Utilizing mixed methods in teaching environments to reduce statistics ...

Copyright © eContent Management Pty Ltd. International Journal of Multiple Research Approaches (2010) 4: 28–39.

Utilizing mixed methods in teaching environments to reduce statistics anxiety ANTHONY J ONWUEGBUZIE Sam Houston State University, Huntsville, TX, USA

NANCY L LEECH University of Colorado at Denver and Health Sciences Center, Denver, CO, USA

MARI MURTONEN University of Turku, Finland

JUHANI TÄHTINEN University of Turku, Finland

ABSTRACT Many students deem statistics courses to be the most difficult in their programs of study, providing mostly negative experiences characterized by high levels of anxiety. Recent research on statistics anxiety has identified several teacher characteristics that help reduce students’ statistics anxiety levels. However, little attention has been placed on the role that the research-based curriculum plays in reducing anxiety levels. Thus, the present paper introduces a curricular framework for alleviating students’ negative feelings towards statistics. Building on the works of Onwuegbuzie and Leech (2004, 2005a), we contend that the best way to accomplish this is by eliminating statistics courses from curricula and replacing these with research methodology courses at different levels that simultaneously teach students both quantitative and qualitative techniques within a mixed methodological framework. We illustrate how quantitative and qualitative research courses can be re-designed as courses in exploratory and confirmatory techniques that teach quantitative and qualitative methodologies within each course, either simultaneously or sequentially. Keywords: mixed methods, statistics, statistics anxiety, qualitative research, student attitudes, methods teaching

UTILIZING MIXED METHODS IN TEACHING ENVIRONMENTS TO REDUCE STATISTICS ANXIETY

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n important goal of many teacher education programs is to graduate teachers who have the necessary skills to be both consumers and producers of educational research. Being a consumer includes 28

the ability to read, to understand, to interpret, to synthesize, and to utilize published research. Being a producer includes the ability to design and to implement or replicate research studies. The ability to be both a consumer and producer of educational research is an essential part of graduate students’ skill sets (Ravid & Leon, 1995). In addition to these, it

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is important for a teacher to model a research attitude for pupils and thus help them to develop a critical attitude toward knowledge. Consequently, many education programs worldwide, including teacher education programs, require their students to enroll in at least one quantitative-based research methodology course (Mundfrom, Shaw, Thomas, Young, & Moore, 2003). Unfortunately, many students find these courses to be the most difficult in their programs of study, and thus typically have negative experiences in these courses (Murtonen & Lehtinen, 2003). Moreover, the vast majority of students report experiencing high levels of anxiety (Onwuegbuzie & Wilson, 2003). This form of anxiety is commonly referred to as statistics anxiety. Onwuegbuzie, DaRos, and Ryan (1997) defined statistics anxiety as an anxiety that comes to the fore when a student encounters statistics in any form and at any level. More specifically, Zeidner (1990) defined statistics anxiety more specifically as: a performance characterized by extensive worry, intrusive thoughts, mental disorganization, tension, and physiological arousal…when exposed to statistics content, problems, instructional situations, or evaluative contexts, and is commonly claimed to debilitate performance in a wide variety of academic situations by interfering with the manipulation of statistics data and solution of statistics problems. (p. 319) Numerous researchers have reported a negative relationship between statistics anxiety and course performance (Elmore, Lewis, & Bay, 1993; Lalonde & Gardner, 1993; Onwuegbuzie & Seaman, 1995; Zanakis & Valenza, 1997; Zeidner, 1991). More specifically, statistics anxiety has been found to be the best predictor of achievement in both research methodology courses (Onwuegbuzie, Slate, Paterson, Watson, & Schwartz, 2000) and statistics courses (Fitzgerald, Jurs, & Hudson, 1996). Even more notably, a causal link between statistics anxiety and course achievement has been established. Specifically, Onwuegbuzie and Seaman (1995) documented a statistically

significant interaction, in which graduate students with high levels of statistics test anxiety who were randomly assigned to a statistics examination that was administered under timed conditions tended to have lower levels of performance than did their high-anxious counterparts who were administered the same test under untimed conditions. In a follow-up experimental investigation among female college students, Onwuegbuzie (1995) reported a statistically significant interaction between statistics test anxiety and type of examination (i.e., timed vs. untimed), with highanxious female students showing a greater decrement in performance than did low-anxious female students in the untimed examination condition. Both sets of researchers interpreted these results within conceptual frameworks developed by Hill (1984) and Wine (1980), who suggested that differences between low- and high-anxious students in evaluative situations are due to differences in attentional foci and motivational dispositions, respectively. Further, using qualitative techniques, Onwuegbuzie (1997) documented that statistics anxiety primarily affects students’ ability fully to understand research articles, as well as to analyze and to interpret statistical data. In addition to being causally linked to course performance, statistics anxiety has been found to moderate the relationship between course achievement and the following variables: research anxiety, study habits, course load, and the number of statistics courses taken (Onwuegbuzie, 2003a). Because statistics anxiety plays a central role in quantitative-based courses, several researchers have examined factors that alleviate or reduce students’ levels of anxiety. Indeed, a growing body of evidence supports the possibility that a professor of educational research may have some power to at least reduce levels of anxiety inherent in the study of educational research methodology and statistics. Strategies that students report help reduce their statistics anxiety levels include being knowledgeable about the nature and manifestations of statistics anxiety in students, encouraging and reassuring students that they can do the work, displaying

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positive attitudes, addressing the anxiety, improving students’ perceived worth of statistics, using humor, incorporating humorous cartoon examples, teaching gimmicks, helping students to understand the course objectives, administering open book/open note examination, administering untimed examinations, using performance assessments (e.g., assigning projects, tasks, assignments, or investigations), exhibiting empathy for students, being flexible, being patient and understanding, having fair and consistent grading practices, being knowledgeable about the topic, having an effective teaching style, asking students to write journals, allowing students to share their levels of apprehension and anxiety about statistics, providing a lecture concerning ways of coping with their anxieties, clearly explaining the subject material, providing sufficient examples and sample problems, providing extensive feedback (especially via one-on-one, face-to-face discussions), using current news stories and similar sources to introduce and to explain basic statistical concepts and methodological issues in research, applying statistics to real-world situations, and promoting cooperative learning in and outside the classroom (Dilevko, 2000; Dillon, 1982; Onwuegbuzie, 2000; Schacht & Stewart, 1990, 1991; Sgoutas-Emch & Johnson, 1998; Wilson, 1996, 1999a, 1999b, 2000; Wilson & Onwuegbuzie, 2003). This list of strategies for reducing statistics anxiety levels primarily involves behaviors and teaching styles that statistics instructors might consider adopting. However, little attention has been placed on the role that the research-based curriculum plays in reducing anxiety levels. Thus, the present paper introduces a curricular framework for alleviating students’ negative feelings towards statistics. This framework is based on the premise that de-emphasizing statistics reduces anxiety levels. Building on the works of Onwuegbuzie and Leech (2004, 2005a, 2009) we contend that the best way to accomplish this is by eliminating statistics courses from curricula and replacing these with research methodology courses at different levels that simultaneously teach students both quantitative and qualitative techniques 30

within a mixed methodological framework. We illustrate how quantitative and qualitative research courses can be re-designed as courses in exploratory and confirmatory techniques that teach quantitative and qualitative methodologies within each course, either simultaneously or sequentially.

REDESIGNING QUANTITATIVE-BASED RESEARCH METHODOLOGY COURSES:

IMPLEMENTING A MIXED METHODS CURRICULUM

Current state of affairs in quantitativebased research methodology courses As noted by Onwuegbuzie and Leech (2005a, 2005b), all introductory research methodology textbooks are written as if there is a one-to-one correspondence between research approach (i.e., quantitative vs. qualitative) and data analysis technique. Specifically, statistical analyses are linked exclusively with quantitative research, whereas qualitative analyses (e.g., thematic analyses) are associated exclusively with qualitative research. Thus, research methodology textbooks perpetuate the myth that statistics only should be used with quantitative research and not with qualitative research. The trend in introductory research methodology textbooks also is reflected in quantitative-based research methodology courses. In particular, in statistics courses, only statistical techniques are taught – comprising either descriptive statistical procedures or inferential statistical procedures. Yet, the use of statistics rarely is sufficient to address completely a quantitative-based research question. For example, in the medical field, in which the socalled ‘Gold Standard’ is most commonly applied (National Research Council, 2002), a question that often is of interest is of the following form: ‘What is the effect of Drug X on Y?’ Such a question routinely is addressed via the use of experimental research designs, in which participants are randomized either to the treatment group (i.e., wherein Drug X is administered) or the control group (i.e., wherein either a placebo, competing drug, or different dose level of Drug X is administered). Alternatively, a

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cross-over (experimental) research design could be employed, in which each participant receives both the treatment and control conditions, with a washout period in between. Whichever type of experimental design is implemented, at the end of a specified time period, the treatment and control groups are compared using a statistical analysis that represents a member of the general lineal model (GLM) family (e.g., t-test, analysis of variance, multiple analysis of variance). Regardless of the level of complexity of the statistical analysis used, we believe that such a research question can never be fully addressed without complementing the statistical data analysis with some form of analysis of qualitative data. In this particular example, knowledge that Drug X leads to a cure rate that is both statistically and practically significantly higher than the drugs used in the control group condition(s) is not sufficient for the researcher(s) to declare that Drug X is relatively effective on Y. In fact, it would be inadvisable to make such a conclusion without any side effect information, which represents qualitative data. For example, if Drug X is found to increase substantially the cure rate of Y, yet the side effects of using this drug can be severe, then any conclusion that Drug X is effective would have to be tempered. Consequently, a qualitative analysis of the side effect data yields information that is vital for addressing the research question. Conveniently, researchers have an array of qualitative data analysis techniques from which to choose (Leech & Onwuegbuzie, 2005a, 2005b). The example above represents just one way that qualitative data can be used to complement a statistical analysis. Using the framework of Onwuegbuzie and Leech (2004), we describe in the next section other ways that qualitative data analyses can help researchers to address quantitative-based research questions in a more comprehensive manner. The role of qualitative data in statistical analyses Even though researchers with quantitative data are more apt to use statistical analyses and with

qualitative data are more likely to utilize qualitative data analyses, both quantitative and qualitative data analysis techniques can be used side-by-side to enhance the interpretation of significant findings in educational research (Onwuegbuzie & Leech, 2004). Onwuegbuzie and Leech (2004) conceptualized that qualitative data analyses can be used in a parallel, concurrent, or sequential manner in order to shed more light on significant findings emerging from statistical analyses. Using qualitative data in this way yields a parallel mixed analysis, concurrent mixed analysis, or sequential mixed analysis, respectively. A parallel mixed analysis can occur under the following three conditions: (a) both quantitative and qualitative data analyses should occur separately; (b) neither type of analysis builds on or interacts with the other during the data analysis stage; and (c) the findings from each type of analysis are neither compared nor consolidated until both sets of data analyses have been completed. Of the three mixed analysis techniques, parallel mixed analyses involve the least amount of mixing because mixing does not occur until the data interpretation stage of the research process, if at all. Notwithstanding, parallel mixed analyses can still be utilized to enhance the interpretation of statistical data (Onwuegbuzie & Leech, 2004). For instance, interpretations of qualitative data extracted from one sample might be combined with interpretations from statistical data obtained from another sample to yield what Tashakkori and Teddlie (2003) refer to as a ‘metainference’ (p. 686), in which both sets of inferences are integrated into a coherent whole – hence enhancing the significance of statistical findings. A concurrent mixed analysis involves the analysis of quantitative and qualitative data types within the same analytical framework. Moreover, in concurrent mixed analyses, quantitative and qualitative data are collected at approximately the same point in time, and the data analysis usually does not occur until all the data (i.e., both quantitative and qualitative data) have been collected. However, unlike the case for parallel mixed analyses, the mixing or integration typically takes

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place at the data analysis stage. Questionnaires that extract both quantitative and qualitative data lend themselves to concurrent mixed analyses. For example, let us suppose that researchers were interested in examining the relationship between statistics anxiety and performance in a statistics course. These investigators could administer a Likert-format scale that has been found consistently to possess good psychometric properties, such as the Statistics Anxiety Rating Scale (STARS; Cruise, Cash, & Bolton, 1985; Cruise & Wilkins, 1980). Then, the researchers could correlate the scores from the STARS with a set of statistics achievement scores. A correlation that was both statistically and practically significant would suggest an important relationship between these two variables; however, because of the correlational design used, causal statements should not be made. However, the meaningfulness of this relationship could be enhanced by including one or more open-ended items asking respondents to describe the role that anxiety plays in statistics courses. The extent to which respondents implicate anxiety as adversely affecting their levels of performance would provide the researchers with more justification to make causal statements. Thus, the inclusion of qualitative data analyses would enable students not only to answer questions of who, where, how many, how much, and what is the relationship between specific variables; students also would be able to address why and how questions. Concurrent mixed analyses also can be employed in quantitative studies by qualitizing data, which is a process by which quantitative data are transformed into data that can be analyzed qualitatively (Tashakkori & Teddlie, 1998). One way of qualitizing data is via narrative profile formation (i.e., modal profiles, average profiles, holistic profiles, comparative profiles, normative profiles), wherein narrative descriptions are constructed from statistical data. As noted by Tashakkori and Teddlie (1998), in sequential mixed analyses, ‘multiple approaches to data collection, analysis, and inference are 32

employed in a sequence of phases’ (pp. 149–150). Here, the data analysis always begins before all the data are collected. When the qualitative data analysis stage follows the quantitative data analysis stage, this is called a sequential quantitative– qualitative analysis (Onwuegbuzie & Teddlie, 2003). This involves ‘forming groups of peoples/ settings on the initial basis of [quantitative] data and then comparing the groups on [qualitative] data (subsequently collected or available)’ (Tashakkori & Teddlie, 1998:135). Sequential quantitative–qualitative analysis techniques that can enhance statistical results include those identified by Onwuegbuzie and Teddlie (2003): (a) qualitative contrasting case analysis, (b) qualitative residual analysis, (c) qualitative follow-up interaction analyses, and (d) qualitative internal replication analysis. Qualitative contrasting analysis involves first using descriptive (i.e., non-inferential) statistical techniques (e.g., total, mean, z-score) on some construct (e.g., statistics anxiety), and then identifying a proportion (e.g., 30%) or a specific number of those who obtained the highest and lowest scores on the numerical measure. In the second phase, new qualitative data (e.g., interviews, focus groups, observations) are collected on the highest- and lowest-scoring groups, followed by a qualitative analysis (e.g., method of constant comparison) of the newly collected data, in an attempt to determine why the two groups differed on the quantitative measure. Qualitative residual analysis involves conducting a GLM analysis (e.g., multiple regression, logistic regression), followed by a residual analysis on the selected model in an attempt to identify any outliers (i.e., participants who do not fit the model). In the second phase, new qualitative data are collected on participants who represent the outlying cases, followed by a qualitative analysis (e.g., domain analysis) of the newly collected data, in an attempt to determine why these participants did not fit the chosen model. Qualitative follow-up interaction analyses involve using qualitative data analysis techniques

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to investigate further statistically significant interactions that emerge from GLM analyses. For example, when Onwuegbuzie and Seaman (1995) found a statistically significant interaction between timed examination condition and levels of statistics anxiety, as described earlier, the significance could have been enhanced by interviewing one or more participants who represented each of the four combinations of students (i.e., high-anxious students in the timed condition, high-anxious students in the untimed condition, low-anxious students in the timed condition, and low-anxious students in the untimed condition) to determine the role that anxiety played in the examination process. Qualitative internal replication analyses involve undertaking a GLM analysis (e.g., multiple regression), followed by an internal replication analysis on the selected model (e.g., jackknife analysis, cross-validation analysis) in order to determine internal replication outliers (i.e., cases who unduly affect the internal replication analysis). In the second phase, new qualitative data are collected on participants who have been identified as outliers, followed by a qualitative analysis (e.g., method of constant comparison) of the newly collected data, in order to determine why they did not fit the chosen model. The role of statistics in qualitative analyses In the previous section, we demonstrated how quantitative data analysis can be enhanced by including quantitative data analysis. In the same vein, qualitative data analysis and interpretation can be improved by including statistical analysis. As conceptualized by Onwuegbuzie and Leech (2004), statistical analyses can enhance qualitative data analyses in a parallel, concurrent, or sequential manner, again, yielding parallel mixed analyses, concurrent mixed analyses, and sequential mixed analyses, respectively. As is the case for parallel mixed analyses in quantitative studies, parallel mixed analysis in qualitative research involves mixing the qualitative and quantitative data at the interpretation stage of the

research process. However, in the latter case, the qualitative component is given priority, whereas in the former case, the quantitative component of the study is given the most weight. As previously stated, concurrent mixed analyses involve the analysis of quantitative and qualitative data types within the same analytical framework, with integration usually occurring at the data analysis stage. The most frequent way of supplementing qualitative analysis with a quantitative analysis is by quantitizing data. Quantitizing involves transforming qualitative data to a numerical form (Tashakkori & Teddlie, 1998). Alternatively stated, when researchers quantitize data, “qualitative ‘themes’ are numerically represented, in scores, scales, or clusters, in order more fully to describe and/or interpret a target phenomenon” (Sandelowski, 2001:231). Quantitizing often involves reporting effect sizes associated with qualitative observations (Onwuegbuzie, 2003b; Sandelowski & Barroso, 2003), which can range from manifest effect sizes (i.e., counting qualitative data in order to determine the prevalence rates of observations, words, or themes) to latent effect sizes (i.e., quantifying non-observable content, e.g, factor-analyzing emergent themes; cf. Onwuegbuzie, 2003b). For instance, Sandelowski and Barroso (2003) showed how effect sizes can be used to conduct metasummaries of qualitative findings. These researchers defined a qualitative metasummary as ‘a form of systematic review or integration of qualitative findings in a target domain that are themselves topical or thematic summaries or surveys of data’ (p. 227). They conducted a qualitative metasummary of 45 published and unpublished reports of qualitative studies of HIV-positive women with results on motherhood, which led to 800 findings being extracted, which were reduced to 93 abstracted findings, from which manifest effect sizes were calculated. Sandelowski and Barroso (2003) found that five results had effect sizes ranging from 25–60%, with both published and unpublished articles contributing approximately equally to the strength of these

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findings. A total of 73 findings had effect sizes that were < 9%, with 47 of them having effect sizes of only 2%. (Discussion of effect sizes in qualitative research, see Onwuegbuzie, 2003b; Onwuegbuzie & Teddlie, 2003; Sandelowski & Barroso, 2003.) In sequential qualitative–quantitative analysis, an initial qualitative data analysis leads to groups of individuals being identified who are similar in some way to each other. These identified groups are then compared to each other using either existing quantitative data, or quantitative data that are collected after the initial qualitative data analysis (Onwuegbuzie & Teddlie, 2003). Onwuegbuzie and Teddlie (2003) have identified the following types of sequential qualitative–quantitative analyses: (a) quantitative extreme case analysis and (b) quantitative negative case analysis. Quantitative extreme case analysis involves first conducting a qualitative data analysis, followed by a legitimation analysis (i.e., validity checks), in order to determine the extreme cases. In the second stage, new quantitative data are collected on all cases, followed by a quantitative analysis (e.g., t-test) of the newly collected quantitative data, wherein the extreme and non-extreme cases are compared, in an attempt to determine why the former cases were so extreme in the first stage. Quantitative negative case analysis involves undertaking a qualitative data analysis, followed by a legitimation analysis, in order to identify negative cases (i.e., participants who do not fit the interpretation or initial theory). In the second stage, new quantitative data are collected on all cases, followed by a quantitative analysis (e.g., t-test) of the newly collected data, in which the negative and non-negative cases are compared, in an attempt to determine why the former did not fit the model in the first phase. Redesigning statistics courses Combining quantitative and qualitative data analyses within the same framework can enhance researchers’ interpretations of data. Such combining of procedures is known as mixed methods data analyses (Onwuegbuzie & Teddlie, 2003) and automatically turns a study into a mixed methods 34

investigation. Mixed methods data analyses allow researchers to utilize qualitative data analyses to inform statistical analyses and, conversely, allow statistical analyses to inform the qualitative data analyses. Therefore, instead of statistics courses only teaching students how to conduct statistical analyses, these courses also should instruct students how to conduct qualitative data analyses. Moreover, instructors of statistics courses should show learners how to use qualitative data analyses to complement statistical analyses. By emphasizing the importance of qualitative analysis in quantitative researchers, at the same time, statistics instructors will help to de-emphasize statistics. Further, as noted by Onwuegbuzie and Leech (2004, 2009), virtually all research methodology textbook authors present their discussions of statistical analyses in separate chapters from their discussions of research design and other stages of the research process. Consequently, in these statistical analysis chapters, authors tend to make little or no reference to research questions, giving the impression that statistical analyses occur in a vacuum. Indeed, until now, statistics has been taught as a series of routine steps, rather than as a holistic, reflective, and integrative process (Onwuegbuzie & Daniel, 2003). Moreover, statistics instructors tend to teach statistics using a bottom-up approach. As such, students who succeed in statistics classes know how to conduct an array of descriptive and inferential statistical analyses but do not know when to conduct these analyses (Onwuegbuzie & Leech, 2009). That is, given a research question, even students who have been exposed to several statistics courses are unable to select reliably the most appropriate statistical analysis. In other words, even the best-trained students find it difficult to apply their statistical knowledge to real-life contexts. With this mind, we recommend that statistics courses be redesigned such that they are taught using a top-down approach. In particular, students should be taught how to link data analyses (i.e., statistical and qualitative) to research questions. Onwuegbuzie and Leech’s (2009) framework could play a useful role here. These authors provided a

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framework for linking research questions to mixed methods data analysis techniques. Specifically, they sub-divided quantitative and qualitative research questions into descriptive, correlation, and comparative research questions. They also identified the types of statistical and qualitative data analysis techniques that lend themselves best to each of these three classes of research questions. Onwuegbuzie and Leech also introduced the concept of mixed methods research questions, which they defined as questions that embed both a quantitative research question and a qualitative research question within the same question. That is, mixed methods research questions combine or mix both the quantitative and qualitative research questions. Moreover, a mixed methods research question necessitates that both quantitative data and qualitative data be collected and analyzed either concurrently, sequentially, or iteratively before the question is addressed. (pp. 14–15) We believe that when students are presented with such a framework before they are presented with the array of statistical analysis techniques, they would be in a better position to link these procedures to future research questions. Such a framework also would keep students cognizant of the important role that qualitative data analysis can play during the statistical analysis process. Indeed, we argue that by using this framework, students would come to view statistics as merely a tool, alongside qualitative data analysis, for addressing an array of research questions. As such, statistics would be de-emphasized. By de-emphasizing statistics, we predict that students’ levels of statistics anxiety would be reduced because a statistical analysis would represent only one step in the data analysis process in particular and in the research process in general. Nevertheless, instructors who use such frameworks should continue to monitor the statistics anxiety levels of their students. Taking the ‘Q’ out of research As can be seen, there is not a one-to-one correspondence between research question and class

of data analysis (i.e., statistical vs. qualitative data analysis). That is, a question that appears to be quantitative-based (e.g., ‘What is the effect of….?’) is not limited only to statistical techniques; such questions often can be addressed also by using qualitative data analysis procedures. Therefore, we believe that the role of statistics in quantitative-based research should be deemphasized to accommodate qualitative research. (Also, we believe that role of qualitative-based research should be de-emphasized to accommodate quantitative research.) This is consistent with the position of Onwuegbuzie and Leech (2005a). Although we have provided a framework for redesigning statistics courses, in time, we would like to see the concept of ‘statistics’ de-emphasized even further. Thus, we recommend that statistics courses be eliminated from students’ programs of study. (We also advocate the elimination of qualitative research courses.) In their place, we call for a series of research design courses to be taught. More specifically, because both statistical analyses and qualitative data analyses can be used to explore and to confirm phenomena (Onwuegbuzie & Leech, 2005a), we propose that statistics courses and qualitative research courses be replaced by courses in exploratory research techniques and confirmatory research techniques. In the future, we would like to see the development of as many of the following research-based courses, and their variants, as possible: (a) Introduction to exploratory research methods; (b) Advanced exploratory research methods; (c) Introduction to confirmatory research methods; (d) Advanced confirmatory research methods; (e) Introduction to interactive research methods; and (f ) Advanced interactive research methods. Here, the exploratory courses would focus on quantitative analyses and qualitative analyses that are considered to be exploratory in nature, with the introductory exploratory course focusing on basic exploratory statistical

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(e.g., descriptive statistics) and qualitative (e.g., coding, keywords-in-context, content analyses, method of constant comparison) analyses, and the advanced exploratory course focusing on more advanced exploratory statistical (e.g., factor analysis, cluster analysis) and qualitative (e.g., domain analysis, taxonomic analysis, componential analysis) analyses. In contrast, the confirmatory courses would center on quantitative analyses and qualitative analyses that are considered to be confirmatory in nature, with the introductory confirmatory course focusing on basic confirmatory statistical (e.g., univariate inferential statistics) and qualitative (e.g., axial coding) analyses, and the advanced confirmatory course focusing on more advanced confirmatory statistical (e.g., multivariate inferential statistics) and qualitative (e.g., selective coding, qualitative comparative analysis, semantic network analysis) analyses. Finally, interactive research methods courses would focus on data-analysis frameworks in which there is interplay between exploratory and confirmatory techniques, with the introductory interactive course focusing on basic interactive analyses (e.g., qualitative contrasting case analysis, qualitative residual analysis, quantitative extreme case analysis), and the advanced interactive course focusing on advanced interactive analyses (e.g., qualitative follow-up interaction analyses, qualitative internal replication analysis, quantitative negative case analysis). One aspect that would remain consistent through all of these courses is that students would be taught how to implement all the following 11 stages of the mixed methods research process (Onwuegbuzie & Leech, 2009): (1) Determining the goal of the study; (2) Formulating the research objective(s); (3) Determining the research purpose; (4) Determining the research question(s); (5) Selecting the mixed methods research design; (6) Collecting the data; (7) Analyzing the data; (8) Interpreting the data; 36

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Validating/legitimating the data and data interpretations; (10) Writing the final report; and (11) Reformulating the research question(s). As such, students would always be made cognizant of the role that the data-analyses in general and statistical analyses in particular play in any given research process. Thus, hopefully, students would change from viewing research-based classes as merely comprising statistics courses to viewing these courses as representing methods courses that teach students how to solve educational and psychological problems. This, in turn, should help to reduce levels of statistics anxiety.

SUMMARY AND CONCLUSIONS Wilson (2001) noted, ‘No discussion of the context of teaching statistics would be complete without acknowledgement of the anxiety that students bring to class’ (p. 2). Recognizing the debilitative nature of statistics anxiety, the present article introduced a curricular framework for alleviating students’ negative feelings towards statistics. This framework is based on the premise that de-emphasizing statistics reduces anxiety levels. Building on the works of Onwuegbuzie and Leech (2004, 2005a, 2009), we provided a framework for re-designing statistics courses by (a) complementing statistical analyses with qualitative data analyses and (b) putting statistics in a more appropriate research context. Moreover, we contend that the best way to reduce the debilitative effect of statistics anxiety on students’ ability to design and implement research is by eliminating statistics courses and qualitative research courses from curricula and replacing these with research methodology courses at different levels that simultaneously teach students both quantitative and qualitative techniques within a mixed-methods framework. We illustrated how quantitative and qualitative research courses can be re-designed as courses in exploratory and confirmatory techniques that teach quantitative and qualitative methodologies

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within each course, either simultaneously or sequentially. We believe that such a re-framing of courses would train students to be researchers who are flexible in their investigative techniques, who are able to combine empirical precision with descriptive precision, who are able to integrate the macro and micro levels of a research issue (Onwuegbuzie & Leech, 2005c), and who are able to collect multiple data using different techniques in such a way that the resulting mixture or combination is likely to result in ‘complementary strengths and nonoverlapping weaknesses’ (Johnson & Turner, 2003:299). We recognize that relatively few faculty have the expertise to teach such mixed methods courses because in their research trainings, they specialized either as a quantitative or a qualitative research methodologist. Thus, we recommend that quantitative and qualitative research methodologist teamteach these exploratory/confirmatory research courses. As contended by Onwuegbuzie and Leech (2005c), the prospect of qualitative and quantitative research methodology faculty team-teaching a course is extremely exciting. Moreover, such courses would send a strong message to policy makers and stakeholders that researchers of all orientations are united along a common goal: to improve the educational experiences of all learners. Moreover, such courses, in time, should compel policy makers to reconsider the present definition of the gold standard (National Research Council, 2002). Rather than experimental research and statistical methods being given preferential status, the gold standard would be associated with studies that exhibit what Onwuegbuzie and Leech (2005d) refer to as ‘interpretive consistency’, which represents ‘the consistency between the interpretations made by the researcher(s) and the procedures/design of the study (e.g., purpose of study, research question, sample size, sampling scheme, research design, data analysis techniques)’ (pp. 7–8). Further, students enrolled in these courses would come to regard research as being a collaborative and interactive endeavor (Onwuegbuzie & Leech, 2005c). Finally, these courses would be able

to incorporate many of the strategies for reducing anxiety documented earlier (Dilevko, 2000; Dillon, 1982; Onwuegbuzie, 2000; Schacht & Stewart, 1990, 1991; Sgoutas-Emch & Johnson, 1998; Wilson, 1996, 1999a, 1999b, 2000; Wilson & Onwuegbuzie, 2003) so that research methods courses would be a more positive experience for students than is currently the case.

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Anthony J Onwuegbuzie, Nancy L Leech, Mari Murtonen and Juhani Tähtinen of mixed methods in social and behavioral research (pp. 297–319). Thousand Oaks, CA: Sage. Lalonde, R. N., & Gardner, R. C. (1993). Statistics as a second language? A model for predicting performance in psychology students. Canadian Journal of Behavioral Science, 25, 108–125. Leech, N. L., & Onwuegbuzie, A. J. (2005a, February). Increasing rigor in qualitative research: The array of tools for qualitative analysis. Paper presented at the annual meeting of the Southwest Educational Research Association, New Orleans, LA. Leech, N. L., & Onwuegbuzie, A. J. (2005b, April). Qualitative data analysis: Ways to improve accountability in qualitative research. Paper presented at the annual meeting of the American Educational Research Association, Montreal, Canada. Mundfrom, D. J., Shaw, D. G., Thomas, A., Young, S., & Moore, A. D. (2003). Introductory graduate research courses: An examination of the knowledge base. Research in the Schools, 10(2), 71–78. Murtonen, M., & Lehtinen, E. (2003). Difficulties experienced by education and sociology students in quantitative methods courses. Studies in Higher Education, 28, 171–185. National Research Council. (2002). Scientific research in education. Washington, DC: National Academy Press. Onwuegbuzie, A. J. (1995). Statistics test anxiety and women students. Psychology of Women Quarterly, 19, 413–418. Onwuegbuzie, A. J. (1997). Writing a research proposal: The role of library anxiety, statistics anxiety, and composition anxiety. Library & Information Science Research, 19, 5–33. Onwuegbuzie, A. J. (2000). Attitudes toward statistics assessments. Assessment and Evaluation in Higher Education, 25, 325–343. Onwuegbuzie, A. J. (2003a). Modeling statistics achievement among graduate students. Educational and Psychological Measurement, 63, 1020–1038. Onwuegbuzie, A. J. (2003b). Effect sizes in qualitative research: A prolegomenon. Quality & Quantity: International Journal of Methodology, 37, 393–409.

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Accepted 27 October 2009

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