Statistical Guide 2. Abstract. Both teaching and learning statistics can be an
arduous and painstaking process. In fact, many professors have attempted to ...
Statistical Guide 1
Running head: STATISTICAL GUIDE FOR STUDENTS
Easing Our Pain: A New Approach to Learning, Teaching, and Applying Statistical Selection Skills Jana Hackathorn, Heather Thornton, Rachel Tennial, and LaMarcus Bolton Psychology Department, Saint Louis University 3511 Laclede Avenue, St. Louis, MO 63103-2010 Corresponding author:
[email protected]
Statistical Guide 2 Abstract Both teaching and learning statistics can be an arduous and painstaking process. In fact, many professors have attempted to develop ways of simplifying this task. Helping students focus on choosing the appropriate statistics became more imperative with advances in statistical software that increased the level of sophistication and amount of statistical techniques available. The current paper discusses the need for a cohesive and comprehensive statistical tool for graduate students. Since hierarchically encoded mnemonic devices are incredibly useful in goal related tasks, a poster has been created to be utilized in both teaching and learning statistical technique selection.
Statistical Guide 3 Easing Our Pain: A New Approach to Learning, Teaching, and Applying Statistical Selection Skills Introduction It is no secret that learning, using, and transferring knowledge of statistics can elicit fear and apprehension among both students and teachers. Many students, and arguably teachers, find the information uninteresting and some possibly harbor anxiety regarding their mathematic competence (Ware & Chastain, 1989; Connor, 2003).
Consequently, that anxiety may be
attributed to initial difficulty understanding seemingly uncomplicated statistical concepts, such as negative correlations or weighted means (Morris, Joiner, & Scanlon, 2002). The lack of understanding and anxiety that individuals have when learning, applying, and possibly teaching statistics is unfortunate, as statistics is an important and large component of many disciplines. Moreover, statistical competence is absolutely essential for conducting, reading, and understanding research (Connor, 2003). Therefore, the purpose of this paper is to provide a multi-purpose tool to be utilized in teaching, learning, and applying statistics. One of the fundamental purposes of statistical courses in college is to equip students with the necessary knowledge to choose between statistical approaches that will address future research questions. Statistical options rely not only on the research question, but also on a set of predetermined assumptions about the participants sampled and the measures used.
If
inappropriate statistical methods are chosen to analyze the data collected, the results may be misleading, if not meaningless (Wang & Zhang, 1998). Before the advent of statistical software, understanding how to conduct each statistical option was important as practically every statistical test required hand calculation. The prevalence of advanced statistical software in universities has lessened the need for emphasis on time-consuming hand calculations in the classroom and
Statistical Guide 4 ultimately opened the door to use more sophisticated statistical techniques. This leaves the student with more options than ever before and frees the professor to provide more instruction on selecting appropriate statistical methods to address students’ potential research questions. The Current Approach While, few tools or guides exist on how to effectively transmit statistical knowledge to students, some psychological professionals have attempted to share their anecdotal recommendations. For example, Connor (2003) suggests using activities that involve students’ bodies and the physical space in the classroom to illustrate statistical concepts, as this practice encourages active learning while also maintaining student interest. Still, others suggest that professors should attempt to move away from a strictly computation format to combat students’ reluctance to enroll in statistical classes due to perceived lack of mathematical prowess or experience (Ware & Chastain, 1989). Ware and Chastain (1989) provide evidence that by teaching statistical selection skills through handouts, lectures, and practicing these skills in exams, a teacher can significantly increase students’ comprehension and retention of statistical techniques as compared to computation-only methods. Additionally, they found no differences in the extent to which students with greater or lesser degrees of math competency learned statistical selection skills. These results demonstrate that even students who are not as skilled or confident in their mathematical proficiency can achieve statistical competency (Ware & Chastain, 1989). A New Approach The question then becomes, “How does one effectively teach statistical selection skills?” Although a vast majority of behavior can be learned through observation and even repetition, it may not be the most appropriate learning style for action-oriented tasks, such as choosing
Statistical Guide 5 appropriate statistical methods. Magnello and Spies (1984) suggest teaching various statistical concepts using models that are consistent with students’ learning styles--particularly those that facilitate processing of large amounts of information.
Accordingly, the authors suggest
implementing mnemonics, such as charts, which organize statistical tests into concepts involving a level of measurement and function (Magnello & Spies, 1984). Mnemonics can be useful because individuals tend to employ unique strategies to learn and organize information and utilizing strategies that mimic one’s intentions increases learning. Thus, linking one’s goals to relevant functions is often an effective strategy (Hard, Loranzo, & Tversky, 2006). A study conducted by Wender and Muehlboeck (2003), provided evidence of the efficiency and effectiveness of teaching causal and functional statistical relationships using animated graphics as a type of mnemonic device.
The researchers utilized the natural hierarchical flow of
information and paired it with a graphic representation of the actual end goal to achieve statistical competence. A hierarchical mnemonic device involves linking actions and concepts to their underlying goals, breaking the information down into manageable units, and then organizing those smaller units into parts that correspond with a set of goals and sub-goals (Levin & Levin, 1990). Benefits of hierarchical encoding include increased memory for tasks and actions because units are chunked based on their causal and functional relationships. Moreover, hierarchical encoding promotes learning because it generates a tangible representation that students can recall when necessary. Finally, hierarchical representations are easier to modify than many other types of mnemonic devices (Hard, et al., 2006). Presumably, if students encode information in a hierarchical manner, they are more likely to successfully utilize that hierarchy to complete the task again later. Consequently, this
Statistical Guide 6 particular mnemonic device may prove especially effective for teaching and learning statistical selection skills because the organization of the structure provides a tangible action plan for execution of various statistical analyses. Developing a New Instrument The current paper provides a hierarchically based illustration, designed as both a teaching aid for professors of introductory statistics courses and a reusable guide for anyone who needs to use or understand statistical analyses. The sole purpose of this tool is to aid teachers in educating their students, as well as increase students’ memory and understanding of appropriate statistical selection. Furthermore, as the authors are current graduate students, we understand the need for a cohesive tool to help students discern which type of statistical analysis to use to answer questions or gain information about their data (e.g. testing differences in means or relationships between variables). The current guide can also be used to aid students in determining which analysis procedures are appropriate (e.g. Two-Way MANOVA). This dilemma is especially salient for first year graduate students, who not only have little practice with these skills, but also lack the confidence to use them. In light of these problems and concerns, the authors decided that a comprehensive introductory statistics guide for graduate students is a necessary component for success. It is the authors’ hope that this tool will enable all graduate students to gain more confidence in their statistical selection skills, and allow for more hands-on and self-directed learning. It is important to note that the use of a hierarchical chart is not a new concept to the world of statistics. In fact, almost every statistical textbook provides some sort of hierarchical flow chart to help students select the appropriate statistical technique. However, this statistical tool
Statistical Guide 7 was created to address what we feel are three shortcomings of current statistical selection tools. First, as far as we know, a detailed all-inclusive flowchart does not currently exist in the field. Students must search through several chapters or even textbooks to discover a chart that includes the type of statistics they desire. Not only is comprehensiveness an issue, but there is also an underlying assumption that students know what they want. A second shortcoming of other tools is that most fail to link both overarching and specific research questions to individual statistical techniques. Most flowcharts simply offer technical assumptions for statistical selection without built-in explanations, again assuming that the student knows what research question each method addresses. Third, current tools provide overly technical suggestions for statistical selection. Most authors choose technical jargon over language for the lay person, complicating the very tools that were meant to ease the burden. Since our integrated hierarchical model uses simple language to guide a student step by step through the selection process, the aforementioned shortcomings are resolved. Navigating the Instrument The actual statistical tool is a large conference poster, available for viewing on the bottom floor of Saint Louis University’s psychology department (see Figure 5). However, due to the size constraints of this paper, the poster has been divided into multiple sections. This division allows the reader to not only examine each specific domain, but also own a convenient and portable format. The first statistical domain (see Figure 1a and Figure 1b) is devoted to the basic concept of describing data and the sample of individuals from which you collected the data. In this section the viewer will encounter representative questions to be used as guides to aid in understanding the makeup of the dataset collected (Figure 1a). As visual representations are also
Statistical Guide 8 important, this section includes guides for determining how to best illustrate and represent the information gathered (Figure 1b). The second domain (see Figure 2a and Figure 2b) is dedicated to understanding the relationships between variables, using correlations and regressions. Most research is concerned with discovering or understanding the links between different variables of interest (Figure 2a). Figure 2b aids in determining which statistical tests will allow the researcher, to determine if a relationship exists, and the nature, function, or condition of that relationship. The third domain (see Figure 3a and Figure 3b) guides the researcher through both parametric and non-parametric tests necessary for drawing inferences about the differences between and within groups for desired variables. If one is examining the differences between multiple groups, Figure 3a offers a multitude of statistical options. However, if one has tested the same group multiple times, Figure 3b offers other statistical solutions. Finally, the fourth domain (see Figure 4a and Figure 4b), focusing on structural equation modeling, includes more sophisticated analyses that provide the researcher with an integrated approach to testing pre-existing theories and established models with multiple variables in the scientific literature. Figure 4a presents approaches for testing models that contain either measurable or abstract variables. Conversely, Figure 4b presents ways to test models that contain both of the aforementioned variable types. Users of the tool should start with a particular research objective as indicated by the large ovals at the top of each of the respected hierarchical charts. Upon choosing a path, users should follow the guided prompts and proceed through each of the labeled “bubbles” or steps. Each hierarchical chain ends with the recommended statistical test that will appropriately answer the questions posed.
Statistical Guide 9 Conclusion We believe the graduate student perspective we bring to teaching, learning, and applying statistical techniques allows us to address shortcomings of prior approaches to statistical selection. Thus, an instrument was created to introduce overarching linkages between statistical techniques, aiding anyone who may lack sufficient statistical selection skills. Although a validation statistic was not computed (e.g., content validity index; Lynn, 1986), the tool was evaluated by multiple subject matter experts to assess content validity. Subsequently, the experts determined that the tool was indeed content valid and accurate. The poster, currently hanging in the basement of Saint Louis University’s psychology department, has already become a staple for several graduate students in determining the correct statistical analyses to use in their research projects. Additionally, some graduate students who are teaching research methods and statistics classes have asked for smaller copies to be used as a handout or as a study guide for their students. Lastly, there has been an expressed interest in other departments, disciplines, and even schools regarding copies of the poster to hang on their walls. In the immediate future, the tool will be presented to other universities as a supplemental teaching instrument. However, it is also a goal to share the tool with practitioners, such as those within commercial institutions and marketing firms.
Statistical Guide 10 References Connor, J. M. (2003). Making statistics come alive: Using space and students’ bodies to illustrate statistical concepts. Teaching of Psychology, 30(2), 131-153. Dunn, P. K. (2003). Understanding statistics using computer demonstrations. Journal of Computers in Mathematics and Science Teaching, 22(3), 261-281. Hard, B. M., Loranzo, S. C., & Tversky, B. (2006). Hierarchical encoding of behavior: Translating perception into action. Journal of Experimental Psychology, 135(4), 588-608. Levin, M. E., & Levin, J. R. (1990). Scientific mnemonomies: Methods for maximizing more than memory. American Educational Research Journal, 27, 301-321. Lynn, M. R. (1986). Determination and quantification of content validity. Nursing Research, 35, 382-385. Magnello, M. E., & Spies, C. J. (1984). Using organization concepts to facilitate the teaching of statistics. Teaching of Psychology, 11, 220-223. Morris, E. J., Joiner, R., & Scanlon, E. (2002). The contribution of computer-based activities to understanding statistics. Journal of Computer-Assisted Learning, 18, 114-124. Varnhagen, C. K., Drake, S. M., & Finley, G. (1997). Teaching statistics with the Internet. Teaching of Psychology, 24(4), 275-278. Wang, Q., & Zhang, B. (1998). Research design and statistical methods in Chinese medical journals. Journal of the American Medical Association, 280, 283-285. Ware, M. E., & Chastain, J. D. (1989). Computer-assisted statistical analysis: A teaching innovation? Teaching of Psychology, 16, 222-227. Ware, M. E., & Chastain, J. D. (1991). Developing selection skills in introductory
Statistical Guide 11 statistics. Teaching of Psychology, 18(4), 219-222. Wender, K. F., & Muehlboeck, J. S. (2003). Animated diagrams in teaching statistics. Behavior Research Methods, Instruments, and Computers, 35(2), 255-258.
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