983) or MacEachren (1995) improved Bertin visual variables with additional variables like saturation, orientation, shape, arrangement, texture and focus.

Figure 5.1: The three degree of effectiveness of the Bertin visual variables in signifying geometric primitives (Bertin 1983; in: DiBiase et al. 1992:204). The visual variables have different level of organization on the plane depending on its perceptual properties (Bertin 1983:48-49). Indeed a variable is selective when it enables to immediately recognize determined characteristics of the variable belonging to the same category, for example all components depicted with red signs are more similar compared to other signs of different colors. A variable is also associative when similar vari-

25

ables can be grouped together as a unique category, for example shape with the same size and color hue are perceived as similar. A variable is said ordered when it immediately allow to classify it in categories. Then, a variable is quantitative when the visual differences between categories of an ordered component enables to perceive immediately the numerical ratio between these categories without recourse to a legend, as. in the next figure it can be affirmed that A>C>B and A=2C and B=C/2 (Bertin 1983:49):

The level of organization allows to represent the components of a plan with suitable visual variables (Bertin 1983: 64-65): • To represent correctly and effectively quantitative components it is advisable to use variation in size. In fact only the size variations are perceived intuitively as quantitative, therefore they are suitable to be used to depict the numerical ratio between signs. This can be achieved, for example, by changing the thickness of a line in linear representations (Bertin 1983:71). • Size and value variables enable dissociative perception of signs and provide a variation in the visual "weight" and "visibility". Signs appear with a different power. • Associative and selective variables correspond to the nominal scale like the color, ordered variables correspond to the ordinal scale as for example the value and quantitative variables corresponds to the ratio scale like the size. • Moreover visual variables can be combined and all combinations are possible (Bertin 1983:184).

26CHAPTER 5. THE MAP REPRESENTATION: CARTOGRAPHY AND VISUAL VARIABLES

The next table summarizes the levels of organization of the different visual variables: Associative

Selective

Ordered

Quantitative

x

x

x

x

Size

x

x

x

Value

x

x x

Planar dimensions (x,y)

Texture

x

x

Color

x

x

Orientation

x

x

Shape

x

Table 5.1: Levels of organization of the seven visual variables by Bertin (1983:69). Graphic representations are a vehicle to communicate. They have three fundamental functions based on the conditions of memorization, which depend of the amount and conceptual level of information. They aim to extend knowledge and to utilize efficiently human memory. The graphic functions are the following (Bertin 1983:160): • Recording information (inventory drawings). Graphics are providing a storage mechanism which avoids memorization’s efforts. • Communicating information (simplified drawings or "messages"). Graphics can be considered as a message which enable to efficiently memorize information and assimilate knowledge. • Processing information. Graphics are used for processing or discovering information by using the following mechanisms: ordering and classing data items, grouping similar data items, or by creating new categories in order to reduce the number of information to process.

Chapter 6

Spatialization 6.1

Definition

The term spatialization in geographic information systems has been introduced by Kuhn (Kuhn 1992). It rises from the need to find new methods to access data in complex and multidimensional information spaces of very large databases. Spatialization is a technique used in information visualization that serves to represent non-spatial data through spatial metaphors such as distance, sale, direction, arrangement or pattern. (Skupin and Buttenfield 1997:116). Spatial metaphors are namely spatial concepts of which people have experienced in their everyday life. Spatialization is therefore a new approach of representation and visualization of information that take advantage of the natural ability of human beings to process spatial information. This allows to generate information spaces that are «both intuitive and internally coherent» (Fabrikant, Skupin and Couclelis 2002:1). According to Fabrikant, Skupin and Couclelis (2002:1) «a spatialized representation differs from ordinary data visualization and geographic visualization in that it may be treated as if it represented spatial information, thus making possible the use of spatial metaphors and spatial analysis techniques for general data exploration». In general, spatialization techniques consist in the transformation of abstract and high - dimensional information spaces into 2D or 3D low dimensional and cognizable digital representations according to specific criteria. In this way, the simplified information space can be accessible to users for further visual interpretations or for exploratory knowledge discovery of very large databases (Skupin and Buttenfield 1997:116). In other words, they reduce the complexity of data contained in large databases as websites or new stories projecting information into a simplified spatial ar27

28

CHAPTER 6. SPATIALIZATION

rangement in order to facilitate the extraction of information.

6.2

Data types in spatialization

There are many types of data from which information are extracted through different application domains (Skupin 2007:1-2): text, audio, video and imagery. Methods to transform information into a spatialized representation are based on the data sources, which vary according to the degree of their structure. On one hand, data are distinguished from low to high structured data. On the other hand, well-structured data can be easily spatialized. For example the population census data which is related to well defined geographic features. Their attribute structure is consistent and data are collected in standard databases. Anyway, most text, audio and image contents are less well structured, which means that their structural elements are not clear distinguished. In the middle are semistructured data, such as XML, which are partially already structured (Skupin 2007:1-2). Moreover, another possibility to categorize data set is in their content dimensionality and network structure. On one hand, if the attributes number in data correspond to the dimension of an n-dimensional space, methods of dimensionality reduction can be already applied. In contrast, if the data express topological relationships with other data, they can be directly conveyed into a low-dimensional display through spatial layouts methods. For example scientific articles in which are quoted other previous articles linked to them: a network display of linked articles connected by unidirectional links (topological relationships) can be created (Skupin 2007:3).

6.3

Spatialization framework

According to S.I. Fabrikant, A. Skupin and H. Couclelis (2002:1), to generate adequate information spaces with the purpose to extract information from large data archive more efficiently, a sound spatialization framework have to be defined. This is motivated by the following two research fields: the research into the interaction of people with abstract data representations which are based on familiar spatial metaphors and the research on computational techniques which deals with the creation of meaningful spatialized visualizations. According to Fabrikant and Skupin (2005:669), the generation of cognitively adequate spatialized displays involves the following two processes called the semantic generalization and the geometric generalization. These

6.3. SPATIALIZATION FRAMEWORK

29

two ontological principles are derived from the geographic information theory. The semantic generalization is «a mathematical transformations to re-arrange data items based on their content and functional relationships into a logically defined coordinate system» (Fabrikant, Skupin and Couclelis 2002:1). The first step to generate a spatialized display is thus applied to the database. It has the objective to find a visual structure that reflect effectively the semantics of raw data using an appropriate spatial metaphor (Fabrikant and Skupin 2005:669). According to Fabrikant and Buttenfield (2001:266), semantic spatializations use cognitive image schemata to allow users to understand and read information spaces intuitively according to their experience with the geographic space. As a result, geographic places can be cognitively associated with location and containment. In addition, routes can be associated with connections and geographic distances. Then, the scale can be associated to hierarchies of details and arrangement, such as concentration or dispersion. The key question, in the semantic generalization, is which spatial metaphor is most likely to be suitable to reflect effectively specific data sets (Fabrikant and Skupin 2005:670). To respond to this question, Fabrikant and Skupin (2005) suggest an ontological design based on a metaphorical mapping process, in which the essential characteristics of row data in a geographic space (source domain) are transformed into a semantic information space by means of adequate spatial metaphors (target domain).

Figure 6.1: Ontological design for the semantic generalization process (Fabrikant and Skupin 2005:671). However, to choose the most suitable spatial metaphor for a specific context and use, four semantic primitives can be associated with different spatial metaphor types (Fabrikant and Skupin 2005:672), as shown in figure 6.2. The four semantic primitives are the following one: locus, tra-

30


jectory, boundary and aggregate. Locus corresponds respectively to the location of a specific information item in an information space (e.g. landmark). Trajectory corresponds to the semantic relationships between items at different locations in an information space (e.g. path or link). Then, boundary corresponds to the delimitation of semantic homogeneity in regions (e.g. border). Finally, aggregate corresponds to the aggregation of entity types, for example classification and cluster of information entities (e.g. region), (Fabrikant and Skupin 2005:673). These semantic primitives are then combined with geographic perspectives according to the context and use of an information space. The geographic perspectives are the following: navigable, vista, formal, experiential and historic. In particular, the navigable space conceptualizes an information space for navigating in it, the vista perspective for analysing patterns, the formal perspective for formalizing it mathematically, the experiential perspective for conceptualizing it mentally, and finally the historic perspective for analysing spatial processes over time (Fabrikant and Skupin 2005:671).

Figure 6.2: Source domains for the semantic generalization process in which semantic primitives are combined with geographic perspectives (Fabrikant and Skupin 2005:672, table 35.1).

6.3. SPATIALIZATION FRAMEWORK

31

The geometric generalization is the «graphic depiction of the spatialized data for information exploration and knowledge construction» (Fabrikant, Skupin and Couclelis 2002:1). It is namely linked to space transformations, space types and symbolism by means of cartographic methods and cartographic generalization. In this phase, the semantic primitives used for the semantic generalization process are namely represented graphically by means of appropriate non-spatial visual variables (Fabrikant and Skupin 2005:669). In particularly, semantic primitives are represented with geometric primitives accordingly to the display scale. So, locus can be represented as point or area, trajectory and boundary by means of lines and then aggregates through points or areas (Fabrikant and Skupin 2005:774-775). Finally, this process ends with the choice of appropriate visual variables, which is also described in chapter 5 ("The map representation: cartography and visual variables").

Figure 6.3: Geometric generalization process (Fabrikant and Skupin 2005:674, figure 35.2).

32


6.4

The concept of similarity and spatializations techniques

6.4.1

The concept of similarity in a document space

Semantic document spaces are generated combining the three space types described in section 4.2, namely the geographic, cognitive and Benediktine spaces. The construction of a document space is based onto the similarity among documents by means of keywords. In addition, their properties are depicted into a n-dimensional Cartesian space (Fabrikant 1996:35). The concept of similarity in an information space refers to the degree of the semantic relatedness among entities in a structure. The similarity between items can be measured in various ways. Sokal and Sneath (1963; in: Fabrikant 1996:36) define three measures types: the coefficient of association, the coefficient of correlation and the measures of distance. The cosine coefficient is an example of association coefficient and serves to calculate the angular distance, or semantic proximity, between two document vectors (or document query) in a coordinate space. It is often used to compare documents in information retrieval, in which a query vector with search keywords (w) is matched against a document vector (d) with specific keywords in a database. The matching coefficient is the following (Salton, 1989; in: Fabrikant 1996:37): P

sim(Wi , Di ) = qP

(

dij wij )

(dij )2

P

(wij )2

The semantic proximity between documents can be also measured with simply distance measures, such as the Manhattan distance (City-block distance) and the Euclidean distance. A general formula is the Minkowski distance. This measure determines the average distance or dissimilarity between two document vectors: dik =

X

|xik − xj k |P

1

P

where: City-block distance if p=1; Euclidean distance if p=2 (Davison 1983; in: Fabrikant 1996:39). Another important similarity measure is the semantic distance model (SDM) which refers to the semantic distance between documents in network displays. It is defined as the number of steps (or nodes) from one items to

6.4. THE CONCEPT OF SIMILARITY AND SPATIALIZATIONS TECHNIQUES33

another along links (Brooks 1995; in: Information Visualization book:28). A last example of similarity measure is the generalized similarity analysis (GSA) by hypertext linkage, in which the document proximity is defines by the similarity between documents (Information Visualization book:53-54): linkij simi link =P j linkik where link(ij) corresponds to the number of hyper-links between document D(i) and D(j). These different similarity measures are important to determine which spatializations technique to use. In the next section are explained the different existing methods.

6.4.2

Spatializations techniques

As pointed out in the above sections, the generation of a 2D or 3D spatialized representation begins with the creation of a simplified visual structure that characterize the non-spatial data by means of spatial metaphors. Visual representations are generated through a transformation of large highdimensional structured data sets into lower-dimensional displays. The process of simplification of the data dimensionality provided by several approaches is called generally dimensionality reduction techniques. The dominant techniques are the following: the multidimensional scaling (MDS), the principal components analysis (PCA), the spring models, the pathfinder network scaling (PFN) and the self-organizing map methods (SOM), (Skupin 2007:3-4). Multidimensional scaling (MDS) techniques create a smaller pseudo-vectors which approximate the high-dimensional structure of data into a lowerdimensionality representation. The proximity characteristics of the raw data structure are preserved (Chen 2006:29). In addition, the item’s nattributes are depicted in a spatial n-dimensional vector space according to the existing similarity between them. The principal components analysis (PCA) technique creates new variables by means of a linear combination of the original variables. This leads to a linear variable reduction. Spring models are planar representations of nodes connected by spring-

34


like forces. These algorithms aim to optimize the arrangement of nodes in a network, in which nodes connected by strong links are depicted closer to each other (IV:30).

Figure 6.4: Multidimensional scaling example (Mark 2001; in: Skupin and Fabrikant 2003:98).


Figure 6.5: Example of principal components analysis technique (Center for Machine Perception 2009).

Figure 6.6: GnuMap: representations of gnutella P2P network by Spring algorithms (aiSee 2005).

36


The pathfinder network scaling (PFNET) is a popular method for representing graphically the most essential links between nodes by means of proximity measures. The purpose of this technique is to help users to detect easily the salient entities relationships. It is especially used by author cocitation analysis. The topology of a PFNET is determined by Minkowsky metric which computes the distance of a path (IV:31,48). Self-organizing map methods (SOM) are a type of neuronal network based on unsupervised learning. They produce low-dimensional displays from high-dimensional data sets preserving topological relationships of the primary data elements. The SOM displays normally appear as a regular twodimensional grid of nodes in which most similar items data are represented closest to each other (Kohonen 2001:106). Other techniques approaches are the spatial layouts. The tree map method is one of them. It represents hierarchically organized data (tree structures) through spatial layouts partitioned by rectangular areas. Each area corresponds to a node of the original tree structure. Moreover, the size and color of the area correspond to the node attributes (Skupin 2007:4).

Figure 6.7: Author co-citation analysis example (Society and Decision Making 2008. Access: 08.07.2009.)


Figure 6.8: A self-organizing map which depict countries on the base of poverty indicators. The figure on the right is a world map in which countries have been coloured with the same color of the figure’s links (Laboratory and Computer and Information Science 2009).

38


Figure 6.9: Examples of a Tree map construction and an interactive Tree map of the market which shows the stock market grouped by sectors. The size of the nodes corresponds to the company’s market capitalization and the color indicates the difference of the current price from the closing price of the day before (green is up, red is down).(eagereyes 2009)


The different approaches can also be combined as in the next figure. It is a 2D representation of Reuters news stories which are created through the combination of two techniques: first a spring-node algorithm (documents as landmarks) and then a Pathfinder scaling technique (documents are placed according to their relative semantic similarity).

Figure 6.10: Reuters news stories are represented as a 2D point configuration (Spacecast 2002). However, there are a limitation in determining the appropriateness of existing spatialization techniques because of the lack of subject testing (Skupin and Buttenfield 1996:616; in: Fabrikant 2001). As a result, more empirical experiments with participants are needed in order to determine if particular spatialized display types are intuitively understood and how these can be improved.

40


6.5

Relevance of GIScience for spatialization

In the field of GIScience and geovisualization, space is used as structure to represent data in a generalized way. Then, they are depicted trough spatial concepts and graphical representation or maps (Fabrikant and Skupin 2005:667). Therefore, GIScience provides a solid theoretical foundation for improving knowledge discovery in data representations (Buckley et al. 2000; Buttenfield et al. 2000; in: Fabrikant and Skupin 2005:668). This concerns particularly the principles of ontological modelling in which are comprised semantic and geographic generalization, association and aggregation and other cartographic techniques (Fabrikant and Skupin 2005:667). It can also contribute to formalize suitable information spaces design because of its conceptualization of space. In addition, «GIScience provides the perspectives of space and place, as well as the necessary visual, verbal, mathematical and cognitive approaches to construct cognitively adequate spatial representations» (National Research Council 1997; in: Fabrikant and Skupin 2005:668). However, until now, most spatializations are generated by researchers outside of GIScience and cartography. For this reason, GIScience should make available its knowledge in order to formalize theoretical and technical research questions for designing suitable spatializations (Fabrikant and Skupin 2005:667-668). For example, cartography may help information visualization in improving visual representations with suitable projection techniques and geometric configurations (discrete/continuous) by emphasizing particular salient data attributes for a specific purpose. Then idea in cartography is to choose the most appropriate representations for users’ preferences, cognitive abilities or domain ontology (Fabrikant and Skupin 2005:681).

6.6

Spatialization examples

In this section are presented a list of spatializations example. The first example is the desktop metaphor which is a computer interface that facilitate the interaction of users with the computer. The metaphor consists in the analogy of the user’s desktop with the monitor of a computer. This can be used as if it is the user’s desktop. Upon this virtual desktop they can place files and folders as if they would be real objects that they place on their real desktop. Consequently, the desktop reflects personality, preferences and tastes of the user. Another example is three dimensional virtual spaces which are being used

6.6. SPATIALIZATION EXAMPLES

41

Figure 6.11: The desktop metaphor.

to map information for easy exploration and navigation. The next figure is the "semantic constellation" of an information space produced by Chaomei Chen (Brunel University). The balls represent documents and their spatial arrangement shows the relationships between them.

Figure 6.12: The "semantic constellation" of an information space produced by Chaomei Chen (Chen 1999) A further example are web-site maps which are created to facilitate the navigation and search of complex web-sites. Hypertext and hypermedia spaces use spatializations, usually 2D representations, already since a long time in order to graphical depict their structure and content. The use of this technique is increased because of the advent of the World Wide Web (Skupin and Buttenfield 1997:118). This can be represented in very different ways. Then are showed some examples of web-site maps: the first one is the TouchGraph Google Browser, an interface created in 2001 that presents a network of connectivity between websites. It allows users to have a better visualization and interaction with information. Moreover, it enables deci-

42


sion makers to display, navigate, and analyse complex data simply and intuitively.

Figure 6.13: Network of connectivity between websites (created with the TouchGraph Browser). Another example is the WebTracer, an application that allows users to reveal the visual structure of the web-hypertext. This is represented as a three dimensional molecular diagram, with pages as nodes (atoms) and links as strings (atomic forces) that connect those nodes together.

Figure 6.14: WebTracer (Nullpointer 2009) The last example is the Nicheworks, an interactive tool for visualising network structures of a large Web-site with hundreds of thousands of nodes. It was developed by Graham Wills at Bell Labs. Finally, cyberspaces can be represented also as three-dimensional infor-

6.6. SPATIALIZATION EXAMPLES

43

Figure 6.15: The Nicheworks tool (An Atlas of Cyberspaces 2007).

mation landscapes. This landscape interface has been created by S. Fabrikant for information searching and browsing using spatial metaphor of the landscape.

Figure 6.16: 3D landscape: topic density surface (Spacecast 2002).

44


6.7

Related project

My work is related to a project called Spacecast. It is a three-phase project which begun in 2000. It aims to test, by means of controlled experiments with participants, the spatial metaphors in spatializations for the information exploration. Previous studies focused on empirical evaluation of 2D spatialized displays of point, network and region, and of 3D spatialized point-displays in which has been depicted data contained in large databases. The purpose to this analyse is to show how points, networks and regions are related to the concept of similarity but also how visual variables influence the perception of the distance-similarity metaphor in network display spatializations. Spacecast involves interdisciplinary researchers from the cognitive science, information science and GIScience and are founded by the National Imagery and Mapping Agency (NIMA). Finally, experiments are being carried out at the Research Unit for Spatial Cognition and Choice, at the University of California, Santa Barbara. This project is in collaboration with researchers at Buffalo University (SUNY). Follow is the web-link of the Spacecast project: http://www.geog.ucsb.edu/~sara/html/research/spacecast.20070103/ research.html. Access: 02.09.2009.

Chapter 7

Method 7.1

Participants

In all, 28 participants carried out the experiment. One half were females and one half were males (N=28, 14 females and 14 males). Their age raged from 20 to 63 and the average is 29.61.

Figure 7.1: Histograms of the participant’s age. 17 of the 28 participants wore glasses, one of them had lack of depth perception and any of them were color-blind.

45

46

CHAPTER 7. METHOD

Figure 7.2: Histograms of participant’s number that wear glasses and have lack of depth perception.

7.1. PARTICIPANTS

47

18 of them rated their ability to read maps as average, one below average and 9 above average. 18 of them pursued occasionally, 6 of them never and four regularly recreational activities that require maps reading (e.g. hiking, sailing or orienteering). The experiment was preferably carried out from people without previous knowledges in spatializations in order to archive spontaneous results that are not influenced from learning or instructions. For this reason I chose, as participants, students from undergraduate geography courses, students of other academic studies or people with no academic background: 14 of them were students at the University of Zurich and 14 were not students. The following histograms (figure 7.3) and table 7.1 show how much professional experience, training or college classes had participants in GIS, cartography, computer graphics and fine arts or graphic design at the moment of the experiment: GIS

Cartography

Computergraphic

Graphicdesign

none

12

13

14

17

5 years

2

2

2

2

Table 7.1: Summary of the professional experience, training or college classes that participants have. As compensation for their participation at the experiment, all the participants received a coupon for the cafeteria of the University of Zurich of value of 5 Swiss francs.

48

CHAPTER 7. METHOD

Figure 7.3: Histograms of participant’s ability to read maps and frequency of recreational activities.

7.1. PARTICIPANTS

49

Figure 7.4: Professional experience, training or college classes that participants had.

50

7.2

CHAPTER 7. METHOD

Apparatus

For showing the 3D representations were used a low cost interactive 3D stereoscopic projector system based on polarization (passive stereo). This apparatus is called Geowall and consists of a computer with a dual-output graphics card, a stereo projector set, a back projection screen, a workstation and a pair of cheap polarized glasses for each user. In particular, stimuli were projected onto a 2.23x1.80 m screen and participants were positioned at a distance of 2.20 m orthogonally to the screen. In addition, all the controls variables, such as lighting conditions in the room and distance between the screen, was preserved constantly for all the participants during the experiment. The Geowall infrastructure is in the Visualisation Lab Nr. 87. It is placed in J floor of the geographic Institute of the University of Zurich.

Figure 7.5: Geowall in the 3D Visualization Lab of the geographic Institute, e University of Zurich

7.2. APPARATUS

51

The next table describes each of these components in detail (GIVA’s 3D Visualization Lab (2009): http://www.geo.uzh.ch/en/units/giscience-giva/services/3d-visualizationlab/ Access: 13.04.2009): Component

Description

a) 3D Stereo projection system: Cyviz Model: Projectors:

Maximum resolution:

Expected lamp life: Stereo converter: Vertical scan: Horizontal scan:

Viz3D (integrated stand) EVO 2, 2500 ANSI lumens (5000 lumen output), 2400 stereo lumens, 2500:1 contrast ratio SXGA+ 1400x1050 (UXGA, SXGA, XGA, SVGA compatible, 4:3 aspect ratio native) 2000 hours Cyviz xpo.2 (resolution: 640x480 to 1280x1024) 60-120 Khz 15-110 Khz

Separate sync, composite sync, and sync on green. Supports frame sequential stereo from any application Supports interlaced stereo video from any VGA source Table 7.2: Geowall’s components

52

CHAPTER 7. METHOD

Component

Description

b) Workstation: Dell Model: CPU: RAM: Disk: Video: Graphics Card (dual head) OS:

Precision 390 E-smart Intel Core Duo E6700 (2.66 GHz, 4 MB Cache, 1066 MHz FSB) 4 GB 2x250 Gb (7,200 rpm) SATA II, 500 Gb External HD Western Digital 750W-256 MB nVidia Quadro FX3500 (MRGA13) Windows XP Pro SP2

c) Software Worldviz Vizard 3.0 Microsoft Office 2007 SPSS 16.0 SAS 9.2 d) Display: Stewart Filmscreen Model:

Luxus Deluxe Screenwall Series, Filmscreen 150, SND120V (video format) Flexible Rear Screen 120" diagonal, Image height: 72" (1829 mm), Image width: 96" (2438 mm), Frame height: 78.5" (1993 mm), O.D. width: 102.5" (2603 mm) 120" 20.4 kg

Material: Size:

Viewing angle: Screen weight: e) Display: Da-lite (front Projection) Model: Size: Maximum height: Minimum height: Lowest bottom (distance from floor):

Picture king 178 cm x 178 cm (square) 325 cm (including tripod legs) 243 cm 51 cm

Table 7.3: Geowall’s components

7.3. DESIGN

7.3 7.3.1

53

Design The independent variables

The independent variable is the circumstance that the experimenter will manipulate. This circumstance is the most important in the experiment and it is independent of the participant’s behaviour (Martin 2008:25,131). Each independent variable has two ore more levels that are presented to the participants, without they have the possibility to change these. In this experiment were evaluated sixty-five different spatialized network displays which depict documents in a very large databases. The documents were represented through points and the relationships between them through lines. Participants had to compare three points to each other for each display. Five independent variables were chosen to be manipulated: two distance variables and three non-spatial visual variables. The distance variables were the Network distance and the Node distance (also called topology). The Network distance is the metric distance along the links which connect the entities together in network displays. Whereas the Node distance corresponds to the number of nodes between the entities. More it exists nodes between two entities, more greater is the Node distance between them. The three non-spatial visual variables were the color hue, the color value and the width of the links which connected the entities together.

7.3.2

The mixed factorial design

The experiment was outlined according to a mixed factorial design, where several variables were combined in a factorial combination. Each level of one independent variable (called factor) was paired with each level of the second, so on and so forth (Martin 2008:179). In this experiment each independent variables had two or three levels. That is explained in the next section 7.4 "Materials". Three levels of the Network distance were presented to the participants. The Network distance between two comparison documents A:2 could be equal, double or triple the comparison documents A:1. In two displays, the Network distance between two comparison points A:2 was 2.5 and 1.5 times the other two comparison points A:1. In all there were chosen 3(+2) levels of the Network distance:

54

CHAPTER 7. METHOD

• 1st level: Network distance A:1 = Network distance A:2. • 2st level: Network distance A:2 = 2 * Network distance A:1. • 3st level: Network distance A:2 = 3 * Network distance A:1. • (4st level: Network distance A:2 = 1.5 * Network distance A:1). • (5st level: Network distance A:2 = 2.5 * Network distance A:1). There were chosen four levels of the independent variable Node distance to be presented to the participants: • 1st level: Node distance ratios = 1 (one node between documents). • 2st level: Node distance = 2 (two nodes between documents). • 3st level: Node distance = 3 (three nodes between documents). • 4st level: Node distance = 4 (four nodes between documents). Furthermore, for each non-spatial visual variables were chosen two or three levels to be presented to the participants. For the displays in which the color hue was changed, two levels of color hues were used: • 1st level: green links. • 2st level: blue links. For the displays in which the color value of the links was changed, three levels of value were chosen: • 1st level: light color value of the links. • 2st level: medium color value of the links. • 3st level: dark color value of the links. For the displays in which the line width was changed, three levels of width were used: • 1st level: thin width of the links. • 2st level: medium width of the links. • 3st level: thick width of the links. The levels of the four variables topology, color hue, color value and line size were combined with the levels of the variable Network distance. In all 65 different network displays were created. These are explained in details in

7.3. DESIGN

55

the section 7.4 "Materials". In addition, the metric Direct distance was maintained constantly in all stimuli. The reason is that in previous experiments (Fabrikant et al. 2004) it was already determined that the Network distance was more relevant compared to it. So it was not considered anymore.

7.3.3

The dependent variables

The dependent variable is the participant’s behaviour in response to manipulations of the independent variables which the experimenter have to measure. This variable is like that, because it is dependent on what the participant does (Martin 2008:26,132). In this case, the dependent variable is the similarity between three comparison documents. During the experiment, the participants had to compare three documents A, 1 and 2 to each other for each display type. It was asked to the participants to compare the similarity between document A and document 1 with the similarity between document A and document 2. Nine answers were possible. If they would have chosen a value of 5 it means that they interpreted document A as equal to documents 1 and 2. If they would have answered with a value between 4 and 1 it means that they rated document A as much more similar to 1 compared to documents A and 2. Then, if they would have chosen a value between 6 and 9 it means that they found the document A as much more similar to documents 2 compared to the documents A and 1. Moreover, it was not explained to the participants what the concept of similarity was. They had to answer intuitively and choose their own measure to evaluate the similarity between the documents. Finally, the dependent variables was evaluated through statistical methods (see chapter 8 "Results and statistical analysis").

7.3.4

The control variables

All circumstances that do not concern the independent variable have to remain constantly during the whole experiment. These control variables are the following: constant lighting conditions in the lab room, constant distance between the screen and the participant, same introduction and explanation about the conduction of the experiment to all the participants and then no instructions about how to rate the dependent variable or how to

56

CHAPTER 7. METHOD

judge the similarity between the comparison document. In particular, the participants had to answer spontaneously, according to their own criteria, without instructions from the tester. Furthermore, the experiment was preferably carried out from people without previous knowledges in spatializations or in information visualization in order to achieve intuitively results that were not influenced from training.

7.3.5

The between-subjects experimental design

In this experiment, participants were divided in two groups. The first group (N=14) saw the displays with the polarized glasses, namely they saw the 3D displays as interactive stereoscopic images. The second group (N=14) saw the displays without the polarized glasses, namely they saw the 3D displays as interactive monoscopic images. This choice had the purpose to compare the two groups (or levels) together in order to determine if there were differences between stereoscopic and monoscopic views in the perception of 3D network displays. If after the independent t-test it results a significantly difference in the similarity rating between the two levels, they will be analysed separately according to a between-subject experimental design. In addition, the results of the previous experiment with 2D networkdisplay spatializations carried out by S.I. Fabrikant, D.R. Montello et al. (Fabrikant et al. 2004:237-252) were compared with the results of this experiment in order to determine if there were differences in perception between 2D and 3D spatializations. There were thus two additional levels to analyse according to a between-subject experimental design, namely the first level corresponds to the scores of the 2D experiment and the second level corresponds to the scores of the 3D experiment.

7.3.6

The within-subject experimental design

If no differences resulted between the scores of the monoscopic and stereoscopic levels, they were aggregated together and analysed according to a within-subject experimental design (N=28). This experimental design presupposed that all the participants saw all stimuli. The sequence in which participants saw the displays was however randomly chosen to avoid learning effects and thus compromise the statistical analysis.

7.3. DESIGN

57

The time needed to complete the experiment depended on the participant’s rapidity to answer to the questions.

7.3.7

The post-test questionnaire

After the main experiment, participants were invited to fill a post-test questionnaire in order to know more about their background as well as their age, gender, problems in deep perception, ability in maps reading and so on and so forth. Moreover, participants were invited as well to respond to questions about how they rated similarities between documents and which measure they used for each display type.

7.3.8

Hypotheses

A hypothesis is a statement about the expected nature of the relationship between the independent and the dependent variables (Martin 2008:26). • 1st null hypothesis: Changes in topology do not influence the similarity judgement between documents of large databases in 3D spatialized network representations. • 2st null hypothesis: Changes in visual variables (color hue, color value and width) do not influence the similarity judgement between documents of large databases in 3D spatialized network representations. • 3st null hypothesis: Similarity ratings do not depends on the cognitive abilities of participants. • 4st null hypothesis: The orientation of the displays does not influences the perception of the distance-similarity metaphor. • 5st null hypothesis: There are no differences in perception between stereoscopic and monoscopic 3D spatialized network representations. • 6st null hypothesis: There are no differences in perception between 2D and 3D spatialized network representations.

58

CHAPTER 7. METHOD

7.4

Materials

The stimuli for the experiment consisted in sixty-five three-dimensional spatialized network displays. They were been created with Vizard 3.0, a software produced to build interactive 3D interfaces and based on Python scripting language. These trials were a replication of the 2D network displays used in a prior experiment conducted by S.I. Fabrikant, D.R. Montello et al. (2004:237-252) in which a random z-coordinate comprised between 0 and 1 had been added to each point of the displays. The 2D network spatializations has been created with ArcMap (ESRI) drawing on Pathfinder Network (PFNET) representations. This study was part of a project called "Spacecast". More information about it are found in the section 6.7 "Related project" and on the following web-page: http://www.geog.ucsb.edu/~sara/html/research/spacecast.20070103/ research.html. Access: 02.09.2009. Moreover, all the 3D stereoscopic displays were dynamic and interactive, i.e. the rotation of the images could be controlled actively by the user. The initial orientation of the 3D displays was quasi parallel to the participant’s sight of view. They were thus rotated 75 degree around the x-axis or 75 degree around the y-axis, so the participants had to rotate the displays to see more clearly the comparison points in the network representations The optimal orientation was however the fronto-parallel one, in which the three comparison points could be seen in their maximal extension and the Network distance between these points was maximized. All the displays represented a network of black points connected to each other with different line types, in which points represented documents of a very large database and lines represented the semantic relationships existing between these documents. To systematically analyse the influence that the four independent variables (topology, color hue, color value and width) had on the judgements of similarities between documents, the stimuli were subdivided in four different blocks. Each block depicted network spatializations in which the lines connecting the points (comparison points and context points) were represented with one of the four different variables mentioned above. Moreover, in all displays the it Network distance ratio between the comparison points was changed: the Network distance of two comparison points could be equal, double or triple the Network distance of the other two comparison points. In addition, the Direct distance between the comparison points was kept constant.

7.4. MATERIALS

59

Seventeen stimuli contained network displays composed by black points which were connected by blue lines (but equal in width and color value). In these displays the topology (number of intervening nodes) between the comparison points A, 1 and 2 was systematically changed and the following topology ratios were used: 1 (2 vs. 2 nodes), 0.67 (2 vs. 3 nodes), 0.5 (1 vs. 2 nodes), 0.33 (1 vs. 3 nodes) and 0.25 (1 vs. 4 nodes). Thus, four levels of this independent variable (1, 2, 3 and 4 nodes) were used to be presented to the participants and five different displays type were created (Node distance ratios). Moreover, each of these display type was combined with the 3(+2) levels of the Network distance and 5 X 3 + 2=17 different trials were created. In eighteen trials the network displays contained black points connected by links with different color hues (but they were equal in topology, color value and width) according to ColorBrewer color schemes (ColorBrewer: http://colorbrewer2.org/), namely green and blue links. In each of these trials the two color hues of the links connecting the comparison points were combined in order to create six different display types. In three trials all links between the comparison points were green. In additional three other trials all green links were compared with all blue links. In the remaining 12 trials all green links were compared with links mixed in color hue (all green links versus one green links and two blue links; all green links versus two green links and one blue link). The links surrounding the comparison points were mixed in color hue. So all these display types were combined with the three levels of the Network distance and 6 X 3 = 18 different trials were created. Fifteen displays contained a network of black point connected by links different in color value (but equal in topology, color hue and width). Three levels of color value were distinguished: light, medium and dark blue value. In each of these trials, the three color values of the links connecting the comparison points were combined in order to create five different display types. In six trials all dark links were compared to all light or medium links. In the remaining nine trials all dark links were compared to links mixed in value (one light link, one link with a medium value and one dark link). The links surrounding the comparison points were mixed in color value. As a result, all these display types were combined with the three levels of the Network distance and 5 X 3 = 15 different trials were created. The additional fifteen displays contained a network of black point connected by links with different line widths (but equal in topology, color hue

60

CHAPTER 7. METHOD

and value). Three levels of width were used: thin, medium and thick. In each of these trials, the three widths of the links connecting the comparison points were combined in order to create five different display types. In six trials all thick links were compared to all thinner links or all links with a medium size. In the remaining nine trials all thick links were compared with links mixed in width (one thin link, one link with a medium width and one thick link). The links surrounding the comparison points were mixed in width. As a result, all these display types were combined with the three levels of the Network distance and 5 X 3 = 15 different trials were created. Finally, in order to reduce the optical illusions of the horizontal-vertical illusion and the filled-interval illusion, the arrangement of the comparison points A, 1 and 2 were systematically changed onto the x,y-axis. However their z-coordinates were maintained equal to 0.5. So, when the displays were disposed in the fronto-parallel orientation, the comparison points were all at the same distance to the user’s line of sight. This allows to determine the angles of the display rotation during the experiment and finally to make suppositions about their influence in the judgement of the similarity between the comparison points. The next table shows all the above-mentioned trials subdivided in the four independent variables (hue, topology, value and width) and in their display types accordingly to the different levels of each: Network distance Trial

hue-BBB

hue-BBR

hue-BRB

1X

2X

3X

7.4. MATERIALS

hue-RBB

hue-RRB

hue-RRR

Topology-21

Topology-22

Topology-31

Topology-32

Topology-41

Value-111

Value-123

61

62

CHAPTER 7. METHOD

Value-222

Value-231

Value-321

width-111

Width-123

Width-222

Width-231

Width-321

7.4. MATERIALS

63

Network distance Trial

1.5X

2.5X

Topology-22 Table 7.5: Matrix of the experiment outlined according to a factorial experimental design: a (3 X 21) + 2 design. One factor, the network distance, had 3 (+ 2) levels. The other factors, namely, hue, value, topology and width, had each 5 or 6 levels (6 + 5 + 5 + 5 = 21).

64

CHAPTER 7. METHOD

7.5 7.5.1

Procedure Pilot test

Before the beginning of the main experiment with the twenty-eighth participants, a pilot test with two subjects was accomplished in order to verify the correct functionality of the experiment’s procedure.

7.5.2

Main experiment

Participants were each individually tested in a ca. 45-minutes session. To be able to accomplish a statistical comparison between monoscopic and stereoscopic 3D representations, participants were subdivided in two groups. One group carried out the experiment according to a monoscopic modus (only one projector was switched on, without polarized glasses) and the second group according to a stereoscopic modus (two projectors was switched on, with polarized glasses). Anyhow, both groups conducted the experiment following the same procedure described below. Procedure: After welcoming the participants, the Geowall basis functionality was explained to them in a short presentation. They were invited to sit in front of the screen and to fill a pre-test questionnaire about their background. They were told that 3D images would appear on the screen and that they will have to interact with them. They would have to respond to a question for each images helped by the mouse. The experiment started. At the beginning an introduction slide appeared on the screen. They were explained that the experiment was subdivided in three parts. The first part comprised thirteen practice trials, where participants could try to interact with the 3D images. Moreover, participants were told that the 3D-network displays represented documents contained in a large database. Documents were depicted as black point and could be books, new stories or journal articles. In the second part the main experiment began with sixty-five 3D-images. In the last part of the experiment, the volunteers were told to fill a post-test questionnaire, in which they had to justify their responses. After this short introduction, the first part of the experiment started. The participants had to consider thirteen images, three 2D-images and ten 3D-network representations but also to compare three comparison documents (points) to each other according to their similarity. The participants

7.5. PROCEDURE

65

had nine possible responds. If they had chosen a value of 5 it meant that they interpreted the document A as equally similar to documents 1 and 2. If they responded with a value between 4 and 1 it meant that they rated the document A as much more similar to 1 compared to documents A and 2. Then, if they chosen a value between 6 and 9 it meant that they found the document A as much more similar to the document 2 compared to documents A and 1.

Figure 7.6: Experiment’s question for each stimulus. After these 13 practice questions the main experiment began. It consisted of sixty-five questions. Participants had to see a succession of sixtyfive 3D-network representations and had to compare the similarity between the document A and the document 1 with the similarity between the document A and the document 2, as in the practical part. All the displays were showed to the participant in random sequences to avoid learning effects. When the experiment with the 3D images ended, the participants were asked to fill a post-test questionnaire in order to understand in which manner they had compared the three comparison documents for each display type. Then, they were given a coupon of 5 CHF as a compensation and thanked for their participation. The following data were recorded during the experiment for the statistical analyse: 1. The similarity ratings pro display and participant (65x28=1820 data). 2. The responses time pro display and pro participant. 3. The total time of the experiment. 4. The angle of the display rotation and the correspondent time. 5. The questionnaire responses.

66

CHAPTER 7. METHOD

Chapter 8

Results and analysis The results of the experiments were processed in SPSS 16.0 in order to perform a statistical evaluation and thus to test the validity of the null hypotheses (see chapter 7.3.7). The statistical analyse consists in the following steps: 1. The descriptive statistic (mean and standard deviation of the similarity ratings) of all the 65 representations. 2. For each displays were made 65 histograms in order to plot the relationship between the variables (independent and dependent). It allowed to make a first graphical evaluation. 3. An analysis of variance compared multiple means values of the two groups (monoscopic and stereoscopic views). When no significant differences had been compute, the two groups could be aggregated and continue the evaluation with all results together (N=28). 4. A one-sample t-test of each representation was made to determine which representation differed from a mean similarity rating of ’5’. 5. Four pairwise Person’s correlations among the dependent variables was made to compute the correlation of the similarity ratings (9-point interval scale) with the network distances (3 different distances: equal, double and triple) and to compute the relative scatter-plot describing the strength of the relationship. 6. A Repeated Measure ANOVA of the averaged similarity ratings among the four variable groups (hue, topology, value and width). 7. A descriptive statistic of the FPP times and a Repeated Measure ANOVA of the averaged FPP times. 8. A descriptive statistic of the responses time and a Repeated Measure ANOVA of the averaged times. 67

68

CHAPTER 8. RESULTS AND ANALYSIS

9. Histograms of the pre and post questionnaires responses.

8.1

Descriptive statistics

The descriptive statistic of the experiment’s results was achieved with SPSS 16.0 (Analyze > Descriptive Statistics > Descriptives) in order to obtain information about the distributions of the dependent variables for each display.

SPSS allowed to complete a number of statistical procedures: measures of central tendency, measures of variability around the mean, measures of deviation from normality and information concerning the spread of the distribution.

The Central tendency measures gave an estimation of how a group did as a whole. In this case the mean value of the similarity rating’s distribution was reported. Measures of variability provided an estimation of how much scores within a group varied. In this case the measures for the distribution’s size (N = number of samplings, Min = smallest value in the distribution, Max = largest value in the distribution) and the Std. Dev (standard deviation, measure of stability or of sampling error) were reported. Measures of the distribution’s shape, the Kurtosis and Skewness, estimated the deviation from normality, i.e. how a distribution deviated from the optimally bell-shaped curve which occurred when all observations were around a mean. The Kurtosis measured the "peakedness" or "flatness" of the distribution. A value near to zero meant that the distribution was close to normal. A positive value meant that the distribution was flatter than normal and a negative value indicated that the distribution was more peaked than normal. In contrast, the Skewness measured the extension to which a distribution deviated from symmetry. A value near to zero meant that the distribution was symmetric, while a positive value indicated a greater number of smaller values and a negative value indicated a greater number of large values. (Department of Psychology at Illinois State University, 2008. Access: 04.08.2009)

The results of the descriptive statistics of all the 65 representations are showed in Appendix B.

8.2. HISTOGRAMS OF THE SIMILARITY RATINGS FOR EACH DISPLAY69

8.1.1

The one-sample Kolmogorov-Smirnov test

Parametric hypothesis tests required that data were approximately normally distributed. For this reason, a one-sample Kolmogorov-Smirnov test was computed to evaluate if the distributions of the similarity ratings were normal. It is a goodness-of-fit test which tested whether a given distribution was not significantly different from an hypothesized one (on the basis of the assumption of a normal distribution). The results of the one-sample K-S test are showed in the Appendix B. It was found that only in three displays the similarity ratings were not normally distributed: hue_BBB_1X, hue_BRB_1X and t1_top22_2X.

8.2

Histograms of the similarity ratings for each display

Histograms were useful to check if the distributions of samples were normal (curve have to be similar to a bell shape). In Appendix B are showed the histograms of the similarity rating for each display.

8.3

The One-sample t-test

The one-sample t-test examined the hypothesis that the mean scores of two samples were identical. The dependent variables were assumed to be normally distributed but also to be independent to each other (SPSS Guide). In this section were examined if the mean similarity ratings of each distribution equalize or significantly differ from a value of ’5’ (mean score of the dependent variable). In Appendix B are showed the results of the one-sample t-test of the similarity rating for each display. It was found that in the topology displays the hypotheses were accepted with 12 over 17 (71%). Then, in value-displays the hypotheses were accepted with 8 over 15 (53%). By hue-displays were found 9 over 18 (50%) accepted one. Finally, the width-displays presented 7 over 15 (47%) accepted hypotheses. For example, in the following three trials, participants rated in average 4.9, 3.9 and 6.2. It meant that in the first display (hue_BBB_2X), they interpreted documents A and 1 as equally similar than A and 2. In the second

70


Figure 8.1: Histograms of the displays in which the similarity ratings were not normally distributed.

8.3. THE ONE-SAMPLE T-TEST

71

display (value_222_1X) they judged documents A as more similar to 1. In the last example (width_123_3X), they rated documents A and 2 as more similar to each other.

Figure 8.2: Example of displays: width_123_3X.

8.3.1

hue_BBB_2X, value_222_1X and

Aggregation of mean similarity judgements for each independent variable

Network distance versus node distance For 17 trials were compared the Network distance with the Node distance along the links. For this purpose, mean values were aggregated to interpret results more systematically as following: • 1 trial, in which Node and Network distances between A:1 and A:2 were equal. • 4 trials, in which the Network distances between A:2 were greater than A:1, but the Node distances was the same. • 4 trials, in which the Network distances between A:1 and A:2 were equal, but the Node distances between A:1 were greater than A:2. • 8 trials, in which the Network distances between A:2 were greater than A:1 and the Node distances between A:1 were greater than A:2.

Node distance

A:1 = A:2 A:1 < A:2

Network distance A:1 = A:2 A:1 < A:2 5.2 4.2 5.7 5.0

Table 8.1: Mean similarity ratings of the 17 topology displays in which the Network and the Node distances between A:2 could be equal or greater the ditances between A:1. From the values reported in the table 8.1 the conclusion was that documents connected by links equal in Node distance were considered from participants equally similar to each other if the Network distance was equal as well (5.2 differed not significantly from 5). In contrast, if the Network

72


distance between A:2 increased, then the documents A:1 were rated as more similar to each other. If the Node distance between the documents A:1 increased but the Network distance did not differ, participants considered the documents connected by links shorter in Node distance as being more similar. With the change of the Network distance (A:2 > A:1) and of the Node distance (A:1>A:2) in a contradictory manner, the documents 1 e 2 were considerated equally similar to document A. The calculation of the mean standard deviation showed however that in the participants responses there were a greater variance by displays with a different number of intervening nodes. This meant that, in average, the Node distance had a light bigger influence compared to the Network distance and it modified significantly the judgement of the distance-similarity metaphor. In fact, when there were a different number of intervening nodes between A:1 (greater number of nodes) compared to A:2 (smaller number of nodes), participants judged A:2 to be more similar to each other if the Network distance were equal. In contrast, if it increased, the participants considerated documents 1 and 2 as equally similar to document A.

Network distance versus width of links For 15 trials were compared the Network distance with the width of the links. For this purpose, the mean values were aggregated to interpret results more systematically. First, the mean values of 5 trials in which the Network distances between A:1 and A:2 was equal were aggregated as following: • 2 trials, where the line width between A:2 was thicker and the line width between A:1 was thinner. • 3 trials, where the line width between A:2 was thicker and between A:1 the links had mixed sizes. Then, the mean values of 10 trials in which the Network distances between A:1 and A:2 varied (the distance between A:2 were greater than the distance between A:1) were aggregated as following: • 4 trials, where the line width between A:2 was thicker and the line width between A:1 was thinner. • 6 trials, where the line width between A:2 was thicker and between A:1 the links had mixed sizes. The table 8.2 shows that documents connected by links with a thicker width were considered significantly more similar in case the Network dis-


Width

A:2 thicker, A:1 thinner A:2 thicker, A:1 mixed

73 Network distance A:1 = A:2 A:1 < A:2 6.2 5.2 6.5 5.6

Table 8.2: Mean similarity ratings of the 15 width displays in which the Network distance between A:2 could be equal or greater the distance between A:1.

tance did not differ. Whether documents A:1 and A:2 were connected between homogeneous (thicker vs. thinner) or heterogeneous links (thicker vs. mixed), the mean similar rating amounted to 6.2 respectively to 6.5. In contrast, if the Network distance between documents A:2 increased and the width of the links between A:2 were thicker compared to A:1 (thinner or mixed width value), the similar ratings averaged to 5.2 and 5.6 (not significantly differ to 5.0). This meant that when the visual variable width was in conflict with the Network distance (links between documents A:2 were thicker and the Network distance were grater compared to A:1), participants judged similarity in very different ways. Some of them based it on the Network distance, some of them in the line width and other judged documents equally similar. As a results, the mean similarity ratings were near to ’5’.

Network distance versus color value of links For 15 trials, the Network distance was compared with the color value of the links. For this purpose, the mean values were aggregated to interpret results more systematically. First, the mean value of five trials, in which the Network distances between A:1 and A:2 were equated, it was aggregated as following: • 2 trials, where the color value between A:2 was darker and the color value between A:1 was lighter. • 3 trials, where the color value between A:2 was darker and between A:1 the color value of the links was mixed. The mean values of 10 trials, in which the Network distances between A:1 and A:2 varied (the distance between A:2 were greater than the distance between A:1), were aggregated as following: • 4 trials, where the color value between A:2 was darker and the color value between A:1 was lighter. • 6 trials, where the color value between A:2 was darker and between A:1 the color value of the links was mixed.

74


Value

A:2 darker, A:1 lighter A:2 darker, A:1 lighter

Network distance A:1 = A:2 A:1 < A:2 5.7 4.3 5.8 5.4

Table 8.3: Mean similarity ratings of the 15 value displays in which the Network distance between A:2 could be equal or greater the ditance between A:1. The table 8.3 shows that documents connected by darker links and with an equal Network distance presented a greater similarity compared to documents connected both by links lighter and mixed in color value. In this case the mean similarity ratings amounted respectively to 5.7 and 5.8. In contrast, if the Network distance between documents A and 2 increased, participants judged documents connected by links shorter in Network distance as more similar, even if they were lighter. In addition, documents connected by links mixed in color value and shorter in Network distance were judged as equal similar to documents connected by links with homogeneous darker color value, but placed more distantly to each other.

Network distance versus color hue of links 18 trials compared the Network distance with the color hue of the links. For this purpose, the mean values were aggregated to interpret results more systematically. First, the mean values of trials in which the Network distances between A:1 and A:2 were equated were aggregated as following: • 1 trial, where links between A:2 and A:1 were both green. • 1 trial, where links between A:2 were green and blue between A:1. • 4 trials, where links between A:2 were green and links between A:1 were mixed in color. The mean value of trials was aggregated, in which the Network distance between A:1 and A:2 varied (the distance between A:2 were greater than the distance between A:1) as following: • 2 trials, where links between A:2 and A:1 were both green. • 2 trials, where links between A:2 were green and blue between A:1. • 8 trials, where links between A:2 were green and links between A:1 were mixed in color. For the trials in which the links assumed a different color hue, that was green, blue or a mixed form of these color hues, participants considered


75

documents connected by links with an homogeneous color hue (green or blue) as more similar to each other, independently of the Network distance variation. In the case that the links were not all homogeneous in color hue, participants considered documents connected by homogeneous links as more similar than documents connected by heterogeneous one. Mean similarity ratings amounted to ’5.9’, which significantly differed to ’5’. In addition, when the Network distance increased, documents 1 and 2 were judged as equal similar: the mean similarity rating amounted to ’4.9’.

Hue

Both green Green (A:2) vs. blue (A:1) Green (A:2) vs. mixed (A:1)

Network distance A:1 = A:2 A:1 < A:2 5.6 4.5 4.8 5.1 5.9 4.9

Table 8.4: Mean similarity ratings of the 18 hue displays in which the Network distance between A:2 could be equal or greater the ditance between A:1.

76

8.4


Pearson’s correlations

In order to analyse the results more systematically, four Pearson’s mean correlations were calculated separately for each independent variable (hue, topology, value and width) and each participant. The mean correlations were calculated on the basis of the Network distance ratios between A:1 and A:2 (1, 0.5, 0.33 and for 2 trials 0.67 and 0.4) with the similarity ratings. In addition, a Pearson’s correlation between the Node distance ratios and the similarity ratings of the topology displays was computed as well. Then, these correlations were normalized by a Fisher’s r-to-z transformation in order to compare them to each other. The value for a Pearson’s correlation can fall between 0.00 (no correlation) and 1.00 (perfect correlation).

Figure 8.3: SAS output of the Pearson’s correlations between Network distance ratios and the similarity ratings of the four visual variables pro participant (CORRHUE, CORRTOPO, CORRVALUE, CORRWIDTH) and the z-scores of the Fisher’s tranformation (zCORRHUE, zCORRTOPO, zCORRVALUE, zCORRWIDTH).

8.4. PEARSON’S CORRELATIONS

77

Figure 8.4: Pearson’s mean correlations between the Network distance ratios and the similarity ratings among the four variables hue, topology, value and width.

Figure 8.5: SAS output of the Pearson’s correlations between the Node distance ratios and the similarity ratings of the topology displays and pro participant (CORRNODE, zCORRNODE).

Figure 8.6: Pearson’s mean correlations between the Node distance ratios and the similarity ratings.

78


Moreover, a one-sample t-test has be computed in order to detect if the correlation’s results were significantly different to 0. As a result, all independent variables hue, value, width and topology were moderately correlated with the independent variable Network distance.

Figure 8.7: One-sample statistics and t-test based on the z-scores of the Pearson’s correlations (test value=0).

Furthermore, a GLM multivariate analysis of variance has be computed as well to determine whether the correlation’s values significantly differ as function of participant gender and academical knowledge. The F-test results demonstrated that there were no significantly differences between these two factors and the correlation’s z-scores.


79

Figure 8.8: Table: GLM multivariate analysis of variance. Test of the between-subject effects between the correlation’s z-scores and the fixed factors gender and academical background.

80


Graphically, the relationship between the Network distance ratios and the similarity ratings (one as the independent, or the predictor variable, and the other as the dependent, or the predicted variable) could be plotted by means of scatter-plots. In these diagrams, the slant of the line represents the degree of the correlation: the steeper the line is, more highly correlated the two variables are (SPSS Tutorial). The scatter-plots of the Person’s correlations are the following:


81

Figure 8.9: Scatter-plots of the correlations between the mean similarity ratings and the Network distance ratios of the topology and the hue displays.

82


Figure 8.10: Scatter-plots of the correlations between the mean similarity ratings and the Network distance ratios of the value and the width displays.


83

Figure 8.11: Scatter-plots of the correlations between the mean similarity ratings (y-axis) and the Network distance ratios (x-axis).

84


Figure 8.12: Scatter-plots of the correlations between the mean similarity ratings and the Node distance ratios.


85

Figure 8.13: Scatter-plots of the correlations between the mean similarity ratings in function of the Network distance ratios and the Node distance ratios.

86

8.5


GLM test

In order to calculate if differences existed in the rated similarities (dependent variable) between female and male participants, geographers and nongeographers, participant’s age, participant’s ability to read maps or frequency of recreational activities related with maps reading, a univariate GLM test (Analyse: General Linear Model: Univariate) was processed. The results were the following: F(1, 26)=0.004 (Sig.=0.949>0.05) for the gender factor, F(1, 26)=0.426 (Sig.=0.520>0.05) for the school factor, F(1, 26)=0.562 (Sig.=0.840>0.05) for the age factor, F(1, 26)=2.002 (Sig.=0.159>0.05) for the map reading’s ability, and F(1, 26)=1.150 (Sig.=0.335>0.05) for the recreational activities factor. This meant that the judgement in similarity between documents did not vary significantly in function of the above mentioned fixed factors.

Figure 8.14: Output of the Repeated-Measures ANOVA.

8.5. GLM TEST

87

Figure 8.15: GLM univariate analysis of variance between the mean similarity ratings of each participant with the follow fixed factors: gender, academical background, age, ability on reading maps and frequency in recreational activities related with map’s reading.

88


8.6

Repeated Measures ANOVA

Repeated measures ANOVA tests allowed here to examine if the mean similarity ratings differed significantly between the four independent variables groups. The assumptions were the following: the distributions of the similarity ratings were normal and independent, and the distributions had the same variances. In SPSS, the MANOVA test, in table "Tests of WithinSubjects Effects" and "Sphericity Assumed" rows, got as result F(3,24)=10.013 and the p-value was < .05.

Figure 8.16: Output of the Repeated-Measures ANOVA. Since the p-value for this hypothesis was significantly small as 0.05, the null hypothesis were confidently rejected. The conclusion was that the similarity ratings between the four independent variables vary significantly to each other. In addition, the post hoc tests reveal that the mean similarity ratings of the width-displays were significantly higher than the other three variables, while the hue, topology and value’s scores were not significantly different from each other (both p>.05).

8.6. REPEATED MEASURES ANOVA

89

Figure 8.17: Repeated-Measures ANOVA: pairwise comparisons of the similarity ratings between the four display types. 1=hue, 2=topology, 3=value, 4=width.

Figure 8.18: Multivariate effects of the similarity ratings.

90


8.7

The fronto-parallel orientation of the displays

The fronto-parallel orientation occurs when the comparison document points A, 1 and 2 lie within a orthogonal plane to the line of sight (within a fronto parallel plane, FFP). This orientation allows participants to see Network (and Direct) distances between the documents A:1 and A:2 in their maximal extension. If participants did not see the three-dimensional displays accordingly to a FFP, the proximal distance between the documents cannot be perceived in an optimal manner and the similarity ratings may vary among the participants in function of the orientation’s angle of the display viewed. So, if the Network distances cannot be clearly perceived, other variable as hue, value or with of links between documents may become the main measure in judging similarities. One important thing in this experiment was that participants did not achieve instructions about how to see, interact and respond to the questions during the whole experiment. Like this, participants had to find intuitively the best orientation in order to judge the similarity between the documents. This implied an increase of responses time, as they needed extra time to rotate and interact with the displays. Apart from the similarity ratings, the angles in which the participants rotate the sixty-five displays during the experiment were registered. These angles allowed to reconstruct in a second time, for the statistical analysis of the results, how many times and how long participants saw the displays in the FP orientation. In addition, the stored angles allowed to determine if they saw the displays in this orientation just before responding to the questions. The angles of the displays rotation could be used to make a playback of each experiment and see how participants rotated the displays during the experiment. The next table summarize the following information: 1. Trial’s name. 2. Total number of participants (N). 3. Average of similarity ratings (from 1 to 9). 4. Standard deviation of similarity ratings. 5. Percentage of the participants that saw the displays in the FP orientation (all angles that were comprised between s´ 5 deg. from a FPP). 6. Percentage of the participants that saw the displays in the FP orientation (all angles that were comprised between s´ 5 deg. from a FPP) just before responding.

8.7. THE FRONTO-PARALLEL ORIENTATION OF THE DISPLAYS

91

7. Percentage of the participants that saw the displays in the FP orientation (all angles that were comprised between s´ 15 deg. from a FPP) just before responding. 8. Average of the time in which the participants saw the displays in the FP orientation, in seconds. 9. Average of the total time that participants spend in seconds in each trial. 10. Percentage of the time in which the participants saw the displays in a FP orientation over the entire total time.

FPP Statistics 1

2

3

4

5

6

7

8

9

10

hue_BBB_1X

28

5.64

1.42

42.9

0

42.9

1.36

9.59

14.19

hue_BBB_2X

28

5.14

1.51

57.1

7.1

25

1.1

10.44 10.51

hue_BBB_3X

28

3.86

1.63

42.9

0

32.1

1.27

10.77 11.81

hue_BBR_1X

28

5.68

1.39

42.9

10.7

39.3

1.08

9.67

hue_BBR_2X

28

5.86

1.65

50

7.1

46.4

1.78

14.43 12.36

hue_BBR_3X

28

3.82

1.87

35.7

7.1

25

1.36

9.76

13.96

hue_BRB_1X

28

6.11

1.55

50

0

25

0.55

12.2

4.52

hue_BRB_2X

28

4.04

2.27

35.7

3.6

32.1

0.55

8.74

6.34

hue_BRB_3X

28

4.11

1.93

53.6

10.7

39.3

0.77

7.35

10.44

hue_RBB_1X

28

5.71

2.07

50

3.6

17.9

0.79

10.57 7.45

hue_RBB_2X

28

5.75

2.05

50

7.1

32.1

1.07

11.94 8.92

hue_RBB_3X

28

5.39

2.35

35.7

3.6

21.4

0.84

15.09 5.58

hue_RRB_1X

28

5.89

1.87

39.3

0

10.7

0.93

12.23 7.6

hue_RRB_2X

28

5.36

2.13

42.9

3.6

35.7

1.41

10.45 13.46

hue_RRB_3X

28

4.79

2.23

39.3

3.6

17.9

0.52

11.41 4.56

hue_RRR_1X

28

4.75

1.46

28.6

3.6

25

0.09

10.14 0.89

hue_RRR_2X

28

5.00

1.72

42.9

3.6

42.9

0.5

13.3

hue_RRR_3X

28

5.18

2.23

32.1

3.6

25

0.6

10.32 5.84

t1_top21_1X

28

5.18

1.96

42.9

10.7

39.3

0.26

8.93

2.94

t1_top21_2X

28

4.64

2.06

28.6

3.6

42.9

0.07

7.85

0.95

t1_top21_3X

28

4.82

2.50

35.7

7.1

35.7

0.08

7.01

1.17

t1_top22_1_5X 28

4.61

1.81

53.6

3.6

39.3

1.23

8.95

13.74

t1_top22_1X

28

5.21

1.57

39.3

10.7

39.3

1.45

12.34 11.77

t1_top22_2_5X 28

4.14

1.58

60.7

7.1

32.1

1.64

9.97

t1_top22_2X

28

4.29

1.67

50

3.6

42.9

1.29

11.43 11.25

t1_top22_3X

28

3.57

1.60

42.9

3.6

21.4

1.82

11.63 15.63

t1_top31_1X

28

6.54

2.10

28.6

14.3

46.4

0.39

7.13

11.15

3.79

16.42

5.43

92


t1_top31_2X

28

5.43

2.18

32.1

7.1

42.9

0.99

10.98 9.02

t1_top31_3X

28

5.00

2.36

50

0

32.1

0.44

8.03

t1_top32_1X

28

4.64

2.08

35.7

3.6

25

0.19

10.76 1.75

t1_top32_2X

28

5.25

1.65

57.1

0

32.1

2.82

13.37 21.12

t1_top32_3X

28

4.18

2.13

46.4

7.1

39.3

0.14

12.23 1.13

t1_top41_1X

28

6.25

2.32

35.7

3.6

32.1

0.26

8.72

t1_top41_2X

28

5.96

2.49

53.6

7.1

35.7

0.81

10.56 7.65

t1_top41_3X

28

4.89

2.39

60.7

7.1

32.1

1.63

11.77 13.82

value_111_1X

28

5.29

1.70

39.3

3.6

25

1.51

11.99 12.63

value_111_2X

28

5.50

1.67

64.3

7.1

32.1

1.21

10.95 11.04

value_111_3X

28

3.96

1.55

35.7

0

32.1

0.75

12.85 5.85

value_123_1X

28

5.29

2.07

53.6

0

28.6

1.2

10.11 11.86

value_123_2X

28

5.96

2.28

28.6

0

53.6

0.55

8.76

value_123_3X

28

5.75

2.53

42.9

3.6

25

1.11

10.62 10.49

value_222_1X

28

6.11

1.40

32.1

7.1

32.1

0.94

11.18 8.44

value_222_2X

28

4.36

1.70

53.6

7.1

14.3

0.73

13.95 5.24

value_222_3X

28

3.46

1.53

32.1

3.6

46.4

1.33

9.9

value_231_1X

28

6.21

1.95

42.9

0

28.6

2.31

12.07 19.18

value_231_2X

28

6.21

2.04

57.1

3.6

39.3

2.11

13.78 15.33

value_231_3X

28

4.36

2.08

39.3

14.3

32.1

0.32

7.96

value_321_1X

28

5.79

1.99

39.3

7.1

35.7

1.07

10.82 9.93

value_321_2X

28

5.11

1.87

39.3

0

42.9

0.54

10.22 5.28

value_321_3X

28

4.93

1.88

39.3

7.1

32.1

0.57

9.61

width_111_1X 28

6.07

1.65

50

10.7

28.6

0.9

10.14 8.92

width_111_2X 28

5.21

1.91

46.4

10.7

35.7

1.96

11.04 17.79

width_111_3X 28

5.43

2.35

42.9

7.1

39.3

1.69

11.55 14.61

width_123_1X 28

6.43

1.95

50

3.6

32.1

1.43

9.25

15.44

width_123_2X 28

6.32

1.36

53.6

14.3

35.7

1.23

13.5

9.12

width_123_3X 28

6.18

2.39

32.1

0

28.6

0.95

14.91 6.38

width_222_1X 28

6.39

1.91

39.3

3.6

28.6

1.87

13.51 13.84

width_222_2X 28

5.79

1.77

60.7

0

32.1

1.95

14.49 13.44

width_222_3X 28

4.29

2.46

67.9

3.6

35.7

1.8

8.89

width_231_1X 28

6.50

1.91

53.6

0

21.4

1.06

10.47 10.13

width_231_2X 28

5.43

2.04

35.7

3.6

21.4

0.57

10.57 5.41

width_231_3X 28

4.68

2.36

50

7.1

21.4

2.01

10.24 19.64

width_321_1X 28

6.46

1.88

32.1

3.6

17.9

1.1

11.55 9.52

width_321_2X 28

5.29

2.05

46.4

7.1

42.9

2.11

12.95 16.29

width_321_3X 28

5.61

2.28

28.6

7.1

42.9

0.99

10.14 9.8

Table 8.5: Summary of the FPP statistics.

5.48

2.94

6.33

13.44

3.97

5.95

20.24


93

In average, 44% of the participants saw the experiment’s trials in the FPorientation. In addition, only the 5% saw the displays in the FP-orientation calculated with an angle comprised between s´ 5 deg. just before responding and about the 33% saw the displays in the FP-orientation with an angle comprised between s´ 15 deg. Moreover, in average, participants saw the displays in the FP-orientation about 29 times and about 4 times just before responding. The sum of the times in which participants saw the displays in the FP-orientation was, in all, about 799 and 97 just before responding. The average time in which a participant saw FPPs of the whole experiment duration was about 69 seconds. The sum of the FPP time was about 32 minutes over 5.5 hours, that corresponded to about 10% of the total time. The average FPP time pro display was instead equal to 1.1 seconds. The display ’t1_top32_2X’ resulted to have the greater percentage of FPP time (21%) and the display ’hue_RRR_1X’ (0.9%) the small percentage of FPP time over the total time. HadF P P (#)

HadEndF P P (#)

F P P T ime(s)

T imeF P P (%)

28.5 799

3.5 97

68.9 1929.5

9.7

Mean Sum

Table 8.6: Summary of the FPP statistics pro participants: number of FPPs which participants saw, number of FPPs they saw just before responding, time and percentage of the time in which they saw FPPs. Analysing the FPP time pro display type there were found the following results: during the whole experiment, participants saw the display in the FP orientation for 216 times (7.7 times pro participant) by hue-displays, 211 times by topology-displays (7.5 times pro participant), 193 times by widthdisplays (6.9 times pro participant) and 179 times by value-displays (6.4 times pro participant). However, just before responding, they saw the display in the FP orientation for 29 times (1.04 times pro participant) by widthdisplays, 28 times by topology-displays (1 times pro participant), 22 times by hue-displays (0.8 times pro participant) and 18 times by value-displays (0.6 times pro participant). Times in which they spent in order to see the displays within a FP orientation in the different display types were the following: 9.6 minutes by width-displays (2.9% of the total time), 7.7 minutes by hue-displays (2.34% of the total time), 7.6 minutes by value-displays (2.3% of the total time) and 7.2 minutes by topology-displays (2.19% of the total time).

94


Had FPP (#)

Had End FPP (#)

Hue

T opology

V alue

W idth

Hue

T opology

V alue

W idth

7.71

7.54

6.39

6.89

0.79

1

0.64

1.04

Max

15

13

11

13

3

5

3

6

Min

4

3

0

1

0

0

0

0

Sum

216

211

179

193

22

28

18

29

Mean

Table 8.7: Summary of the amount of FPP pro participants in average and FPP time pro variable.

Time FPP (s)

FPP time over total time (%)

Hue

T opology

V alue

W idth

Hue

T opology

V alue

W idth

Mean

16.58

15.5

16.27

20.55

2.34

2.19

2.30

2.90

Max

58.64

56

93.84

87.75

Min

0.17

0.13

0

0.06

Sum

464.18

434.1

455.7

575.48

Table 8.8: Summary of the amount of FPP pro participants in average and FPP time pro variable.

The calculation of the repeated measures ANOVA among the for variable groups gave the following results: 1. The number of FPP gave as results F(3,24)=2.550 (significance=0.061>0.05). This meant there were no significantly differences among the four variables groups.

Figure 8.19: MANOVA test: within-subject effects of the number of FPP participants saw during the entire experiment among the dependent variables.


95

2. The number of FPP just before responding gave as result F(3,24)=0.994 (significance=0.4>0.05). This meant there were no significantly differences among the four variables groups regarding the number of times in which participants saw FPP just before responding.

Figure 8.20: MANOVA test: within-subject effects of the number of FPP participants saw just before responding among the dependent variables. 3. The time in which participants saw the displays according to a FPorientation gave as result F(3,24)=0.876 (significance=0.457>0.05). This meant there were no significantly differences among the four variables groups regarding the times in which participants saw FPP during the experiment. The FPP time, the number of FPP saw during the experiment and the number of FPP saw just before responding did not differ in function of the variation of the Network distances, respectively F(1,26)=0.65, 2.16 and 0.128 (Sig.=0.629, 0.084 and 0.972 > 0.05). Finally, the FPP time did not differ between female and male participants F(1,26)=1.251 (Sig.=0.274>0.05), as well as between geographers and non-geographers F(1,26)=0.300 (Sig.=0.589>0.05).

Figure 8.21: MANOVA test: within-subject effects of the FPP time among the dependent variables.

96


Figure 8.22: GLM multivariate analysis of variance: tests of betweensubject effects.

Figure 8.23: GLM univariate analysis of variance: tests of between-subject effects.

8.8. RESPONSE TIME

8.8

97

Response time

In general, participants responded to each network display question with an averaged time of 11 seconds. The faster response was 7s and the slowest was 15.1s. Across all trials types, 71% of participants responded slowly at the beginning of the experiment and more quickly toward the end of the experiment. The repeated-measures of ANOVA revealed that there were no significantly differences in response time across the four group of variables: F(3, 24) = 2.527 (significance=0.063 > 0.05). However, the faster mean response time of the four group variables were 10.1s for the 17 topology trials, then, in descending order, 10.98s for the value trials, 11.02s for the hue trials and finally 11.6s for the width trials.

Figure 8.24: GLM Repeated Measures ANOVA: tests of within-subject effects among the independent variables hue, topology, value and width. Moreover, the response time did not differ between female and male participants F(1,26)=0.021 (Sig.=0.886>0.05), among the age F(1,26)=0.804 (Sig.=0.643>0.05), among the ability in map reading F(1,26)=2.048 (Sig.=0.153>0.05) and among the frequency in recreational activities with maps F(1,26)=0.933 (Sig.=0.408>0.05). In contrast, the response time varied significantly between geographers and non-geographers F(1,26)=6.701 (Sig.=0.016 10: isvalue = True else: iswidth = True except: linksw.append(s[2]) ishue = True

163

ballfile.close() ballsz[label1] = .5 ballsz[label2] = .5 ballsz[labelA] = .5 \# Shift points so that the average location is at 0,0,0 \# This is to make the swarm rotate around its center. sumx = 0 sumy = 0 sumz = 0 for i in range(0,len(ballsx)): sumx = sumx + ballsx[i] sumy = sumy + ballsy[i] sumz = sumz + ballsz[i] avx = sumx / len(ballsx) avy = sumy / len(ballsx) avz = sumz / len(ballsx) for i in range(0,len(ballsx)): ballsx[i] = ballsx[i] - avx ballsy[i] = ballsy[i] - avy ballsz[i] = ballsz[i] avz \# Put all points in one group swarm = viz.addGroup() for i in range(0,len(ballsx)): allballs.append(0) \# Make each point a ball for i in range(0,len(ballsx)): allballs[i] = swarm.add('models/ball.wrl') \#allballs[i].color(random.random(),random.random(),random.random ())

allballs[i].color(0,0,0) \#scale ball size for visible but not to large (M. Neun, 11. March 2008) allballs[i].scale(1.6,1.6,1.6) \# Translate each point to its proper location for i in range(0,len(ballsx)): allballs[i].translate(ballsx[i],ballsy[i],ballsz[i]) for i in range(0,len(linksa)): viz.startlayer(viz.LINES) if ishue: if linksw[i] == 'red': viz.vertexcolor(.45,.45,.7) else: viz.vertexcolor(.1,.62,.46) elif isvalue: \#Color values (Color Brewer): if linksw[i] == 100: viz.vertexcolor(.02,.44,.69) if linksw[i] == 66: viz.vertexcolor(.45,.66,.85) if linksw[i] == 33: viz.vertexcolor(.74,.79,.88) else: viz.vertexcolor(.4,.4,.7) if iswidth: \# Line width lw = int(linksw[i]) if lw == 3: viz.linewidth(10) elif lw == 2:

164

APPENDIX C. VIZARD SCRIPT: 3D STIMULI

else: else:

viz.linewidth(5) viz.linewidth(2)

viz.linewidth(7) ia = linksa[i] ib = linksb[i] viz.vertex(ballsx[ia],ballsy[ia],ballsz[ia]) viz.vertex(ballsx[ib],ballsy[ib],ballsz[ib]) viz.endlayer(swarm) \# Move the swarm so that it is visible swarm.translate(0,1.8,2.4) \# Rotate such that FPP is not visible global randomNumber randomNumber = random.randint(1,3) print randomNumber if randomNumber == 1: swarm.setAxisAngle([1,0,0, 75], viz.REL\_LOCAL) else: swarm.setAxisAngle([0,1,0, 75], viz.REL\_LOCAL) \# Add labels 1, 2, and A, put them in the right \# locations, and make them billboards scale = .08 one = swarm.add(TEXT3D,'1') one.color(1,0,0) one.scale(scale,scale,scale) one.translate(ballsx[label1],ballsy[label1],ballsz[label1]) one.billboard() two = swarm.add(TEXT3D,'2') two.color(1,0,0) two.scale(scale,scale,scale) two.translate(ballsx[label2],ballsy[label2],ballsz[label2]) two.billboard() A = swarm.add(TEXT3D,'A') A.color(1,0,0) A.scale(scale,scale,scale) A.translate(ballsx[labelA],ballsy[labelA],ballsz[labelA]) A.billboard() print bfile \# Calculate euclide distance bw. A1, A2 and 12: posA = allballs[labelA].getPosition(viz.REL\_GLOBAL) pos1= allballs[label1].getPosition(viz.REL\_GLOBAL) pos2= allballs[label2].getPosition(viz.REL\_GLOBAL) distA1 = vizmat.Distance(posA, pos1) distA2 = vizmat.Distance(posA, pos2) dist12 = vizmat.Distance(pos1, pos2) print 'nodes count = ', nodecount print '3D distanzen A1: \%s, A2: \%s, 12: \%s' \% (distA1,distA2,dist12) viz.go(viz.QUAD\_BUFFER | viz.FULLSCREEN) viz.viewdist(1.2)

165

\# Names of the files containing point coordinates fnames = ['hue\_BBB\_1X','hue\_BBB\_2X','hue\_BBB\_3X','hue\_BBR\_1X','hue\_BBR\_2X',' hue\_BBR\_3X','hue\_BRB\_1X','hue\_BRB\_2X','hue\_BRB\_3X','hue\_RBB\_1X','hu e\_RBB\_2X','hue\_RBB\_3X','hue\_RRB\_1X','hue\_RRB\_2X','hue\_RRB\_3X','hue\ _RRR\_1X','hue\_RRR\_2X','hue\_RRR\_3X','t1\_top21\_1X','t1\_top21\_2X','t1\_ top21\_3X','t1\_top22\_1X','t1\_top22\_1\_5X','t1\_top22\_2X','t1\_top22\_2\_ 5X','t1\_top22\_3X','t1\_top31\_1X','t1\_top31\_2X','t1\_top31\_3X','t1\_top3 2\_1X','t1\_top32\_2X','t1\_top32\_3X','t1\_top41\_1X','t1\_top41\_2X','t1\_t op41\_3X','value\_111\_1X','value\_111\_2X','value\_111\_3X','value\_123\_1X' ,'value\_123\_2X','value\_123\_3X','value\_222\_1X','value\_222\_2X','value\_ 222\_3X','value\_231\_1X','value\_231\_2X','value\_231\_3X','value\_321\_1X', 'value\_321\_2X','value\_321\_3X','width\_111\_1X','width\_111\_2X','width\_1 11\_3X','width\_123\_1X','width\_123\_2X','width\_123\_3X','width\_222\_1X',' width\_222\_2X','width\_222\_3X','width\_231\_1X','width\_231\_2X','width\_23 1\_3X','width\_321\_1X','width\_321\_2X','width\_321\_3X'] fwarmup=['warmup1\_hue\_BBR\_2X','warmup2\_hue\_RRB\_3X','warmup3\_hue\_BRB\_ 3X','warmup4\_t1\_top22\_2\_5X','warmup5\_t1\_top32\_3X','warmup6\_t1\_top41\ _2X','warmup7\_value\_111\_2X','warmup8\_value\_321\_1X','warmup9\_width\_111 \_2X','warmup10\_width\_222\_3X'] \# Randomize the names random.shuffle(fnames) random.shuffle(fwarmup) \# Get name of file to store data fname = input('Datafile name?') fname = 'data/' + fname + '.txt' swarm = 0 if viz.running(): datfile = open(fname,'w') msg = add(TEXT3D,'') msg.scale(.03,.03,.03) msg.translate(-.4,2,1) msg.color(1,0,0) \# Move the eyepoint and buttons down a little so the center of the \# swarm is above the center of the screen. hyoffset = .1 translate(HEAD\_POS,0,-hyoffset,0) bottom = add('models/bottom.wrl') bottom.scale(0.9,1,1) bottom.translate(0,1.45-hyoffset,1.15) bottom.visible(OFF) \# Add a transparent panel in front of each rating number \# so that we can tell which one was selected but1 = add('models/button.wrl') but2 = add('models/button.wrl') but3 = add('models/button.wrl') but4 = add('models/button.wrl') but5 = add('models/button.wrl') but6 = add('models/button.wrl') but7 = add('models/button.wrl') but8 = add('models/button.wrl') but9 = add('models/button.wrl')

166


but1.color(RED) but1.scale(1.1,1.375) but2.scale(1.1,1.375) but3.scale(1.1,1.375) but4.scale(1.1,1.375) but5.scale(1.1,1.375) but6.scale(1.1,1.375) but7.scale(1.1,1.375) but8.scale(1.1,1.375) but9.scale(1.1,1.375) but1.translate(-0.098,1.452-hyoffset,1.14) boffset = 0.05 but2.translate(boffset-0.109,1.452-hyoffset,1.14) but3.translate(boffset-0.069,1.452-hyoffset,1.14) but4.translate(boffset-0.029,1.452-hyoffset,1.14) but5.translate(boffset+0.0115,1.452-hyoffset,1.14) but6.translate(boffset+0.0518,1.452-hyoffset,1.14) but7.translate(boffset+0.094,1.452-hyoffset,1.14) but8.translate(boffset+0.136,1.452-hyoffset,1.14) but9.translate(boffset+0.178,1.452-hyoffset,1.14) \# Load the next question button nextq = add('models/nextq.wrl') nextq.scale(0.7, 1.4, 1) nextq.translate(.32,1.5,1) nextq.visible(OFF) \# Load the screen screen = add('models/screen.wrl') screen.scale(1.3, 1.3, 1) screen.translate(0,1.8,1) \# Add textures to apply to screen scr2 = add('models/intro.bmp') scr3 = add('models/warmup1.bmp') scr4 = add('models/warmup2.bmp') scr5 = add('models/warmup3.bmp') scr6 = add('models/ballprac.bmp') \# Description of the 10 practice questions. scr8 = add('models/ballintro.bmp') \# Description of the 65 experiment questions. scr9 = add('models/ballend.bmp') \# End of the experiment. \# Load the proceed button proceed = add('models/proceed.wrl') proceed.scale(1.3,1.3,1) proceed.translate(0,1.5,1) \# Don't allow mouse navigation mouse(OFF) \# Background color white clearcolor(1,1,1) \# Add some light to brighten things up \# and create shading on the balls lite = add(LIGHT) lite.position(-5,3,0)

167

\# Global variables ballsx = [] ballsy = [] ballsz = [] allballs = [] label1 = 0 label2 = 0 labelA = 0 INCREMENT = .5 rot = 0 yloc = 0 xang=0 yang=0 firsttime = 1 tstart=0 rating = 0 trial = 0 wtrial = 0 startballs = 0 screen2 = 1 screen2b = 0 screen3 = 0 screen4 = 0 screen5 = 0 screen6 = 0 screen7 = 0 screen8 = 0 screen9 = 0 mousedata(ABSOLUTE,ABSOLUTE) def onmousedown(button): global rot,rating,boffset,trial,wtrial,firsttime,xang,yang,startballs,screen2 global screen2b, screen3,screen4,screen5,screen6,screen7,screen8,screen9 if button == MOUSEBUTTON\_LEFT: rot = 1 \# Find out which button is selected object = pick() if object.valid(): \# Change button appearance when selected \# Is it the next proceed button? if object == proceed: if startballs: proceed.visible(OFF) screen.visible(OFF) bottom.visible(ON) nextq.visible(ON) \# Clear out the old set of points if swarm: swarm.remove() firsttime = 1 xang = 0 yang = 0 ReadFile(fnames[0]) return elif screen2: screen2 = 0

168


screen.texture(scr2) screen.scale(1.3,1.3,1) screen.visible() screen3 = 1 return elif screen3: screen3 = 0 screen.texture(scr3) screen.scale(1.3,1,1) proceed.visible(OFF) nextq.visible() screen.visible() bottom.visible() screen4 = 1 return elif screen7: \#warmup screen msg.message("warmup \%s" \% (wtrial+1)) ReadFile(fwarmup[wtrial]) wtrial = wtrial + 1 screen.visible(OFF) bottom.visible() nextq.visible() proceed.visible(OFF) return \# Next question button elif object == nextq and rating > 0: if startballs: \# Record rating for this trial datfile.write(str(rating)) trial = trial + 1 \# If we're at the end of the list, bail. if trial >= len(fnames): screen8 = 0 screen9 = 0 screen.texture(scr9) screen.scale(1.5,1.4,1) screen.visible() swarm.visible(OFF) bottom.visible(OFF) nextq.visible(OFF) but1.alpha(0) but2.alpha(0) but3.alpha(0) but4.alpha(0) but5.alpha(0) but6.alpha(0) but7.alpha(0) but8.alpha(0) but9.alpha(0) return onkeydown('q') datfile.write('\nTRIAL ' + str(trial+1) + ' + fnames[trial] +'\n') \# Reset rating buttons to default color but1.alpha(0) but2.alpha(0)

'

169

but3.alpha(0) but4.alpha(0) but5.alpha(0) but6.alpha(0) but7.alpha(0) but8.alpha(0) but9.alpha(0) \# Clear out the old set of points if swarm: swarm.remove() \# Read in next set of points firsttime = 1 xang = 0 yang = 0 ReadFile(fnames[trial]) rating = 0 return elif screen4: \# Reset rating buttons to default color but1.alpha(0) but2.alpha(0) but3.alpha(0) but4.alpha(0) but5.alpha(0) but6.alpha(0) but7.alpha(0) but8.alpha(0) but9.alpha(0) datfile.write('warmup1 ' + str(rating) + '\n') screen4 = 0 screen.texture(scr4) screen5 = 1 rating = 0 return elif screen5: \# Reset rating buttons to default color but1.alpha(0) but2.alpha(0) but3.alpha(0) but4.alpha(0) but5.alpha(0) but6.alpha(0) but7.alpha(0) but8.alpha(0) but9.alpha(0) datfile.write('warmup2 ' + str(rating) + '\n') screen5 = 0 screen.texture(scr5) screen6 = 1 rating = 0 return elif screen6: \# Reset rating buttons to default color but1.alpha(0) but2.alpha(0) but3.alpha(0) but4.alpha(0)

170


but5.alpha(0) but6.alpha(0) but7.alpha(0) but8.alpha(0) but9.alpha(0) datfile.write('warmup3 ' + str(rating) + '\n') screen6 = 0 bottom.visible(OFF) nextq.visible(OFF) proceed.visible() screen.texture(scr6) screen.scale(1.5,1.4,1) screen7 = 1 rating = 0 return elif screen7: \#warmup screen \# Reset rating buttons to default color but1.alpha(0) but2.alpha(0) but3.alpha(0) but4.alpha(0) but5.alpha(0) but6.alpha(0) but7.alpha(0) but8.alpha(0) but9.alpha(0) datfile.write('warmup3d' + str(wtrial) + ' ' + str(rating) + '\n') msg.message("warmup \%s" \% (wtrial+1)) rating = 0 \# Clear out the old set of points if swarm: swarm.remove() ReadFile(fwarmup[wtrial]) wtrial = wtrial + 1 screen.visible(OFF) bottom.visible() nextq.visible() proceed.visible(OFF) if wtrial == 10: screen7 = 0 screen8 = 1 return elif screen8: \# save last warmup decision datfile.write('warmup3d' + str(wtrial) + ' ' + str(rating) + '\n') msg.message("") \# Begin actual ball rotation trials \# Reset rating buttons to default color but1.alpha(0) but2.alpha(0) but3.alpha(0) but4.alpha(0) but5.alpha(0)

171

but6.alpha(0) but7.alpha(0) but8.alpha(0) but9.alpha(0) screen8 = 0 bottom.visible(OFF) nextq.visible(OFF) proceed.visible() screen.visible() screen.texture(scr8) screen.scale(1.5,1.4,1) startballs = 1 swarm.visible(OFF) datfile.write('TRIAL 1 ' + fnames[0]+'\n') rating = 0 return \# Find out which rating button it is and change it's color if object == but1: rating = 1 but1.alpha(.3) else: but1.alpha(0) if object == but2: rating = 2 but2.alpha(.3) else: but2.alpha(0) if object == but3: rating = 3 but3.alpha(.3) else: but3.alpha(0) if object == but4: rating = 4 but4.alpha(.3) else: but4.alpha(0) if object == but5: rating = 5 but5.alpha(.3) else: but5.alpha(0) if object == but6: rating = 6 but6.alpha(.3) else: but6.alpha(0) if object == but7: rating = 7 but7.alpha(.3) else: but7.alpha(0) if object == but8: rating = 8 but8.alpha(.3) else: but8.alpha(0)

172


if object == but9: rating = 9 but9.alpha(.3) else: but9.alpha(0) \#Don't let mouse motion move the swarm when mouse button is up def onmouseup(button): global rot rot = 0 mousedata(ABSOLUTE,ABSOLUTE) \#Rotate the swarm when mouse moves and left button is down def mousemove(x,y): global rot,yloc,xang,yang,firsttime,tstart \# If left button is down if rot == 1: \# Start the clock at first rotation if firsttime == 1 and startballs: tstart = time.time() firsttime = 0 \# Record the current angle of rotation xang = xang + x*INCREMENT yang = yang + y*INCREMENT if startballs: msg = '\%8.3f \%5.1f \%5.1f\n' \% (time.time() tstart,xang, yang) datfile.write(msg) \# Rotate the swarm if swarm: mousedata(RELATIVE,RELATIVE) swarm.rotate(0,1,0,x*INCREMENT,RELATIVE\_LOCAL) swarm.rotate(1,0,0,y*INCREMENT,RELATIVE\_WORLD) def onkeydown(key): global datfile,rating if key == 's': ReadFile(fnames[0]) if key == 'q': datfile.close() quit() \#Call commands callback(KEYDOWN\_EVENT,onkeydown) callback(MOUSEUP\_EVENT,onmouseup) callback(MOUSEDOWN\_EVENT,onmousedown) callback(MOUSEMOVE\_EVENT,mousemove)

Appendix D

SAS Script: Pearson’s Correlation

173

174

APPENDIX D. SAS SCRIPT: PEARSON’S CORRELATION

*Master Thesis, Sara Maggi, University of Zurich, August 2009; title 'Pearsons Correlations of Network-Distance Ratios with Similarity'; title2 'for the four Line-Display Groups: hue, topology, value and width.'; data correlations3d; INPUT userid simil1 simil2 simil3 simil4 simil5 simil6 simil7 simil8 simil9 simil10 simil11 simil12 simil13 simil14 simil15 simil16 simil17 simil18 simil19 simil20 simil21 simil22 simil23 simil24 simil25 simil26 simil27 simil28 simil29 simil30 simil31 simil32 simil33 simil34 simil35 simil36 simil37 simil38 simil39 simil40 simil41 simil42 simil43 simil44 simil45 simil46 simil47 simil48 simil49 simil50 simil51 simil52 simil53 simil54 simil55 simil56 simil57 simil58 simil59 simil60 simil61 simil62 simil63 simil64 simil65 ; * create actual variables from order variables; ARRAY SIM(65) simil1 simil2 simil3 simil4 simil5 simil6 simil7 simil8 simil9 simil10 simil11 simil12 simil13 simil14 simil15 simil16 simil17 simil18 simil19 simil20 simil21 simil22 simil23 simil24 simil25 simil26 simil27 simil28 simil29 simil30 simil31 simil32 simil33 simil34 simil35 simil36 simil37 simil38 simil39 simil40 simil41 simil42 simil43 simil44 simil45 simil46 simil47 simil48 simil49 simil50 simil51 simil52 simil53 simil54 simil55 simil56 simil57 simil58 simil59 simil60 simil61 simil62 simil63 simil64 simil65; ARRAY ACTUAL(65) act1-act65 (1 .5 .33 1 .5 .33 1 .5 .33 1 .5 .33 1 .5 .33 1 .5 .33 1 .5 .33 .67 1 0.4 .5 .33 1 .5 .33 1 .5 .33 1 .5 .33 1 .5 .33 1 .5 .33 1 .5 .33 1 .5 .33 1 .5 .33 1 .5 .33 1 .5 .33 1 .5 .33 1 .5 .33 1 .5 .33); *CALCULATE WITHIN-SUBJECT CORRELATIONS of NETWORK-DISTANCE RATIOS WITH SIMILARITY for ALL LINE DISPLAY QUESTIONS; ARRAY CROSPROD(65) cross1-cross65; ARRAY SQUARE(65) squar1-squar65; DO I=1 TO 65; CROSPROD(I)=SIM(I)*ACTUAL(I); SQUARE(I)=SIM(I)**2; END; *Direct-distance/similarity correlations (positive is dist=sim); CORRHUE = ((18*(SUM(OF cross1 cross2 cross3 cross4 cross5 cross6 cross7 cross8 cross9 cross10 cross11 cross12 cross13 cross14 cross15 cross16 cross17 cross18)))-((sum(of simil1 simil2 simil3 simil4 simil5 simil6 simil7 simil8 simil9 simil10 simil11 simil12 simil13 simil14 simil15 simil16 simil17 simil18))*(sum(of act1 act2 act3 act4 act5 act6 act7 act8 act9 act10 act11 act12 act13 act14 act15 act16 act17 act18))))/(sqrt((18*(squar1+squar2+squar3+squar4+squar5+squar6+squar7+ squar8+ squar9+squar10+squar11+squar12+squar13+squar14+squar15+squar16+squar17+squar18)((simil1+simil2+ simil3+ simil4+simil5+simil6+simil7+simil8+simil9+simil10+simil11+simil12+simil13+ simil14+simil15+simil16+simil17+simil18)**2))*(26.2008))); CORRTOPO = ((17*(SUM(OF cross19 cross20 cross21 cross22 cross23 cross24 cross25 cross26 cross27 cross28 cross29 cross30 cross31 cross32 cross33 cross34 cross35)))-((sum(of simil19 simil20 simil21 simil22 simil23 simil24 simil25 simil26 simil27 simil28 simil29 simil30 simil31 simil32 simil33 simil34 simil35))*(sum(of act19 act20 act21 act22 act23 act24 act25 act26 act27 act28 act29 act30 act31 act32 act33 act34 act35))))/(sqrt((17*(squar19+squar20+squar21+squar22+ squar23+ squar24+ squar25+squar26+squar27+squar28+squar29+squar30+squar31+squar32+squar33+squar34+squar35)((simil19+simil20+simil21+simil22+simil23+simil24+simil25+simil26+simil27+simil28+simil29+simil30+ simil31+simil32+simil33+simil34+simil35)**2))*(21.4094))); CORRVALUE = ((15*(SUM(OF cross36 cross37 cross38 cross39 cross40 cross41 cross42 cross43 cross44 cross45 cross46 cross47 cross48 cross49 cross50)))-((sum(of simil36 simil37 simil38 simil39 simil40 simil41 simil42 simil43 simil44 simil45 simil46 simil47 simil48 simil49 simil50))*(sum(of act36 act37 act38 act39 act40 act41 act42 act43 act44 act45 act46 act47 act48 act49 act50))))/(sqrt((15*(squar36+squar37+squar38+squar39+squar40+squar41+squar42+squar43+squar44+ squar45+squar46+ squar47+squar48+squar49+squar50)-((simil36+simil37+simil38+simil39+simil40+ simil41+simil42+simil43+simil44+simil45+simil46+simil47+simil48+simil49+simil50)**2))*(18.1950))); CORRWIDTH = ((15*(SUM(OF cross51 cross52 cross53 cross54 cross55 cross56 cross57 cross58 cross59 cross60 cross61 cross62 cross63 cross64 cross65)))-((sum(of simil51 simil52 simil53 simil54 simil55 simil56 simil57 simil58 simil59 simil60 simil61 simil62 simil63 simil64 simil65))*(sum(of act51 act52 act53 act54 act55 act56 act57 act58 act59 act60 act61 act62 act63 act64 act65))))/(sqrt((15*(squar51+squar52+squar53+squar54+squar55+squar56+squar57+squar58+squar59+ squar60+squar61+squar62+squar63+squar64+squar65)-((simil51+simil52+simil53+simil54+simil55+simil56+ simil57+simil58+ simil59+ simil60+simil61+simil62+simil63+simil64+simil65)**2))*(18.1950))); *Fisher's r to z'; zCORRHUE =.5*(log(1+CORRHUE)-log(1-CORRHUE)); zCORRTOPO =.5*(log(1+CORRTOPO)-log(1-CORRTOPO)); zCORRVALUE =.5*(log(1+CORRVALUE)-log(1-CORRVALUE)); zCORRWIDTH =.5*(log(1+CORRWIDTH)-log(1-CORRWIDTH)); cards;

175

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

5 9 7 9 9 8 2 8 8 2 7 6 8 4 5 5 6 2 6 8 5 6 7 7 6 7 7 8 8 5 5 6 6 4 6 5 8 8 8 9 5 7 9 8 7 5 2 9 6 2 5 4 7 3 5 5 4 6 7 6 6 6 8 6 7 5 6 7 4 8 5 3 6 2 3 5 1 2 1 2

4 5 7 9 1 8 2 2 2 2 6 7 8 7 2 5 6 6 3 3 6 6 7 6 4 8 7 7 8 7 6 6 6 6 3 4 8 8 6 2 5 7 8 8 2 3 3 6 3 4 4 2 6 4 3 5 3 6 5 2 4 6 7 6 2 5 3 6 3 4 4 2 3 2 3 8 3 1 9 5

5 7 7 1 8 8 8 2 2 8 7 3 7 4 6 3 3 2 5 7 5 4 7 3 6 5 5 2 3 7 4 4 6 4 6 3 4 9 3 8 5 5 8 5 7 2 4 8 4 3 3 5 3 6 5 4 5 4 5 6 4 5 6 5 7 3 5 6 3 7 2 4 4 4 6 1 2 3 5 7

5 5 1 8 8 8 8 2 8 8 3 8 2 4 9 5 8 2 5 9 3 5 6 5 5 4 5 3 4 8 4 4 6 5 7 4 4 7 2 7 3 5 8 6 7 5 4 7 4 2 5 5 5 5 2 4 6 6 3 3 4 6 7 4 7 5 4 7 7 6 5 3 6 3 2 5 9 5 2 2

5 2 7 8 8 8 2 2 2 2 7 8 6 2 2 5 7 8 3 2 5 3 6 4 4 5 8 5 2 4 6 6 6 4 4 6 3 7 3 1 7 5 5 6 3 5 8 3 3 5 5 8 5 3 3 5 4 4 3 3 6 6 4 3 4 7 7 6 4 7 3 2 4 2 3 2 1 5 2 2

5 5 7 7 9 2 2 8 8 8 4 2 4 6 7 2 3 3 5 5 6 6 6 4 5 2 3 2 3 3 6 6 6 3 6 7 7 8 1 7 6 8 8 3 7 4 8 3 4 5 2 5 3 4 6 3 5 4 3 4 5 8 6 3 7 4 7 4 4 7 2 6 2 4 6 2 5 3 9 6

2 6 1 8 9 2 2 8 8 2 3 2 4 7 2 3 7 6 9 1 4 6 7 6 4 5 3 7 8 3 4 4 6 4 6 2 8 8 9 8 3 7 9 8 7 2 3 9 3 1 5 4 7 4 3 4 3 7 7 4 4 7 8 7 6 4 7 7 4 7 4 4 7 4 3 5 3 1 4 1

6 9 1 5 2 2 2 2 2 8 2 7 8 2 8 2 7 8 3 3 5 6 7 5 4 1 7 9 4 3 6 5 6 4 4 7 7 9 8 2 7 5 9 7 3 2 2 8 3 4 3 3 4 2 5 5 2 6 6 3 6 4 6 6 3 3 3 8 2 4 2 2 3 2 2 1 3 3 2 2

7 3 8 5 7 2 8 2 8 2 4 5 6 4 5 3 8 3 7 9 4 5 7 4 5 3 4 3 3 8 4 4 6 4 7 7 2 8 3 8 7 5 9 3 7 3 3 6 3 3 3 4 5 5 3 4 5 4 2 5 5 4 7 2 7 3 5 7 5 3 2 4 2 3 4 2 6 4 2 3

5 6 3 7 9 2 8 8 8 2 8 7 7 4 2 2 5 7 3 2 4 5 5 6 6 4 7 3 6 8 4 4 4 4 7 2 5 5 7 6 3 5 3 7 7 7 4 4 4 4 6 5 5 3 4 6 6 3 6 6 4 5 6 7 6 4 3 4 4 4 6 5 4 2 2 9 6 5 2 1

5 7 9 7 7 8 8 8 2 2 6 4 3 3 3 8 8 3 4 8 6 4 6 6 4 7 4 6 6 3 6 4 6 6 4 8 3 4 6 3 7 5 7 3 2 6 4 6 3 4 4 2 3 3 6 5 3 7 6 3 7 4 4 6 3 3 3 8 7 4 3 2 6 2 3 1 2 4 3 1

9 4 2 8 3 8 8 2 8 8 8 7 7 5 2 7 7 6 3 7 5 5 5 4 5 3 3 3 5 7 6 4 6 4 6 7 3 5 3 7 7 5 6 2 7 2 3 3 3 2 3 3 2 3 5 3 5 4 2 7 6 4 4 3 6 5 5 6 3 4 2 2 2 3 3 4 2 2 6 3

5 5 7 8 7 2 2 8 8 8 3 5 8 5 3 1 5 5 4 9 3 4 4 6 7 6 4 8 7 6 4 4 4 4 6 2 2 2 7 8 5 5 2 6 8 3 3 3 6 4 5 3 4 4 2 2 2 4 5 4 3 2 3 6 7 3 4 5 7 4 4 2 3 4 2 4 1 6 2 1

176

APPENDIX D. SAS SCRIPT: PEARSON’S CORRELATION

17

18

19

20

21

22

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25

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6 5 6 4 3 8 5 2 5 4 5 4 5 3 3 5 8 9 9 6 9 8 8 7 8 5 6 7 8 5 5 7 9 9 9 7 5 4 7 6 3 3 6 6 8 3 8 7 8 4 6 2 4 3 1 8 6 8 7 5

5 3 4 4 7 5 1 5 9 5 6 4 3 2 2 5 9 7 9 1 5 6 1 1 5 5 5 5 7 3 1 9 9 9 1 6 5 7 7 7 5 2 4 4 2 4 5 6 7 6 5 3 2 7 5 7 6 5 8 7

4 4 4 4 4 3 3 5 1 7 2 5 2 5 4 4 5 8 5 4 3 6 1 2 8 5 5 6 5 6 5 5 8 5 7 5 3 4 5 5 3 4 3 2 8 2 8 8 4 6 2 5 4 6 7 6 7 3 3 7

5 4 5 4 3 5 3 7 2 8 5 5 6 5 4 1 5 1 4 9 5 5 5 2 9 4 5 5 4 5 1 1 2 3 7 3 5 3 7 7 5 3 5 3 8 6 4 4 5 8 4 6 5 5 6 5 5 2 3 7

5 3 5 3 5 9 5 4 5 8 6 4 6 3 3 9 5 7 5 3 5 5 8 1 1 6 4 5 5 3 9 9 8 1 2 7 7 3 5 7 6 4 3 4 3 6 6 4 4 4 4 5 4 4 2 5 8 7 3 3

4 5 3 5 5 5 5 2 1 8 3 7 5 2 4 9 8 3 1 8 1 2 1 2 3 5 5 4 3 7 3 6 8 2 4 4 7 4 3 5 2 4 2 3 8 3 3 3 4 6 4 5 2 4 2 2 2 3 5 4

4 4 5 4 4 4 5 9 3 7 4 3 6 5 4 1 7 7 9 9 8 2 5 9 3 4 6 7 7 5 3 9 9 9 1 4 6 3 5 3 4 3 6 6 7 4 3 9 6 2 5 2 2 4 3 8 4 5 7 5

4 4 4 4 7 5 3 5 1 5 3 2 6 4 2 9 9 9 8 1 1 8 9 3 2 6 5 7 7 5 7 8 1 6 1 7 4 5 7 3 2 2 4 5 1 4 8 7 4 2 2 1 5 7 4 3 7 8 3 5

3 5 4 4 3 9 9 8 8 5 4 4 3 4 4 3 5 8 1 8 1 6 1 7 8 5 4 7 4 6 7 1 1 1 3 5 4 4 4 7 3 5 4 4 7 4 5 4 6 6 6 1 5 4 6 2 5 1 8 3

7 5 7 4 3 7 5 8 3 2 3 4 4 4 3 1 5 5 9 8 3 7 2 5 1 4 5 5 7 4 1 7 5 8 7 4 5 7 5 7 4 2 3 5 7 4 7 4 4 4 4 1 2 4 6 2 7 4 5 3

4 4 4 4 4 3 6 6 5 7 6 4 4 4 4 9 4 5 9 1 7 4 4 4 2 5 4 5 7 3 8 4 6 9 1 4 3 5 5 6 3 3 7 4 1 9 4 6 6 4 6 3 8 4 2 7 6 4 4 4

3 5 3 3 4 3 5 4 5 1 4 3 3 3 3 9 5 4 3 9 8 4 4 5 5 7 4 4 5 5 6 1 5 1 8 8 7 7 5 6 2 4 3 2 7 7 5 3 5 6 2 2 3 4 6 7 5 3 4 6

; run; proc PRINT; VAR userid CORRHUE CORRTOPO CORRVALUE CORRWIDTH zCORRHUE zCORRTOPO zCORRVALUE zCORRWIDTH; run; proc MEANS; VAR CORRHUE CORRTOPO CORRVALUE CORRWIDTH zCORRHUE zCORRTOPO zCORRVALUE zCORRWIDTH; run;

7 5 4 5 2 5 4 8 6 5 4 3 3 2 4 1 3 1 9 8 7 7 7 3 9 4 5 4 4 5 9 1 2 1 7 6 4 6 6 7 3 2 4 7 7 4 4 4 5 6 4 2 6 4 4 6 7 7 5 7

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Personal declaration: «I hereby declare that the submitted thesis is the result of my own independent work. All external sources are explicitly acknowledged in the thesis».

Zurich, October 2009 Sara Maggi

Evaluation of 3D Spatializations

Evaluation of 3D Spatializations

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