# Examining the effectiveness of innovative instructional methods on reducing statistics anxiety for graduate students in the social sciences.

Statistics anxiety is prevalent among students whose academic
background has little statistical training. The development and
psychometric properties of statistics anxiety scales and the factors
affecting statistics anxiety have been extensively studied for more than
twenty years, but few studies focused on how to reduce the statistics
anxiety for graduate students in the social sciences. The present study
explores how statistics anxiety can be reduced by various innovative
instructional methods. A repeated measures ANCOVA with controlling for
individual differences is utilized to analyze a sample data from 21
social science graduate students at a Midwest university. The study
shows that the combining application-oriented teaching methods with
instructors' attentiveness to students' anxiety is a
significantly effective way (p < .02, [[eta].sup.2] = .29) to reduce
students' anxiety in learning statistics.

KEY WORDS: Statistics anxiety: Statistics education; Learning statistics; Teaching statistics; Innovative instructional methods; Teaching strategy

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Many graduate students in the social sciences need to take statistics as part of the academic training, but these students often do not necessarily have backgrounds in statistics or mathematics from their undergraduate degree or other graduate training. In the classrooms, statistics anxiety is noticeably prevalent among graduate students whose academic background has little statistical training. According to Onwuegbuzie. Slate, Paterson, Watson, and Schwartz (2000), 75% to 80% of graduate students appear to experience uncomfortable levels of statistics anxiety. As a result, conducting statistics is often rated as the lowest skill in terms of academic competence (Huntley, Schneider, and Aronson, 2000).

Statistics anxiety has been defined simply as anxiety that occurs as a result of encountering statistics in any form and at any level (Onwuegbuzie, DaRos, & Ryan, 1997), and has been found to negatively affect learning (Onwuegbuzie & Seaman, 1995). Many researchers (Lazar, 1990; Lalonde & Gardner, 1993; Onwuegbuzie, 2000b) suggested that learning statistics is as difficult as learning a foreign language. On the other hand, statistics anxiety sometimes is not necessarily due to the lack of training or insufficient skills, but due to the misperception about statistics and negative experiences in a statistical class. For instance, students often think they do not have enough mathematics training so that they cannot do well in statistical classes. With fear of failing the course, they delay enrolling in statistics courses as long as possible, which often leads to failure to complete their degree programs (Onwuegbuzie, 1997). The lack of self-efficacy and higher anxiety in statistics keep many students away from engaging in research work or further to pursue an academic career. Therefore, statistics becomes one of the most anxiety-inducing courses in their programs of study (Blalock, 1987; Caine, Centa, Doroff, Horowitz, & Wisenbaker, 1978; Schacht & Stewart, 1990; Zeidner, 1991).

In the literature, statistics anxiety has been extensively studied for more than two decades. The majority of the studies have focused primarily on measurement of and factors contributing to statistics anxiety. The development of statistics anxiety instruments was derived from mathematics anxiety assessment. For example, the Statistical Anxiety Scale (Pretorius & Norman, 1992) was developed by replacing the word "mathematics" with the word "statistics" in some items of the Mathematics Anxiety Scale (Fennema & Sherman, 1976; Betz, 1978). The reliability and factor analysis results showed good psychometric properties of the Statistics Anxiety Scale. In 1991, Zeidner replaced the word "mathematics" with the word "statistics" in a 40-item version of the Mathematics Anxiety Rating Scale (Richard & Woolfolk, 1980) and developed the Statistics Anxiety Inventory. Cruise and Wilkins (1980) and Cruise, Cash. and Bolton (1985) developed another statistics anxiety scale, called Statistics Anxiety Rating Scale (STARS), and Baloglu (2002) studied its psychometric properties. Watson, Kromrey, Ferron, Lang, and Hogarty (2003) incorporated the STARS along with a survey of attitude toward statistics into a multimedia program, called EncStat (Encouraged About Statistics), that was designed to identify students with statistics anxiety or negative attitudes toward statistics. Recently, Piotrowski, Bagui, and Hemasinha (2002) developed a new instrument to assess statistics anxiety for psychological graduate students.

The other focus of the literature on statistic anxiety is about the factors affecting statistics anxiety (see Onwuegbuzie & Wilson, 2000 for a review). Specifically, three types of factors are identified: (a) situational factors, such as math experience (Betz, 1978; Roberts & Bilderback, 1980; Tomazic & Katz, 1988; Zeidner, 1991 ; Wilson, 1997; Balo_lu, 2001; Hong & Karstensson, 2002; Balo_lu, 2003), statistics experience (Sutarso, 1992), computer experience (Zimmer & Fuller, 1996), and research experience (Trimarco, 1997); (b) dispositional factors, such as math self-concept or self-esteem (Zeidner, 1991), scholastic competence or multiple intelligences (Birenbaum & Eylath, 1994; Daley & Onwuegbuzie, 1997; Onwuegbuzie, 2000c), perfectionism (Onwuegbuzie & Daley, 1999; Walsh & Ugumba-Agwunobi, 2002), hope (Onwuegbuzie. 1998b), and procrastination (Onwuegbuzie, 2000a; Walsh & Ugumba-Agwunobi, 2002); and (c) personal factors, such as learning style (Onwuegbuzie, 1998a; Wilson & Onwuegbuzie, 2001), age (Baloglu, 2003), gender (Betz, 1978; Roberts & Bilderback, 1980; Demaria-Mitton, 1987; Benson, 1989; Benson & Bandalos, 1989; Hong & Karstensson, 2002; Baloglu, 2003), and ethnicity (Bell, 1998; Onwuegbuzie. 1999).

Unfortunately, sparse studies have been found on how to reduce the anxiety in learning statistics for graduate students in the social sciences (Onwuegbuzie & Wilson, 2000). Schacht and Stewart (1990) reported incorporating humorous cartoon examples in statistics classes were perceived by the students to helpful in statistics anxiety reduction. Journal writing was suggested to be another effective tool in reducing levels of anxiety (Smith, Miller, & Robertson, 1992; Sgoutas-Emch & Johnson, 1998). However, theses studies did not find a statistically significant decrease in anxiety levels. Forte (1995) argued for an effective teaching approach that incorporates computer usage, real-world applications, humor, statistical language practice, and group-learning principles. Additionally, Dolinsky (2001) suggested creating a collaborative environment in which using active learning strategies as the primary method to teach statistics. These teaching methods reveal promise to reduce students' statistics anxiety, yet more innovations of teaching statistics are needed (Huntley, Schneider, & Aronson, 2000). More importantly, empirical studies are needed to examine the effectiveness of these methods in reducing statistics anxiety.

The purpose of this study is to explore various instructional methods and their impacts on students' statistics anxiety. Specifically, the study examines whether the proposed innovative teaching methods could reduce the statistics anxiety for graduate students in social sciences. It is hypothesized that the implementation of several innovative instructional methods, centered on the combination of application-oriented teaching methods with instructor's attentiveness to students' anxiety, has positive impacts on reducing statistics anxiety. A repeated measures ANCOVA with controlling for individual differences is employed to support this research hypothesis.

Methods

Participants

The participants were 21 graduate students who enrolled in a course on Introductory Statistical Methods offered by the College of Education at a Midwest university. The mean age of the sample was 37 years, ranging from 23 years to 55 years. 19 of the 21 participants were women. Nineteen participants were Caucasian, one was African American, and one was Asian.

The information about the participants' academic background is shown in Table 1. As can be seen in Table 1, in average, the participants had taken around 3 courses on mathematics or statistics. The participants had some overall teaching experience with mean score of 7.52 years, but little teaching experience in mathematics or statistics; seventeen of the 21 participants had zero teaching experience in mathematics or statistics. In terms of academic research experience, the participants had mean score of 2.24 on a 5-point Likert scale ranging from 1 (little experienced) to 5 (very experienced), but less experience (1.33) in statistical computer programs.

In sum, most of the participants were Caucasian women non-traditional students who had taken a few undergraduate quantitative courses, had some teaching experience in non-quantitative courses, and had some research experience, but little background in statistical computer programs.

Instruments

The Statistics Anxiety Scale (Pretorius & Norman, 1992) was implemented in the present study. The Statistics Anxiety Scale was developed by modifying the Mathematics Anxiety Rating Scale (Betz, 1978). The word "mathematics" was replaced with the word "statistics" in the scale. Responses on the Statistics Anxiety Scale were obtained on a 5-point Likert scale ranging from 1 (strong agree) to 5 (strong disagree). High scores on this scale would be an indication of a high level of statistics anxiety. Pretorius and Norman (1992) reported a reliability coefficient of .90 for the Statistics Anxiety Scale. The current study had reliability coefficients of .94 for the pretest and .98 for the posttest. The mean scores on the 10 items in the instrument at pretest and posttest will be analyzed as the outcome measures of statistics anxiety in the present study.

In addition, a demographic questionnaire was used to collect the students' information on demographics, teaching experiences, and statistical or mathematical background. The data from this questionnaire allows us to conduct the repeated measures analysis with controlling for these individual differences.

Procedures

At the beginning of the class, the students were informed about the class orientation as well as the opportunity to participate in the pilot study. The students will not be penalized for not participating or rewarded for participating in the study. They are informed that the outcome of the study should be beneficial for future classes. The Statistics Anxiety Scale (Pretorius & Norman, 1992) was implemented at the beginning and at the end of the course to measure the students' statistics anxiety levels.

The following innovative instructional methods were employed in the class throughout the course of the instruction:

Application-oriented teaching methods. Forte (1995) and Wilson (1998) suggested that applying statistics to real-world situations be helpful in alleviating anxiety in statistics classes. Smith, Miller, and Robertson (1992), Dunn (1996), Sgoutas-Emch and Johnson (1998), and Dolinsky (2001) also found that writing assignment was an effective way to help students to form positive attitudes toward to statistics. Following these suggestions. two specific application-oriented teaching methods were implemented: (a) Essay writing. We asked the students to write an essay biweekly to their bosses or friends who do not have any knowledge in statistics. The essays reflected what students learned in the class using layperson's language based on a real example from their work or daily life. This practice helps students translate what they have learned in class to a daily life application. This exercise also helps students form an optimistic perception that statistics is practical and exists in everyday life, rather than abstract and difficult to comprehend; and (b) Journal article critiquing. The other writing assignment was to critique a published quantitative journal article, which allows students to apply the course content to evaluating quantitative journal articles. This exercise exposes students to the use of statistics in the academic field, and consequently students feel more comfortable and confident about using statistics in their own research projects in the future.

Instructors' attentiveness to students' anxiety. Encouragement from instructors (Wilson & Onwuegbuzie, 2001), humorous teaching style (Schacht & Stewart, 1990; Forte, 1995; Wilson, 1998), addressing the anxiety, and providing coping strategies to students (Dillon, 1982; Wilson, 1998) were advocated to be effective instruction practices for reducing students' statistics anxiety. The following specific instructional innovations incorporating these ideas to help students reduce their statistics anxiety were implemented in this present study: (a) Orientation letter. An orientation letter was sent to students a week before the class starts, to prepare the students mentally (what to expect) and logistically (what is required) ready for taking the statistics course. In the letter, we addressed issues about how to easily and quickly get the textbooks, how to review the necessary background knowledge in math, how to face the problems associated with statistics anxiety, and how to get help if they have any concerns or questions; (b) Flexible and extra office hours. In addition to regular scheduled office hours, we also offered flexible office hours by appointment and on-site (right before and immediate after class) office hours. Faculty's availability and their accessibility to help sometimes provide the milieu for reducing anxiety; (c) Midterm class survey. At the midpoint of the course-work, a survey inquiring students' concerns was conducted. This practice gave students a formal way to express their concerns, issues, and suggestions. The class was adjusted according to students' suggestions thereafter; (d) Cheat sheet. Instead of totally open- or totally closed-book final examination, we requested students to prepare a cheat sheet and bring it to the exam instead of textbooks and class notes. The process of preparing the cheat sheet assisted students to review course content and evaluate their own levels of competency. The cheat sheet helps them to feel relaxed if students have anxiety about memorizing the details, but after all, they still need to understand the concepts; and (e) Optional pass/fail grading system. We allowed students to take the course on a pass/fail basis as an alternative to the regular letter grading system, which dramatically reduced their anxiety about doing poorly in the class. As a matter of fact, the students who chose to be graded on the pass/fail basis got would-be grades higher than the class average.

The above teaching strategies are meant to remove the stressors for anxiety students potentially experience in learning statistics, and to provide a supportive rather than anxiety provoking environment for optional performance. Combining the application-oriented teaching methods with the instructors' attentiveness to students' anxiety is expected to have positive impact on reducing students' statistics anxiety.

Data Analysis

A repeated measures ANCOVA of data from an one-group pretest-posttest quasi-experimental design with controlling for demographical and academic background covariates was employed to analyze the pretest-posttest mean scores on the Statistics Anxiety Scale. We would want to see a significant decrease in students' statistics anxiety from the sample data.

Results

The mean scores of statistics anxiety at pretest and posttest were 3.25 and 2.82 with standard deviations of 1.24 and 1.10, respectively, which showed that the statistics anxiety was empirically reduced. The Pearson correlation coefficients between statistics anxiety and age and academic background at pretest and posttest are listed in Table 2. From Table 2 we can see that age and "years of overall teaching experience" were positively related to statistics anxiety. All other academic background variables were negatively related to statistics anxiety with the smallest correlation for "years of teaching experience in math or stats." These results are consistent with the findings in the literature (Betz, 1978; Sutarso, 1992; Zimmer & Fuller, 1996; Trimarco, 1997; Wilson, 1997; Baloglu, 2003). In addition, Table 2 also shows that the correlations were fairly consistent across the time.

SPSS program was used for the repeated measures ANCOVA with controlling for age, "number of math or stats courses ever taken," and "self-rating on experience in academic research." Since the participants were predominantly Caucasian women, gender and ethnicity were not included in the repeated measures analysis. Since most of the people in the sample were classroom teachers, "years of overall teaching experience" was confounded with age; and therefore it was also not included in the analysis. Moreover, "years of teaching experience in math or stats" was not included in the analysis because only four out of 21 participants had teaching experience in math or stats. Lastly, since most of the participants rated themselves little experience in statistical computer programs. the variable of "self-rating on experience in statistical computer programs" was also not included in the repeated measures analysis. There were no missing data or outliers. The assumptions for the repeated measures analysis were met.

The results of the repeated measures ANCOVA are shown the in Table 3. First of all, the results indicate that statistics anxiety was significantly (p < .02, [n.sup.2] = .29) reduced after implementing the innovative instructional methods. Additionally, the results for between subjects suggest that age (p < .04, [n.sup.2] = .24), "number of math or stats courses ever taken" (p < .05, [n.sup.2] = .21), and "self-rating on experience in academic research" (p < .02, [n.sup.2] = .26) had significant effects on statistics anxiety, that is, students who were older, had taken fewer math or stats courses, and had less research experience exhibited more statistics anxiety. However, as indicated by the insignificant interaction effects of time with these individual differences, the effects of these individual differences did not change significantly from pretest to posttest-which is consistent with the results of the correlational analysis above.

Discussion

Statistics anxiety is prevalent among graduate students in the social sciences. Although the development and psychometric properties of statistics anxiety measurements and situational, dispositional, and personal factors affecting statistics anxiety have been extensively studied for more than twenty years, few studies focused on how to reduce the statistics anxiety for graduate students in the social sciences. The present study explores whether application-oriented teaching methods combined with the instructors' attentiveness to students' anxiety would reduce the statistics anxiety. The results of the repeated measures ANCOVA with controlling for individual differences show that statistics anxiety was significantly reduced after implementing the innovative instructional methods. The results also show that the individual differences, such as age, "number of math or stats courses ever taken," and "self-rating on experience in academic research," had significant effects on statistics anxiety, but the effects of these individual differences on statistics anxiety did not change significantly from pretest to posttest.

The findings of this study provide the initial empirical evidence to support that innovative teaching methods have the potential to effectively reduce statistics anxiety as suggested in the literature. This study also tries to incorporate the ideas from the literature (Schacht & Stewart, 1990; Forte, 1995; Wilson, 1998; Wilson & Onwuegbuzie, 2001), and implement a comprehensive and systematic approach, namely the application-oriented teaching methods combined with the instructors' attentiveness to students' anxiety, to help graduate students in the social sciences learn statistics more effectively with less anxiety. We assert that a more balanced and systematic approach is better than piecemeal approach because the latter will not provide students the supportive learning environment needed. For instance, several methods used in the study, such as optional grading system, more flexible office hours, orientation letter, and the cheat sheet, are all measures that make it easier for students to pass the course. For most students with statistics anxiety, thought of failing the course is a huge stressor; therefore, even if they have the capability to learn statistics, the fear of failure overrides their ability. The application-oriented teaching methods, on the other hand, dispel the misconception about statistics that it is useless and that it is only for people with good math skills. Applying the class contents to daily life and actual research articles makes more meaning for students, and also have them feel more comfortable and close to learning statistics.

Some people might argue that the design of the study makes it harder to interpret the findings since so many different methods are employed at the same time. As discussed above, we believe that in order to reduce the anxiety a supportive learning environment is needed. The instructional methodology is important, but is not sufficient to reduce the anxiety, because anxiety may not necessarily due to lack of competence, rather, it is a multidimensional construct (Onwuegbuzie & Daley, 1999). For this sake, the intervention needs to be multidimensional as well. Fear of asking for help, fear of teachers, and test anxiety are identified as three out of six factors for anxiety constructs (Cruise, Cash, & Bolton, 1985); accordingly, this study addresses these concerns by the instructor's attentiveness to the factors that make students anxious.

The findings about the significant reduction of statistics anxiety in this study support the effectiveness of the multidimensional pedagogical intervention for reducing statistics anxiety. The implications for teaching statistics to social sciences graduate students can be speculated in three ways: 1) It is critical that instructors be aware of students' anxiety issues and be available and accessible for help; 2) The organization of the class should be structured to provide a supportive learning environment; and 3) Multiple instructional methods and evaluation measures should be supplied. Certainly, more practical problem solving exercises will help too.

We acknowledge that the sample size is small and that the analysis would not have enough statistical power to detect real differences. Nonetheless, the present study still shows statistically significant results at p = .05 level with an observed statistical power of .70. More importantly, this study also shows a substantive significance with a large effect size ([n.sup.2] >. 14) as defined by Cohen (1988, p. 287), which implies that a larger sample would yield more statistically and substantively significant results. Therefore, the finding from the present study-that the application-oriented teaching methods combined with the instructors' attentiveness to Students' anxiety is a significantly effective way to reduce students' anxiety in learning statistics-was strongly supported by the empirical data even with the small sample. We also noticed that since mainly due to the small sample we did not find significant differences in the effects of individual differences on statistics anxiety from pretest to posttest, we do not know for what type of students or under what conditions the innovative instructional methods reduce their statistics anxiety more. Thus, in further research, it would be interesting to explore this aspect of effectiveness of the innovative instructional methods, by utilizing a larger sample.

We also understand that the present study lacks a control group and the results may not lead to a causal inference about the effectiveness of the innovative teaching methods on reducing statistics anxiety. However, this one-group pretest-posttest quasi-experimental design is frequently used in the social sciences (Cook & Campbell, 1979). This is not because researchers in the social sciences lack the knowledge of how to construct true experiments but because they understand the limitations of statistical inference in field settings. For example, it is not ethical to withhold from a group of students teaching methods that may have potential to enhance students' learning. Whatever the reason, we still often achieve some knowledge using this quasi-experimental design even the outcome variables are subject to multiple influences other than the treatment alone (Cook & Campbell, 1979). Therefore, this lack of causal evidence does not seem to limit the adoption of these potentially effective teaching methods.

In conclusion, a systematic and comprehensive instructional approach that includes application-oriented teaching methods and instructors' attentiveness to students' anxiety issues is found to have benefits in reducing statistics anxiety for graduate students in social sciences. Due to the prevalence of statistics anxiety among graduate students who have little quantitative analysis background, it is important to continue to explore innovative teaching methods to better serve the students.

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Wei Pan, Assistant Professor of Quantitative Educational Research; Mei Tang, Associate Professor of Counseling, University of Cincinnati.

Correspondence concerning this article should be addressed to Wei Pan, Division of Educational Studies, University of Cincinnati. EO. Box 210002, Cincinnati, OH 45221-0002; Email: wei.pan@uc.edu

Author note: This research was supported by a grant from the College of Education, Criminal Justice, and Human Services, University of Cincinnati. The authors are indebted to Robert Kallmeyer for data collection and management.

KEY WORDS: Statistics anxiety: Statistics education; Learning statistics; Teaching statistics; Innovative instructional methods; Teaching strategy

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Many graduate students in the social sciences need to take statistics as part of the academic training, but these students often do not necessarily have backgrounds in statistics or mathematics from their undergraduate degree or other graduate training. In the classrooms, statistics anxiety is noticeably prevalent among graduate students whose academic background has little statistical training. According to Onwuegbuzie. Slate, Paterson, Watson, and Schwartz (2000), 75% to 80% of graduate students appear to experience uncomfortable levels of statistics anxiety. As a result, conducting statistics is often rated as the lowest skill in terms of academic competence (Huntley, Schneider, and Aronson, 2000).

Statistics anxiety has been defined simply as anxiety that occurs as a result of encountering statistics in any form and at any level (Onwuegbuzie, DaRos, & Ryan, 1997), and has been found to negatively affect learning (Onwuegbuzie & Seaman, 1995). Many researchers (Lazar, 1990; Lalonde & Gardner, 1993; Onwuegbuzie, 2000b) suggested that learning statistics is as difficult as learning a foreign language. On the other hand, statistics anxiety sometimes is not necessarily due to the lack of training or insufficient skills, but due to the misperception about statistics and negative experiences in a statistical class. For instance, students often think they do not have enough mathematics training so that they cannot do well in statistical classes. With fear of failing the course, they delay enrolling in statistics courses as long as possible, which often leads to failure to complete their degree programs (Onwuegbuzie, 1997). The lack of self-efficacy and higher anxiety in statistics keep many students away from engaging in research work or further to pursue an academic career. Therefore, statistics becomes one of the most anxiety-inducing courses in their programs of study (Blalock, 1987; Caine, Centa, Doroff, Horowitz, & Wisenbaker, 1978; Schacht & Stewart, 1990; Zeidner, 1991).

In the literature, statistics anxiety has been extensively studied for more than two decades. The majority of the studies have focused primarily on measurement of and factors contributing to statistics anxiety. The development of statistics anxiety instruments was derived from mathematics anxiety assessment. For example, the Statistical Anxiety Scale (Pretorius & Norman, 1992) was developed by replacing the word "mathematics" with the word "statistics" in some items of the Mathematics Anxiety Scale (Fennema & Sherman, 1976; Betz, 1978). The reliability and factor analysis results showed good psychometric properties of the Statistics Anxiety Scale. In 1991, Zeidner replaced the word "mathematics" with the word "statistics" in a 40-item version of the Mathematics Anxiety Rating Scale (Richard & Woolfolk, 1980) and developed the Statistics Anxiety Inventory. Cruise and Wilkins (1980) and Cruise, Cash. and Bolton (1985) developed another statistics anxiety scale, called Statistics Anxiety Rating Scale (STARS), and Baloglu (2002) studied its psychometric properties. Watson, Kromrey, Ferron, Lang, and Hogarty (2003) incorporated the STARS along with a survey of attitude toward statistics into a multimedia program, called EncStat (Encouraged About Statistics), that was designed to identify students with statistics anxiety or negative attitudes toward statistics. Recently, Piotrowski, Bagui, and Hemasinha (2002) developed a new instrument to assess statistics anxiety for psychological graduate students.

The other focus of the literature on statistic anxiety is about the factors affecting statistics anxiety (see Onwuegbuzie & Wilson, 2000 for a review). Specifically, three types of factors are identified: (a) situational factors, such as math experience (Betz, 1978; Roberts & Bilderback, 1980; Tomazic & Katz, 1988; Zeidner, 1991 ; Wilson, 1997; Balo_lu, 2001; Hong & Karstensson, 2002; Balo_lu, 2003), statistics experience (Sutarso, 1992), computer experience (Zimmer & Fuller, 1996), and research experience (Trimarco, 1997); (b) dispositional factors, such as math self-concept or self-esteem (Zeidner, 1991), scholastic competence or multiple intelligences (Birenbaum & Eylath, 1994; Daley & Onwuegbuzie, 1997; Onwuegbuzie, 2000c), perfectionism (Onwuegbuzie & Daley, 1999; Walsh & Ugumba-Agwunobi, 2002), hope (Onwuegbuzie. 1998b), and procrastination (Onwuegbuzie, 2000a; Walsh & Ugumba-Agwunobi, 2002); and (c) personal factors, such as learning style (Onwuegbuzie, 1998a; Wilson & Onwuegbuzie, 2001), age (Baloglu, 2003), gender (Betz, 1978; Roberts & Bilderback, 1980; Demaria-Mitton, 1987; Benson, 1989; Benson & Bandalos, 1989; Hong & Karstensson, 2002; Baloglu, 2003), and ethnicity (Bell, 1998; Onwuegbuzie. 1999).

Unfortunately, sparse studies have been found on how to reduce the anxiety in learning statistics for graduate students in the social sciences (Onwuegbuzie & Wilson, 2000). Schacht and Stewart (1990) reported incorporating humorous cartoon examples in statistics classes were perceived by the students to helpful in statistics anxiety reduction. Journal writing was suggested to be another effective tool in reducing levels of anxiety (Smith, Miller, & Robertson, 1992; Sgoutas-Emch & Johnson, 1998). However, theses studies did not find a statistically significant decrease in anxiety levels. Forte (1995) argued for an effective teaching approach that incorporates computer usage, real-world applications, humor, statistical language practice, and group-learning principles. Additionally, Dolinsky (2001) suggested creating a collaborative environment in which using active learning strategies as the primary method to teach statistics. These teaching methods reveal promise to reduce students' statistics anxiety, yet more innovations of teaching statistics are needed (Huntley, Schneider, & Aronson, 2000). More importantly, empirical studies are needed to examine the effectiveness of these methods in reducing statistics anxiety.

The purpose of this study is to explore various instructional methods and their impacts on students' statistics anxiety. Specifically, the study examines whether the proposed innovative teaching methods could reduce the statistics anxiety for graduate students in social sciences. It is hypothesized that the implementation of several innovative instructional methods, centered on the combination of application-oriented teaching methods with instructor's attentiveness to students' anxiety, has positive impacts on reducing statistics anxiety. A repeated measures ANCOVA with controlling for individual differences is employed to support this research hypothesis.

Methods

Participants

The participants were 21 graduate students who enrolled in a course on Introductory Statistical Methods offered by the College of Education at a Midwest university. The mean age of the sample was 37 years, ranging from 23 years to 55 years. 19 of the 21 participants were women. Nineteen participants were Caucasian, one was African American, and one was Asian.

The information about the participants' academic background is shown in Table 1. As can be seen in Table 1, in average, the participants had taken around 3 courses on mathematics or statistics. The participants had some overall teaching experience with mean score of 7.52 years, but little teaching experience in mathematics or statistics; seventeen of the 21 participants had zero teaching experience in mathematics or statistics. In terms of academic research experience, the participants had mean score of 2.24 on a 5-point Likert scale ranging from 1 (little experienced) to 5 (very experienced), but less experience (1.33) in statistical computer programs.

In sum, most of the participants were Caucasian women non-traditional students who had taken a few undergraduate quantitative courses, had some teaching experience in non-quantitative courses, and had some research experience, but little background in statistical computer programs.

Instruments

The Statistics Anxiety Scale (Pretorius & Norman, 1992) was implemented in the present study. The Statistics Anxiety Scale was developed by modifying the Mathematics Anxiety Rating Scale (Betz, 1978). The word "mathematics" was replaced with the word "statistics" in the scale. Responses on the Statistics Anxiety Scale were obtained on a 5-point Likert scale ranging from 1 (strong agree) to 5 (strong disagree). High scores on this scale would be an indication of a high level of statistics anxiety. Pretorius and Norman (1992) reported a reliability coefficient of .90 for the Statistics Anxiety Scale. The current study had reliability coefficients of .94 for the pretest and .98 for the posttest. The mean scores on the 10 items in the instrument at pretest and posttest will be analyzed as the outcome measures of statistics anxiety in the present study.

In addition, a demographic questionnaire was used to collect the students' information on demographics, teaching experiences, and statistical or mathematical background. The data from this questionnaire allows us to conduct the repeated measures analysis with controlling for these individual differences.

Procedures

At the beginning of the class, the students were informed about the class orientation as well as the opportunity to participate in the pilot study. The students will not be penalized for not participating or rewarded for participating in the study. They are informed that the outcome of the study should be beneficial for future classes. The Statistics Anxiety Scale (Pretorius & Norman, 1992) was implemented at the beginning and at the end of the course to measure the students' statistics anxiety levels.

The following innovative instructional methods were employed in the class throughout the course of the instruction:

Application-oriented teaching methods. Forte (1995) and Wilson (1998) suggested that applying statistics to real-world situations be helpful in alleviating anxiety in statistics classes. Smith, Miller, and Robertson (1992), Dunn (1996), Sgoutas-Emch and Johnson (1998), and Dolinsky (2001) also found that writing assignment was an effective way to help students to form positive attitudes toward to statistics. Following these suggestions. two specific application-oriented teaching methods were implemented: (a) Essay writing. We asked the students to write an essay biweekly to their bosses or friends who do not have any knowledge in statistics. The essays reflected what students learned in the class using layperson's language based on a real example from their work or daily life. This practice helps students translate what they have learned in class to a daily life application. This exercise also helps students form an optimistic perception that statistics is practical and exists in everyday life, rather than abstract and difficult to comprehend; and (b) Journal article critiquing. The other writing assignment was to critique a published quantitative journal article, which allows students to apply the course content to evaluating quantitative journal articles. This exercise exposes students to the use of statistics in the academic field, and consequently students feel more comfortable and confident about using statistics in their own research projects in the future.

Instructors' attentiveness to students' anxiety. Encouragement from instructors (Wilson & Onwuegbuzie, 2001), humorous teaching style (Schacht & Stewart, 1990; Forte, 1995; Wilson, 1998), addressing the anxiety, and providing coping strategies to students (Dillon, 1982; Wilson, 1998) were advocated to be effective instruction practices for reducing students' statistics anxiety. The following specific instructional innovations incorporating these ideas to help students reduce their statistics anxiety were implemented in this present study: (a) Orientation letter. An orientation letter was sent to students a week before the class starts, to prepare the students mentally (what to expect) and logistically (what is required) ready for taking the statistics course. In the letter, we addressed issues about how to easily and quickly get the textbooks, how to review the necessary background knowledge in math, how to face the problems associated with statistics anxiety, and how to get help if they have any concerns or questions; (b) Flexible and extra office hours. In addition to regular scheduled office hours, we also offered flexible office hours by appointment and on-site (right before and immediate after class) office hours. Faculty's availability and their accessibility to help sometimes provide the milieu for reducing anxiety; (c) Midterm class survey. At the midpoint of the course-work, a survey inquiring students' concerns was conducted. This practice gave students a formal way to express their concerns, issues, and suggestions. The class was adjusted according to students' suggestions thereafter; (d) Cheat sheet. Instead of totally open- or totally closed-book final examination, we requested students to prepare a cheat sheet and bring it to the exam instead of textbooks and class notes. The process of preparing the cheat sheet assisted students to review course content and evaluate their own levels of competency. The cheat sheet helps them to feel relaxed if students have anxiety about memorizing the details, but after all, they still need to understand the concepts; and (e) Optional pass/fail grading system. We allowed students to take the course on a pass/fail basis as an alternative to the regular letter grading system, which dramatically reduced their anxiety about doing poorly in the class. As a matter of fact, the students who chose to be graded on the pass/fail basis got would-be grades higher than the class average.

The above teaching strategies are meant to remove the stressors for anxiety students potentially experience in learning statistics, and to provide a supportive rather than anxiety provoking environment for optional performance. Combining the application-oriented teaching methods with the instructors' attentiveness to students' anxiety is expected to have positive impact on reducing students' statistics anxiety.

Data Analysis

A repeated measures ANCOVA of data from an one-group pretest-posttest quasi-experimental design with controlling for demographical and academic background covariates was employed to analyze the pretest-posttest mean scores on the Statistics Anxiety Scale. We would want to see a significant decrease in students' statistics anxiety from the sample data.

Results

The mean scores of statistics anxiety at pretest and posttest were 3.25 and 2.82 with standard deviations of 1.24 and 1.10, respectively, which showed that the statistics anxiety was empirically reduced. The Pearson correlation coefficients between statistics anxiety and age and academic background at pretest and posttest are listed in Table 2. From Table 2 we can see that age and "years of overall teaching experience" were positively related to statistics anxiety. All other academic background variables were negatively related to statistics anxiety with the smallest correlation for "years of teaching experience in math or stats." These results are consistent with the findings in the literature (Betz, 1978; Sutarso, 1992; Zimmer & Fuller, 1996; Trimarco, 1997; Wilson, 1997; Baloglu, 2003). In addition, Table 2 also shows that the correlations were fairly consistent across the time.

SPSS program was used for the repeated measures ANCOVA with controlling for age, "number of math or stats courses ever taken," and "self-rating on experience in academic research." Since the participants were predominantly Caucasian women, gender and ethnicity were not included in the repeated measures analysis. Since most of the people in the sample were classroom teachers, "years of overall teaching experience" was confounded with age; and therefore it was also not included in the analysis. Moreover, "years of teaching experience in math or stats" was not included in the analysis because only four out of 21 participants had teaching experience in math or stats. Lastly, since most of the participants rated themselves little experience in statistical computer programs. the variable of "self-rating on experience in statistical computer programs" was also not included in the repeated measures analysis. There were no missing data or outliers. The assumptions for the repeated measures analysis were met.

The results of the repeated measures ANCOVA are shown the in Table 3. First of all, the results indicate that statistics anxiety was significantly (p < .02, [n.sup.2] = .29) reduced after implementing the innovative instructional methods. Additionally, the results for between subjects suggest that age (p < .04, [n.sup.2] = .24), "number of math or stats courses ever taken" (p < .05, [n.sup.2] = .21), and "self-rating on experience in academic research" (p < .02, [n.sup.2] = .26) had significant effects on statistics anxiety, that is, students who were older, had taken fewer math or stats courses, and had less research experience exhibited more statistics anxiety. However, as indicated by the insignificant interaction effects of time with these individual differences, the effects of these individual differences did not change significantly from pretest to posttest-which is consistent with the results of the correlational analysis above.

Discussion

Statistics anxiety is prevalent among graduate students in the social sciences. Although the development and psychometric properties of statistics anxiety measurements and situational, dispositional, and personal factors affecting statistics anxiety have been extensively studied for more than twenty years, few studies focused on how to reduce the statistics anxiety for graduate students in the social sciences. The present study explores whether application-oriented teaching methods combined with the instructors' attentiveness to students' anxiety would reduce the statistics anxiety. The results of the repeated measures ANCOVA with controlling for individual differences show that statistics anxiety was significantly reduced after implementing the innovative instructional methods. The results also show that the individual differences, such as age, "number of math or stats courses ever taken," and "self-rating on experience in academic research," had significant effects on statistics anxiety, but the effects of these individual differences on statistics anxiety did not change significantly from pretest to posttest.

The findings of this study provide the initial empirical evidence to support that innovative teaching methods have the potential to effectively reduce statistics anxiety as suggested in the literature. This study also tries to incorporate the ideas from the literature (Schacht & Stewart, 1990; Forte, 1995; Wilson, 1998; Wilson & Onwuegbuzie, 2001), and implement a comprehensive and systematic approach, namely the application-oriented teaching methods combined with the instructors' attentiveness to students' anxiety, to help graduate students in the social sciences learn statistics more effectively with less anxiety. We assert that a more balanced and systematic approach is better than piecemeal approach because the latter will not provide students the supportive learning environment needed. For instance, several methods used in the study, such as optional grading system, more flexible office hours, orientation letter, and the cheat sheet, are all measures that make it easier for students to pass the course. For most students with statistics anxiety, thought of failing the course is a huge stressor; therefore, even if they have the capability to learn statistics, the fear of failure overrides their ability. The application-oriented teaching methods, on the other hand, dispel the misconception about statistics that it is useless and that it is only for people with good math skills. Applying the class contents to daily life and actual research articles makes more meaning for students, and also have them feel more comfortable and close to learning statistics.

Some people might argue that the design of the study makes it harder to interpret the findings since so many different methods are employed at the same time. As discussed above, we believe that in order to reduce the anxiety a supportive learning environment is needed. The instructional methodology is important, but is not sufficient to reduce the anxiety, because anxiety may not necessarily due to lack of competence, rather, it is a multidimensional construct (Onwuegbuzie & Daley, 1999). For this sake, the intervention needs to be multidimensional as well. Fear of asking for help, fear of teachers, and test anxiety are identified as three out of six factors for anxiety constructs (Cruise, Cash, & Bolton, 1985); accordingly, this study addresses these concerns by the instructor's attentiveness to the factors that make students anxious.

The findings about the significant reduction of statistics anxiety in this study support the effectiveness of the multidimensional pedagogical intervention for reducing statistics anxiety. The implications for teaching statistics to social sciences graduate students can be speculated in three ways: 1) It is critical that instructors be aware of students' anxiety issues and be available and accessible for help; 2) The organization of the class should be structured to provide a supportive learning environment; and 3) Multiple instructional methods and evaluation measures should be supplied. Certainly, more practical problem solving exercises will help too.

We acknowledge that the sample size is small and that the analysis would not have enough statistical power to detect real differences. Nonetheless, the present study still shows statistically significant results at p = .05 level with an observed statistical power of .70. More importantly, this study also shows a substantive significance with a large effect size ([n.sup.2] >. 14) as defined by Cohen (1988, p. 287), which implies that a larger sample would yield more statistically and substantively significant results. Therefore, the finding from the present study-that the application-oriented teaching methods combined with the instructors' attentiveness to Students' anxiety is a significantly effective way to reduce students' anxiety in learning statistics-was strongly supported by the empirical data even with the small sample. We also noticed that since mainly due to the small sample we did not find significant differences in the effects of individual differences on statistics anxiety from pretest to posttest, we do not know for what type of students or under what conditions the innovative instructional methods reduce their statistics anxiety more. Thus, in further research, it would be interesting to explore this aspect of effectiveness of the innovative instructional methods, by utilizing a larger sample.

We also understand that the present study lacks a control group and the results may not lead to a causal inference about the effectiveness of the innovative teaching methods on reducing statistics anxiety. However, this one-group pretest-posttest quasi-experimental design is frequently used in the social sciences (Cook & Campbell, 1979). This is not because researchers in the social sciences lack the knowledge of how to construct true experiments but because they understand the limitations of statistical inference in field settings. For example, it is not ethical to withhold from a group of students teaching methods that may have potential to enhance students' learning. Whatever the reason, we still often achieve some knowledge using this quasi-experimental design even the outcome variables are subject to multiple influences other than the treatment alone (Cook & Campbell, 1979). Therefore, this lack of causal evidence does not seem to limit the adoption of these potentially effective teaching methods.

In conclusion, a systematic and comprehensive instructional approach that includes application-oriented teaching methods and instructors' attentiveness to students' anxiety issues is found to have benefits in reducing statistics anxiety for graduate students in social sciences. Due to the prevalence of statistics anxiety among graduate students who have little quantitative analysis background, it is important to continue to explore innovative teaching methods to better serve the students.

Table 1 Participants' Academic Background (n = 21) Variable M SD Number of math or stats courses ever taken 3.24 1.92 Years of overall teaching experience 7.52 9.57 Years of teaching experience in math or stats 0.90 2.10 Self-rating on experience in academic research (a) 2.24 0.94 Self-rating on experience in statistical computer 1.33 0.58 programs (a) (a) The rating is on a 5-point Likert scale ranging from 1 (little experienced) to 5 (very experienced). Table 2 Pearson Correlation Coefficients Between Statistics Anxiety and Age and Academic Background (n = 21) Statistics Anxiety Variable Pretest Posttest Age .33 .59 ** Number of math or stats courses ever taken -.44 * -.35 Years of overall teaching experience .26 .48 * Years of teaching experience in math or stats -.17 -.06 Self-rating on experience in academic research (a) -.45 * -.21 Self-rating on experience in statistical computer -.39 -.24 programs (a) The rating is on a 5-point Likert scale ranging from 1 (little experienced) to 5 (very experienced). * p < .05. ** p < .01. Table 3 Repeated Measures ANCOVA for Statistics Anxiety (n = 21) Source df F p [[eta].sup.2] Within subjects Time 1 6.90 .02 .29 Time x Age 1 2.03 .17 .11 Time x PreMath 1 1.74 .20 .09 Time x ResExp 1 2.81 .11 .14 Error 17 (0.44) Between subjects Age 1 5.23 .04 .24 PreMath 1 4.54 .05 .21 ResExp 1 6.10 .02 .26 Error 17 (1.29) Note. Values enclosed in parentheses represent mean square errors. Time = Pretest vs. Posttest; PreMath = Number of math or stats courses ever taken; ResExp = Self-rating on experience in academic research.

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Wei Pan, Assistant Professor of Quantitative Educational Research; Mei Tang, Associate Professor of Counseling, University of Cincinnati.

Correspondence concerning this article should be addressed to Wei Pan, Division of Educational Studies, University of Cincinnati. EO. Box 210002, Cincinnati, OH 45221-0002; Email: wei.pan@uc.edu

Author note: This research was supported by a grant from the College of Education, Criminal Justice, and Human Services, University of Cincinnati. The authors are indebted to Robert Kallmeyer for data collection and management.

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Author: | Tang, Mei |
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Publication: | Journal of Instructional Psychology |

Geographic Code: | 1USA |

Date: | Jun 1, 2004 |

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