Measuring statistics anxiety using a stage theory.

Abstract

To test a stage theory of statistics anxiety, we developed three scales to measure statistics anxiety at the input (Statistical Input Anxiety Scale), processing (Statistical Processing Anxiety Scale), and output (Statistical Output Anxiety Scale) stages of the learning process in statistics courses. This study examined the psychometric properties of these three scales among 90 African-American graduate students. Partial evidence of construct-related validity was provided via exploratory factor analysis, which revealed one specific factor for each scale. Also, score reliability coefficients were borderline. Implications are discussed.

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Statistics anxiety refers to the anxiety experienced when encountering statistics in any form and at any level (Onwuegbuzie, DaRos, & Ryan, 1997). Much of the research has conceptualized statistics anxiety as being situation-specific, with symptoms that occur during (a) a particular experience or in a particular setting involving the exposure to statistical ideas, problems, or issues; (b) instructional situations involving statistics or research; or (c) in situations which require students to use statistical methodology in an evaluative context (Feinberg & Halperin, 1978; Onwuegbuzie & Daley, 1996; Onwuegbuzie & Seaman, 1995; Zeidner, 1991). Experiences beset with statistics anxiety can have an enormous influence on the academic performance and achievement of students to such an extent that some may even postpone enrolling in statistics and research methods courses until the end of their programs. According to Onwuegbuzie and Wilson (2003), between two-thirds and four-fifths of graduate students experience uncomfortable levels of statistics anxiety to the extent that they regard their research and statistical methodology courses as a negative experience.

In Onwuegbuzie and Seaman's (1995) experimental study of graduate students with high levels of anxiety, the researchers found a significant interaction between statistics test anxiety and the type of examination that was administered (i.e., timed vs. untimed). Specifically, graduate students with high levels of statistics anxiety who were randomly assigned to a statistics examination given under timed conditions reported lower levels of performance than did high-anxious graduate students taking the same examination under untimed conditions.

Also using an experimental design, Onwuegbuzie and Daley (1996) examined the role of examination-taking coping strategies and study coping strategies in the anxiety/performance relationship. In this study, graduate students enrolled in a statistics course were randomly assigned to either an untimed or timed examination. It was revealed that both types of copy strategies played a key role in explaining variance in test anxiety. In addition, students in the timed examination performed more poorly than students exposed to the untimed examination. Further, a significant interaction was found between examination-taking coping strategies and examination condition, with students with poor examination-taking coping strategies not performing as well in the timed as they did in the untimed condition. However, no such interaction was found between study coping strategies and examination condition. According to the researchers, the findings were consistent with an information-processing model, which suggests that different processes related to test anxiety affect examination performance in statistics classes.

Several studies have documented a negative relationship between statistics anxiety and course performance (Cruise, Cash & Bolton, 1985; Onwuegbuzie & Seaman, 1995; Zanakis & Valenza, 1997; Zeidner, 1991). More specifically, statistics anxiety has been found to be a significant predictor of achievement in research methodology courses (Onwuegbuzie, Slate, Paterson, Watson, & Schwartz, 2000) and statistics courses (Fitzgerald, Juts, & Hudson, 1996). In a more recent study, Onwuegbuzie (2003) used path analysis techniques to understand the role of statistics anxiety in the statistics context. In this study, his Anxiety-Expectation Mediation (AEM) model was confirmed, in which both statistics anxiety and expectation were bi-directionally related to statistics achievement and, at the same time, moderated the relationship between statistics achievement and several cognitive, affective, and demographic variables. The role that statistics anxiety plays in the AEM model is consistent with Wine's (1980) theory of Cognitive-Attentional-Interference theory. According to Wine's theory, anxiety interferes with academic performance by interfering with a student's ability to receive, understand, and process new material. In the statistics leaning context, anxiety reduces the memory process efficiency when students are attempting to understand new terminology, rules, formulae, equations, or the like (Onwuegbuzie & Wilson, 2003).

The debilitative nature of statistics anxiety suggests that research into the nature of statistics anxiety holds great promise for improving statistics performance in the classroom. Studies have led to statistics anxiety being conceptualized as being multidimensional (Cruise et al., 1985; Onwuegbuzie, 1997; Onwuegbuzie et al., 1997). In an in-depth phenomenological study, Onwuegbuzie et al. (1997) identified four generalized components of statistics anxiety, specifically, instrument anxiety, content anxiety, interpersonal anxiety, and failure anxiety. In addition, each of these components comprised several subcomponents. Cruise et al. (1985) used factor analysis to identify the following six subcomponents of statistics anxiety: (a) worth of statistics, (b) interpretation anxiety, (c) test and class anxiety, (d) computational self-concept, (e) fear of asking for help, and (f) fear of statistics teachers. Furthermore, Onwuegbuzie (1997) expanded statistics anxiety to include four additional dimensions experienced by graduate students while writing their research proposals: perceived usefulness of statistics, fear of statistical language, fear of application of statistics knowledge, and interpersonal anxiety.

Although these conceptualizations of statistics anxiety help our understanding of statistics anxiety, they all suggest that anxiety associated with learning statistics is somewhat static, remaining relatively constant for the duration of the stimulus (e.g., reading a statistics textbook, interpreting statistical output). However, it is likely that statistics anxiety is more of a sequential and interactive process. Like statistics anxiety, foreign language anxiety is a complex phenomenon that has been found to be the best predictor of foreign language achievement (MacIntyre & Gardner, 1994a). Several studies have adopted Tobias's (1977, 1986) model of the effects of anxiety on learning and have theorized that foreign language anxiety occurs at each of the following stages: input, processing, and output (MacIntyre & Gardner, 1994b). This led to these authors developing three scales to measure anxiety at each of these stages: Input Anxiety Scale, the Processing Anxiety Scale, and the Output Anxiety Scale (MacIntyre & Gardner, 1994a).

In order to test the score validity of MacIntyre and Gardner's (1994a) Input Anxiety Scale, Processing Anxiety Scale, and Output Anxiety Scale, in relation to its measure of anxiety at each of these three stages of foreign language learning, Onwuegbuzie, Bailey, and Daley (1999a), administered the scales to 258 university students. By using three separate exploratory factor analyses, structural validity for one factor for each scale was reveled, accounting for 43% and 45% of the variance in scores (Onwuegbuzie et al., 1999a). Even though the confirmatory factor analyses discovered that the three scales did not represent either a single one-dimensional construct underlying foreign language anxiety or MacIntyre and Gardner's (1994) three-stage model of anxiety, with the removal of some items the scales did confirm the three-stage model. Based on these findings, the researchers concluded that this was possibly evidence that modifications to the scales are needed (Onwuegbuzie, Bailey, & Daley, 1999b). Onwuegbuzie et al. (1999b) studied the relationship between achievement and anxiety at the input, processing, and output stages as it related to anxiety in process of learning a foreign language. The researchers administered the Input Anxiety Scale, the Processing Anxiety Scale, and the Output Anxiety Scale, developed by MacIntyre and Gardner (1994), to 224 college students enrolled in either Spanish, French, or German courses. Onwuegbuzie et al. (1999a) reported a small but significant negative association between achievement in a foreign language and the level of anxiety scores on the Input Scale, the Processing Scale, and the Output Scale.

It has been stated in the literature that learning statistics is analogous to learning a foreign language (Lalonde & Gardner, 1993); therefore, the study of statistics anxiety can be paralleled to the study of foreign language achievement and anxiety (Lalonde & Gardner, 1993; Lazar, 1990; Onwuegbuzie, 2003). By using Tobias' (1986) model of the effects of anxiety on learning, it is possible that statistics anxiety can occur at each of the following three states of the statistical learning process: input, processing, and output. Statistics anxiety at the input stage (i.e., input anxiety) represents the fear experienced by students when they are initially presented with a new statistical word or formula. The level of anxiety at this stage is a function of the student's ability to receive, concentrate on, and encode external stimuli. Anxiety produced at this stage may reduce the efficacy of input. This may occur when the anxious student's ability to attend to statistical material presented by the instructor diminishes, and nominal stimuli become ineffective due to an inability to represent input internally (Tobias, 1986). Students with high levels of input anxiety typically attend more to task-irrelevant information and material, reducing the ability to receive input (Onwuegbuzie & Daley, 1996). Statistics anxiety at the processing stage denotes the apprehension experienced when cognitive operations are performed on external stimuli--that is, when students typically are attempting to organize and store input. The amount of anxiety involved at this stage appears to be related to the difficulty of the material presented, the extent to which memory is relied upon, and the level of organization of the presented material (Tobias, 1986). According to Tobias (1986), anxiety at this stage can debilitate learning by interfering with the processes that transform the input information and generate a solution to the problem. That is, anxiety may reduce the effectiveness with which memory processes are utilized to solve the task. In particular, high levels of processing anxiety may reduce a student's ability to understand statistical text.

Finally, statistics anxiety at the output stage involves the worry experienced when students are required to demonstrate their ability to produce previously learned material. In particular, statistics anxiety at this stage involves interference that appears after processing has been completed, but before it has been reproduced effectively as output (Tobias, 1986). Tobias (1986) theorized that output anxiety interferes with the retrieval of previous learned material. High levels of anxiety at this stage might hinder students' ability to analyze statistical data and to write statistical reports. In an attempt to test this stage theory of statistics anxiety, we developed three scales, along the lines of MacIntyre and Gardner (1994b), to measure statistics anxiety at the input, processing, and output stages. The purpose of the current study was to examine the psychometric properties of these three scales and the extent to which they adequately measure and reflect the three-stage conceptualization among African-American graduate students, a population found to experience high levels of statistics anxiety (Onwuegbuzie, 1999).

Method

Participants Participants were 90 African-American graduate (i.e., Master's and Doctoral) students attending a Historically Black College and University in the eastern United States, who were enrolled either in a statistics, measurement, or research methodology course. In order to participate in the study, students were required to sign an informed consent document that was given during the first class session of the semester. The majority (82.2%) of the participants was female. Ages of the participants ranged from 22 to 62 years (M = 28.62, SD = 7.40).

Instruments and Procedure Participants were administered the Statistical Input Anxiety Scale (SIAS), the Statistical Processing Anxiety Scale (SPAS), and the Statistical Output Anxiety Scale (SOAS). These scales represented modifications of the scales developed by MacIntyre and Gardner (1994a), namely, the Input Anxiety Scale, the Processing Anxiety Scale, and the Output Anxiety Scale. The SIAS, SPAS, AND SOAS each contain six 5-point Likert-format items (i.e., 1 = strongly agree, 2 = agree, 3 = neutral, 4 = disagree, 5 = strongly disagree) that assess how anxious students feel at the input, processing, and output stages statistics learning context, respectively. All negative items were key-reversed before scoring, such that high scores on any of these scales represent high levels of anxiety at the corresponding stage. Sample items for the SIAS include "I am not bothered by statisticians speaking too quickly" and "I get upset when research findings contain too much statistical terminology." Sample items for the SPAS include, "I do not worry when I hear new or unfamiliar statistical terminology, I am confident that I can understand it" and I feel anxious if a statistics class seems disorganized. Finally, sample items for the SOAS include, "I may know the proper statistical terminology expression but when I am nervous it just won't come out" and "I get upset when I know how to analyze statistical data but I just cannot interpret them."

Results

Score Reliability Reliability is the extent to which scores that are generated from an instrument demonstrate consistency (Crocker & Algina, 1986). Cronbach's Coefficient Alpha provides information about the degree to which the items in a scale measure similar characteristics (Campbell & Stanley, 1990). Coefficient Alpha, a measure of internal consistency, was determined for each scale, yielding the following reliability estimates: .65 (95% confidence interval [CI] = .52, .75) for the SIAS, .60 (95% CI = .46, .72) for the SPAS, and .65 (95% CI = .52, .75) for the SOAS.

Construct-Related Validity Validity is the extent to which an instrument yields scores that measure what the instrument is supposed to measure (Kerlinger, 1999). Furthermore, construct-related validity is the extent to which an instrument can be interpreted as a meaningful measure of some characteristic or quality (Campbell & Stanley, 1990). Establishing structural validity is an important step in providing evidence of construct-related validity (Messick, 1989, 1995).

In an attempt to assess the structural validity of scores pertaining to the SIAS, SPAS, SOAS, an exploratory factor analysis was conducted for set of scores. Moreover, a maximum likelihood (ML) factor analysis was employed to determine the number of factors underlying the scale. This technique, which is more valid for identifying the number and nature of the latent factors that are responsible for covariation in a data set than is principal components factor analysis (Hatcher, 1994), is perhaps the most commonly used method of common factor analysis (Lawley & Maxwell, 1971). Using a varimax rotation, and a criteria of .3 or greater for deeming a factor loading practically significant (Lambert & Durand, 1975), the ML factor analysis revealed (a) one specific factor for the Statistical Input Anxiety Scale, which explained 38.6% of the total variance; (b) one specific factor for the Statistical Processing Anxiety Scale, which explained 39.4% of the total variance; and (c) one specific factor for the Statistical Output Anxiety Scale, which explained 37.4% of the total variance. For the SIAS, all items had structure coefficients greater than .40, except for Item 2 ("It does not bother me if my statistics notes are disorganized before I study them"), which had a structure coefficient of. 18. With respect to the SPAS, four of the six items had structure coefficients greater than .40. However, Item 3 ("The only time that I feel comfortable during statistics tests is when I have had a lot of time to study") and Item 4 ("I feel anxious if a statistics class seems disorganized") had small structure coefficients of. 16 and -.11, respectively. Finally, with regard to the SOAS, all items had structure coefficients greater than .3, with these indices ranging from .38 (i.e., Item 6: "When I become anxious during a statistics test, I cannot remember anything I studied.") to .82 ("I never feel tense when I have to apply statistical knowledge").

Invariance of Scales Descriptive statistics were computed for each scale (range = 6 - 30). The mean for the SIAS was 20.38 (SD = 3.91), for the SPAS, 18.22 (SD = 3.31), and for the SOAS, 18.86 (SD = 3.62). A series of dependent t-tests, using the Bonferroni adjustment (Huberty, 1994), revealed that the SIAS generated statistically significantly higher mean scores than did the SPAS (t = 6.6, p < .0001) and the SOAS (t = 3.5, p < .001). No statistically significant difference emerged between the SPAS and SOAS (t = -1.7, p > .05). The effect size corresponding to the difference between SIAS and SPAS was 0.60 and that corresponding to the difference between SIAS and SPAS was 0.42. Using Cohen's (1988) criteria, these effect sizes were in the moderate range. These findings indicate that students reported significantly higher levels of input anxiety than processing anxiety and output anxiety.

Finally, a series of independent t-tests, after implementing the Bonferroni adjustment, revealed no statistically significant gender difference with respect to SOAS (t = 1.2, p > .05). However, females (M = 20.76, SD = 4.02) reported statistically significantly (t = 2.6, p < .01) higher levels of statistics anxiety associated with input anxiety than did males (M = 18.54, SD = 2.82). The associated Cohen's (1988) d effect size was 0.58. Similarly, females (M = 18.54, SD = 3.48) reported statistically significantly (t = 2.7, p < .01) higher levels of statistics anxiety associated with processing anxiety than did males (M = 16.86, SD = 1.86). The associated effect size was 0.52.

Summary of Findings In summary, the statistical analyses revealed four major findings. First, the score reliabilities pertaining to the three scales (i.e., Statistical Input Anxiety Scale, Statistical Processing Anxiety Scale, Statistical Output Anxiety Scale) were borderline, ranging from .60 to .65. Second, the factor analysis revealed one specific factor for each of the three scales, with the proportion of variance explained by the underlying items ranging between 37.4% and 39.4%. Third, scores pertaining to the Statistical Input Anxiety Scale were significantly higher than scores pertaining to both the Statistical Processing Anxiety Scale and the Statistical Output Anxiety Scale. Finally, females reported significantly higher levels of statistics anxiety associated with input anxiety and processing anxiety than did males.

Discussion

All three scales, namely, the Statistical input Anxiety Scale, the Statistical Processing Anxiety Scale, and the Statistical Output Anxiety Scale, were found to possess psychometric properties that needed room for improvement. With respect to score reliability, the alpha coefficients ranged from .60 to .65, slightly less than the .70 cutpoint recommended by Nunnally and Bernstein (1994). With respect to validity, evidence of construct-related validity was established via factor analysis. This analysis revealed one specific factor for each scale. However, the proportion of variance explained in each case was lower than the 50% or more that is typically explained in factor solutions (Henson, Capraro, & Capraro, 2001; Henson & Roberts, in press).

The utility of administering these three statistics anxiety scales is that they can help to identify the locus of information processing difficulties. That is, these scales can help to identify the stage at which statistics anxiety is most debilitative for a particular student. Such information could help instructors to target interventions more specifically. The finding that scores pertaining to the Statistical Input Anxiety Scale were significantly higher than scores pertaining to both the Statistical Processing Anxiety Scale and the Statistical Output Anxiety Scale suggests that for a large proportion of students, statistics anxiety is most severe at the input stage. This finding has important implications for statistics instructors because it indicates that students are most anxious when they are initially presented with a new statistical word or formula. This anxiety likely stems from a student's inability to receive, concentrate on, and encode novel statistical information (Tobias, 1986). Students with high levels of input anxiety typically attend more to task-irrelevant information and material, reducing the ability to receive input (Onwuegbuzie & Daley, 1996). Students with high levels of input anxiety are likely to benefit from interventions that primarily focus on anxiety management and reduction. This anxiety reduction could be accomplished through a number of cognitive and behavioral techniques, such as mental and emotive imagery, relaxation therapy, systematic desensitization, thought stopping, cognitive and covert modeling, cognitive restructuring, biofeedback, meditation, and neurolinguistic programming (Gilliland & James, 1983). Such students also should be given information about how to direct attention away from self-centered worries and onto appropriate tasks during examinations (Wine, 1980). Students with high levels of input anxiety also are likely to benefit from study techniques that emphasize understanding and deeper levels of processing of the statistical material rather than rote memorization.

The finding that females reported significantly higher levels of statistics anxiety associated with input anxiety and processing anxiety than did males indicates that females are likely to benefit even more greatly from the aforementioned interventions. In fact, this result suggests that the three scales should be used to determine other demographic predictors of statistics anxiety at each of the three stages of the learning process. For example, racial differences in input anxiety, processing anxiety, and output anxiety could be examined. Unfortunately, because all the present sample members were African-Americans, examining racial differences was beyond the scope of the present study. Identification of demographic predictors of input anxiety, processing anxiety, and output anxiety, as well as other predictors (e.g., cognitive, affective), would help statistics instructors further to target their interventions.

Taken together, the findings of this study indicate that more work is needed on these scales. However, on a positive note, these results should be interpreted in the context that each of the three scales only contained six items. The psychometric properties were close to being borderline acceptable. Therefore, the current findings suggest that by increasing both the number of items and the sample size, measures of anxiety can be developed that will yield reliable and valid scores. Also, these scales will allow researchers to furnish incremental validity for the multidimensionality of anxiety in statistics courses. Thus, the exploration of relationships involving each of these three stages of statistics anxiety is an important area for further research.

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Onwuegbuzie is an associate professor in the Department of Educational Measurement. Whitcome is an instructor of statistics at the University of Nevada, Reno.