Attitudes Toward Statistics Among Swiss ... - Hogrefe eContent

Swiss Journal of Psychology, 71 (3), 2012, 149–155

D. Zimprich: SwissJ. Attitudes Psychol. Toward 71 (3) © Statistics 2012 Verlag Among Hans Swiss Huber, Psychology Hogrefe AG, Stu dents Bern

Short Research Note

Attitudes Toward Statistics Among Swiss Psychology Students Daniel Zimprich University of Erlangen-Nuremberg, Germany

Abstract. Students’ attitude toward statistics plays an important role in their statistics achievement. The present research tests the factorial structure and predictors as well as outcomes of the Survey of Attitudes Toward Statistics in a sample of 346 Swiss psychology students. A confirmatory factor analysis validated the four-factor structure of the questionnaire (Affect, Cognitive Competence, Value, and Difficulty). Last math grade and sex were predictors of students’ attitude toward statistics, which in turn explained 30% of the variance in statistics achievement. The results demonstrate the importance of students’ feelings and opinions about statistics, over and above competence variables. Keywords: attitudes toward statistics, statistics achievement, confirmatory factor analysis

In Switzerland, graduation from the Bachelor of Science and Master of Science programs in psychology require the successful completion of statistics courses. Especially among psychology students, however, there appears to be an aversion to statistics, which may be driven by a general antiquantitative bias, a lack of understanding of the power of analytical models, and an underestimation of the extent to which scientific methods and statistics are employed in the social sciences (Forte, 1995). Traditionally, the outcome variable of statistics courses is students’ statistics achievement, measured, for example, by the percentage of students successfully completing the course. There is, however, a “subjective side” to statistics as well which cannot be assessed using achievement tests, comprising the feelings, thoughts, and opinions regarding statistics, like statistics anxiety (Zeidner, 1991), self-judged statistics competence (e.g., Onwuegbuzie, 2003), and attitudes toward statistics (e.g., Berk & Nanda, 1998). The interest in these subjective judgments and feelings about statistics stems from the fact that they are associated with statistics achievement and, thus, the successful completion of statistics courses (e.g., Harris & Schau, 1999). Findings point to higher statistics achievement if feelings toward and judgments about statistics are more positive, implying that students’ attitudes and beliefs can hamper (or enhance) learning statistics. In fact, attitudes toward statistics have been reported to be the best single predictor of achievement in statistics (Fitzgerald, Jurs, & Hudson, 1996). Moreover, instructors and students alike believe that a more positive attitude toward statistics may improve the climate in statistics courses, enhance the persistence of students, and generally increase course enrollment (Gal, Ginsburg, & Schau, 1997). DOI 10.1024/1421-0185/a000082

Several instruments have been developed to measure attitudes toward statistics. These instruments include the Statistical Anxiety Rating Scale (Cruise, Cash, & Bolton, 1985), the Bad Attitude Toward Statistics Scale (Berk & Nanda, 1998), the Statistics Attitude Survey (Roberts & Bilderback, 1980), the Attitudes Toward Statistics Scale (Wise, 1985), and the Statistics Anxiety Inventory (Zeidner, 1991). Although these instruments all tap similar aspects of attitudes toward or feelings about statistics, they differ in the number of items and subscales, which also implies that they differ in the number of latent dimensions underlying the items. For instance, the Statistics Attitude Survey introduced by Roberts and Bilderback (1980) comprises only a total score and hence can be assumed to measure a single common factor, whereas the Statistical Anxiety Rating Scale developed by Cruise et al. (1985) is composed of six subscales, implying that six common factors underlie the items designated to measure anxiety. However, the factorial structure of most of these instruments has not been explored in more detail. Moreover, when researchers did use factor analysis to examine the dimensional structure of the instruments mentioned, they almost always used exploratory instead of confirmatory factor analysis. Another instrument developed to measure students’ attitudes toward statistics is the Survey of Attitudes Toward Statistics (SATS) by Schau, Stevens, Dauphinee, and Del Vecchio (1995). Attitudes toward statistics can be defined as “a summation of feelings and emotions experienced over time in the context of learning statistics” (Gal et al., 1997, p. 41). Unlike most other instruments, the SATS has been investigated in more detail using confirmatory factor analSwiss J. Psychol. 71 (3) © 2012 Verlag Hans Huber, Hogrefe AG, Bern

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D. Zimprich: Attitudes Toward Statistics Among Swiss Psychology Students

ysis. For example, previous studies examined its dimensional structure and degree of measurement invariance across sex (Dauphinee, Schau, & Stevens, 1997) or across sex and time of measurement (Hilton, Schau, & Olsen, 2004). Cashin and Elmore (2005) found that the SATS predicted statistics achievement over and above demographic variables. Previous studies examining the structure of the SATS employed item parceling, which refers to a process by which item scores are combined into a number of sum scores or average scores (parcels) prior to factor analysis. One reason why item parcels have gained popularity is that, compared to items, their distributions typically more closely approximate normality, a prerequisite for many parameter estimation procedures. Also, model fit is, in general, better than in item-level factor analysis (MacCallum, Widaman, Zhang, & Hong, 1999). Note that parceling differs from creating subscales because parceling is done in an ad-hoc fashion. As a consequence, parcels do not usually have a meaningful interpretation, but represent a heuristic device for combining items (Bandalos & Finney, 2001). Therefore, results across studies are difficult to compare when based on different item parcels – as is the case for research on the SATS structure. Moreover, parcels may mask deviations of the individual items from the proposed model. For example, if more than one factor underlies the items forming a parcel, the factorial structure based on the parcel represents a confounding of different factors, but will oftentimes go unnoticed (Kim & Hagtvet, 2003). Along the same line, Little, Cunningham, Shahar, and Widaman (2002) recommended conducting item-level factor analysis if one is interested in the structure of a set of items. In the present study, the 28 SATS items were factor analyzed in order to gain insight into the structure of statistics attitudes. Once the structure of attitudes toward statistics has been established, a natural question is what affects these attitudes and which variables are affected by statistics attitudes. In their model of statistics anxiety, Onwuegbuzie and Wilson (2003) categorized its antecedents as being situational (e.g., statistics experience), dispositional (e.g., procrastination), or personal (e.g., sex). Zeidner (1991), for example, found that the dispositional variable “prior achievement in mathematics” influenced the level of statistics anxiety. One reason for this influence is the obvious partial overlap of statistics with mathematics. Due to this overlap, both seem to evoke similar feelings and attitudes, which also explains why mathematics anxiety and statistics anxiety are strongly related (Onwuebuzie, 2003). Many students appear to believe that statistics is mathematics, and so they merely transfer attitudes toward mathematics to statistics – with the accompanying, oftentimes negative, expectations (Gal et al., 1997). The role of sex in statistics achievement and related attitudes is controversial. Contrary to conventional wisdom, women outperform men in statistics achievement, although the effect size is small (Schram, 1996). Yet, a number of studies show that female students report higher levels of statistics anxiety and more negative attitudes toward statisSwiss J. Psychol. 71 (3) © 2012 Verlag Hans Huber, Hogrefe AG, Bern

tics (Roberts & Bilderback, 1980; Rodarte-Luna & Sherry, 2008; but see Cashin & Elmore, 2005). Again, effect sizes are small, implying that there is only a minor gender difference in statistics anxiety and attitudes toward statistics. A possible source of gender differences stems from research showing that women with higher levels of math selfconcept are more likely to attribute success in statistics to themselves, while those with lower levels of math self-concept attribute success in statistics to external causes (Rodarte-Luna & Sherry, 2008). Thus, a gender effect may reflect different levels of self-efficacy or self-concept (Onwuegbuzie, 2003). As mentioned above, the major outcome variable of statistics attitudes or statistics anxiety is statistics achievement. Importantly, it seems that, besides ability or knowledge variables, above all the emotions and feelings one has toward statistics determine the amount of statistics learning and understanding (Fitzgerald et al., 1996; Onwuegbuzie, 2003). Critically, then, a subject as analytical and, for many, dry as statistics is approached emotionally in the sense that it is beset with and surrounded by fear and insecurity. The present study followed three aims. First, we examined the structure of the Survey of Attitudes Toward Statistics (SATS; Schau et al., 1995) in a sample of Swiss psychology students. The goal was to replicate the four-factor structure of the SATS in an independent sample. Extending previous research, the SATS items were factor analyzed directly instead of in parcels (see Little et al., 2002), as in most published work on this questionnaire (Dauphinee et al., 1997; Hilton et al., 2004). Second, we included mathematics achievement and sex as predictors of statistics attitudes. The goal was to investigate the contribution of a dispositional and a personal variable in accounting for statistics attitudes. Eventually, on the outcome side, statistics achievement was regressed on statistics attitudes, thereby examining the extent to which the “objective side” of statistics is affected by the “subjective side.”

Methods Participants The sample comprised N = 346 psychology students from the University of Zurich who had enrolled in either of two undergraduate introductory statistics courses. The participants’ average age was 22 years (SD = 4.2 years, range 18 to 51). Most participants were female (80%), and all reported German being their native language. All students participated on a voluntary basis. Participants completed the SATS scale (Schau et al., 1995). In addition, 301 participants took a written statistics test (45 participants did not take the written test; with respect to their attitudes toward statistics, these participants did not differ from the rest of the sample).


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Measures

Statistical Analyses

Attitudes Toward Statistics

All confirmatory factor analyses were conducted using SAS/STAT® software, version 8 (SAS Institute, 1999). The absolute goodness-of-fit of models were evaluated using the χ² test and two additional criteria, the comparative fit index (CFI) and the root mean square error of approximation (RMSEA). Values of CFI above .90 are considered adequate, whereas RMSEA values below .06 indicate acceptable model fit. To compare the relative fit of nested models, the χ² difference test was used, which was complemented by 90% RMSEA confidence intervals.

The students’ attitudes toward statistics were measured using a German version of the Survey of Attitudes Toward Statistics (SATS; Schau et al., 1995). The German version was generated using a forward-backward translation procedure with the aid of a native American-English speaker. This procedure was repeated until all inconsistencies had been resolved. The SATS consists of 28 Likert-type items requiring answers on a 7-point scale with 1 = strongly disagree and 7 = strongly agree as endpoints. Nine of the 28 items are positively worded; the remaining 19 items are negatively worded. Negatively worded items were reversed so that higher scores always indicated a more positive attitude. The SATS encompasses four attitude components: Affect (6 items) assesses students’ positive and negative feelings about statistics (e.g., “I will like statistics”), Cognitive Competence (6 items) describes students’ intellectual knowledge and skills regarding statistics (e.g., “I will make a lot of math errors in statistics”), Value (9 items) captures attitudes about the usefulness and relevance of statistics (e.g., “I use statistics in my everyday life”), and Difficulty (7 items) measures students’ opinions about the difficulty of statistics (e.g., “Statistics is a complicated subject”). In the present sample, Cronbach’s αs for these subscales were .84, .81, .84, and .75 for Affect, Cognitive Competence, Value, and Difficulty, respectively.

Statistics Achievement Statistics achievement was measured using a written statistics test consisting of 20 multiple-choice items, with five to seven response alternatives each. Students were given 30 min to complete the test. An item was scored as correct if all the correct and only the correct response alternatives were marked. Cronbach’s α for the 20 items was .90. On average, using the item-to-construct balance technique (Little et al., 2002, p. 166), three parcels of statistics achievement were constructed. Briefly, the three items with the highest loadings on a common factor were selected to anchor the three parcels of statistics achievement. Subsequently, the three items with the next highest loadings were added to the parcels in an inverted order. This procedure was repeated until all items had been assigned to a parcel. As a result, there were two parcels consisting of seven items each and one parcel consisting of six items.

Mathematics Grade As a measure of mathematics achievement, students were asked to report their last mathematics grade from high school, ranging from 1 to 5, whereby higher values denote better grades.

Results Raw data were checked for departures from both univariate and multivariate normality, and for the presence of outliers. Skewness and kurtosis estimates of the 28 SATS items did not exceed 1 or –1, and there were no outliers (average skewness –0.07; average kurtosis –0.36). The normalized estimate of Mardia’s coefficient of multivariate kurtosis was –0.44. Hence, the univariate and multivariate distributional properties of the 28 SATS items warranted the use of maximum likelihood parameter estimation. Table 1 contains some descriptive statistics of the four SATS scales in the sample. Means and standard deviations were comparable to previous studies (e.g., Chiesi & Primi, 2009). Table 1 Descriptive statistics of the SATS scales SATS scale

Mean

SD

Affect (negative versus positive)

21.53

7.43

Cognitive competence (low vs. high)

26.59

6.59

Value (low vs. high)

41.82

9.31

Difficulty (difficult vs. easy)

22.63

6.05

9.85

3.56

Statistics achievement

Mathematics grade 4.52 0.95 Notes. SATS = Survey of Attitudes Toward Statistics (Schau et al., 1995), SD = standard deviation. N = 346.

Factorial Structure of Attitudes Toward Statistics Analysis of the factorial structure of the SATS started with Model A, a model of four correlated factors in which each item was specified to load on the factor it was designated to measure. As Table 2 shows, Model A achieved an acceptable fit according to the RMSEA, but not according to the χ² difference test or the CFI. A statistically significant lack of fit as indexed by the χ² difference test is more or less typical in social science research because of the sensitivity of the test especially in large samples or, as is the case here, with many degrees of freedom. The CFI, however, showed that the model could be improved. Swiss J. Psychol. 71 (3) © 2012 Verlag Hans Huber, Hogrefe AG, Bern

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Table 2 Sequence of estimated models and fit criteria Model χ²

df

Δχ²

A

703 * 344

B

616*

342

83*

C

618*

344

2

D

657*

368

Δdf CFI

RMSEA RMSEA 90% CI

.897

0.055

0.049–0.061

2

.921

0.048

0.042–0.054

2

.921

0.048

0.042–0.054

.919

0.048

0.042–0.054

E 811* 478 .917 0.045 0.040–0.050 Notes. df = degrees of freedom, CFI = comparative fit index, RMSEA = root mean square error of approximation, CI = confidence interval. Models A to D are based on N = 346. Model E was estimated with missing statistics achievement data present for 45 students. *p < .01.

Upon inspection of the residual covariance matrix, Model A did not adequately account for the associations between Items 10 and 19 or Items 14 and 21. Items 10 (“Statistics is not useful to the typical professional”) and 19 (“I will have no application for statistics in my profession”) both refer to the usefulness of statistics in professional life. By contrast, Items 14 (“I will be under stress during statistics class”) and 21 (“I am scared by statistics”) refer to relatively strong negative emotions elicited by statistics. In Model B, two residual covariances were estimated (Items 10 and 19 and Items 14 and 21). As can be seen from Table 2, Model B achieved a significantly better model fit than Model A. Also, the CFI was acceptable. Therefore, Model B was selected as an adequate description of the data. The residual covariances corresponded to r = .25 (Items 10 and 19) and r = .16 (Items 14 and 21). Note that because Items 10 and 19 both belonged to the Value factor while Items 14 and 21 belonged to the Affect factor, the two residual covariances did not compromise the four-factor structure – although the modified model should be investigated in an independent sample. On average, Model B explained 38% of the variance in the 28 SATS items. The four factors were significantly correlated, with the strongest correlation emerging between Affect and Cognitive Competence (r = .86), and the weakest correlation between Value and Difficulty (r = .51). An anonymous reviewer suggested collapsing Affect and Cognitive Competence due to their strong correlation. However, an additional model with this correlation constrained to one showed a worse fit to the data (χ² = 680, df = 343, CFI = .903, RMSEA = .053). Moreover, the difference in fit compared to Model B was statistically significant (Δχ² = 64, Δdf = 1), implying that Affect and Cognitive Competence were not perfectly correlated. Extending previous research, a second-order factor model was specified (Model C), with the four factors Affect, Cognitive Competence, Value, and Difficulty loading on a common factor. As Table 2 shows, doing so did not alter model fit, implying that the associations among the first-order factors were able to be captured more parsimoniously by a second-order factor. The second-order factor, which can be interpreted as a general attitude toward statistics, explained 78%, 92%, 37%, and 69% of the variance of Affect, Cognitive Competence, Value, and Difficulty, reSwiss J. Psychol. 71 (3) © 2012 Verlag Hans Huber, Hogrefe AG, Bern

spectively. Thus, it appeared as if Value was the attitude component most disparate compared to the other three factors of attitude toward statistics.

Predictors and Outcomes of Attitudes Toward Statistics In a second set of analyses, predictor variables and outcome variables of attitudes toward statistics were introduced. In a first model, sex was incorporated into the model as a predictor of the second-order factor. There was, however, no statistically significant effect of sex. Moreover, sex accounted for only about 0.5% of the variance in the second-order factor of general attitudes toward statistics. In the next model (Model D), the four first-order factors were regressed on sex. The only statistically significant effect of sex was for Difficulty: On average, female students judged statistics as being more difficult than male students did. Sex explained about 4% of the variance in Difficulty, corresponding to a small to medium effect size. Sex explained 0% (Affect) to 0.5% (Value) of the variance of the remaining three factors. Taken together, there was only a small to medium effect for the subjective impression of the difficulty of statistics, showing that female students considered statistics to be more difficult than their male counterparts did. Subsequently, the last mathematics grade from high school was introduced as an additional predictor (besides sex). Mathematics grade and sex were unrelated, showing that female students’ mathematics achievement was equal to male students’. First, only the second-order factor was regressed on mathematics grade. Results showed that this general attitude toward statistics was positively associated with mathematics grade in the sense that a better mathematics grade led to a more favorable attitude toward statistics. Mathematics grade accounted for 5% of the variance in the second-order factor. In order to examine the relations between statistics attitudes and mathematics grade in more detail, the four first-order factors were also regressed on mathematics grade (Model D). Three statistically significant paths emerged. Mathematics grade had a positive effect on Affect (R2 = 4%), Cognitive Competence (R2 = 8%), and Value (R2 = 2%), but not on Difficulty. To summarize, mathematics achievement was positively associated with attitudes toward statistics in the sense that those with higher achievement had more positive attitudes. Effects were in the small to medium range. An exception was the subjective opinion about the difficulty of statistics, which was independent of mathematics achievement, but related to sex. Turning to the outcome side of attitudes toward statistics, statistics achievement was introduced as a latent variable measured via three items parcels. The data of the 45 students who did not take the statistics test were treated as missing at random. In a first model, statistics achievement was regressed on the second-order factor, that is, the factor of general attitudes toward statistics. The regression was statistically sig-


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Figure 1. Model of attitudes toward statistics with predictors and outcomes (based on Model E). Math = Math grade, Cogn. Comp. = cognitive competence, Diffic. = difficulty, Statistics Achievem. = statistics achievement. All path coefficients are standardized. Gray-colored paths are not statistically significant.

nificant and positive, showing that those with more positive attitudes toward statistics also had higher statistics achievement. In terms of effect size, the regression was large with statistics attitude accounting for 20% of the variance in statistics achievement. In addition, there was a direct effect of mathematics grade on statistics achievement, explaining an additional 6% of the variance. In a second model, statistics achievement was regressed on the four first-order factors of attitudes toward statistics directly (Model E). In total, the four attitudes toward statistics factors accounted for 30% of the variance in statistics achievement. The strongest predictor was Affect with a standardized regression coefficient of β = 0.43, followed by Cognitive Competence (β = 0.37), and Value (β = 0.08). The effect of Value, however, was not statistically significant. Notably, the effect of Difficulty on statistics achievement was negative (β = –0.42), indicating the presence of suppression because, bivariately, they were positively correlated (r = .25). Thus, the suppression could be characterized as a negative net suppression (Krus & Wilkinson, 1986), which implies that the measure of perceived Difficulty of statistics suppresses achievement-irrelevant variance in Affect and Cognitive Competence, thus enhancing their effects on statistics achievement.1 Concretely, if affect and cognitive competence are held constant, those who judged statistics as being easier performed worse on the test. One reason might be that they had prepared less for the test. Model E is depicted in Figure 1.2

Discussion Negative attitudes toward statistics and statistics anxiety are common among undergraduate and graduate students 1

2

in the social sciences. At the same time, statistics has become more and more important not only in science, but also in terms of statistical literacy in everyday life in information-driven societies (Wallmann, 1993). The measurement of and factors affecting attitudes toward statistics and statistics anxiety have been the focus of much research during the past 20 years (e.g., Berk & Nanda, 1998; Chiesi & Primi, 2009; Cruise et al., 1985; Onwuegbuzie, 2003; Roberts & Bilderback, 1980; Wise, 1985). In the present study, the structure of the Survey of Attitudes Toward Statistics (SATS; Schau et al., 1995) was examined in a sample of psychology students from Zurich. One might wonder how selective the sample of Zurich psychology students was. Selectivity effects may have entered the analysis in two ways. First, due to the fact that only students from Zurich were examined, effects may have been different at other universities with a different statistics curriculum. Because of the Bologna process, though, the study of psychology has, at least across Europe, been unified. Accordingly, the descriptive statistics of the SATS were comparable to previous studies (e.g., Chiesi & Primi, 2009). The second possible selectivity effect stems from nonresponses. However, even if this did alter the level of statistics attitudes and statistics achievement, it is unclear whether and to which extent covariances between variables were affected. Unlike previous studies, the 28 items were factor analyzed directly (instead of in parcels, see Zimprich, Allemand, & Lachmann, 2012). The results are in line with other studies on the structure of the SATS in which four correlated factors of Affect, Cognitive Competence, Value, and Difficulty were found (Chiesi & Primi, 2009; Dauphinee et al., 1997; Hilton et al., 2004). One has to keep in mind, however, that by factoring the individual items directly, the structure of the SATS was tested much more rigorously than in previous studies: If

A circumstance that might complicate the interpretation of the suppression effect is that the four SATS factors are strongly correlated, which might give rise to problems of multicollinearity. However, whereas multicollinearity only refers to associations among predictors, for a suppression effect the associations of the predictors with the dependent variable are crucial, too. Moreover, large standard errors of the estimates are indicative of multicollinearity, which is not the case in Model E. For reasons of completeness and to avoid unnecessary clutter in Figure 1, the residual correlations (after accounting for math grade and sex differences) among the four SATS factors are reported here: Affect with Cognitive Competence, r = .78, Affect with Value, r = .65, Affect with Difficulty, r = .73, Cognitive Competence with Value, r = .65, Cognitive Competence with Difficulty, r = .73, Value with Difficulty, r = .51. Swiss J. Psychol. 71 (3) © 2012 Verlag Hans Huber, Hogrefe AG, Bern

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one used, for example, three parcels for each of the four factors, a covariance matrix with 78 variances and covariances would be the basis for analysis. In the present study, however, the models were based on 406 distinct item variances and covariances, which naturally required larger models and, thus, represented a more accurate and critical way of examining the SATS structure. In accordance with this line of reasoning, MacCallum et al. (1999) pointed out that parceled solutions are expected to provide a better model fit because they have fewer parameters to estimate and fewer chances for residuals to be correlated. Moreover, one cannot draw strong conclusions regarding models for individual items from a specific model that fits parcel data (Little et al., 2002). In that sense, the present study demonstrated that the four-factor structure of the SATS also holds for the 28 items, not just for item parcels. In accordance with previous findings, Affect and Cognitive Competence were most strongly correlated, while Value was relatively independent. Extending prior research, in the present study, a second-order factor of a general attitude toward statistics was specified, which described the data equally well but was more parsimonious. Thus, there is a broader level of generalization of individual differences in statistics attitudes that is not captured by the first-order analysis alone. Note that Value was relatively distinct from the other three first-order factors as indexed by its low loading on the second-order factor. In judging the value of statistics, students are thus able to disregard their feelings toward statistics to a certain extent. Previous studies revealed that factors contributing to negative attitudes toward statistics are, for example, misconceptions or mistaken beliefs about statistics, but also the course instructor’s attitude and lack of connection to real-world problems (Gal et al., 1997). Thus, positive or negative attitudes toward statistics have their origin in the student herself, driven both by (oftentimes negative) expectations and mathematical achievement. Attitudes are also shaped by experience with statistics, with practical applications being the most effective teaching strategy identified by statistics course participants that provoked more positive attitudes (e.g., Pan & Tang, 2005). In the present study, the focus was on mathematical achievement and sex. The results showed that negative statistics attitudes are not only due to insufficient skills like mathematics achievement, but also to gender differences that might stem from negative expectations or a lack of self-efficacy. Mathematics achievement was a predictor of statistics attitudes, a finding that is in line with previous studies (Onwuegbuzie, 2003). The main reason for the influence of mathematics achievement is that mathematics and statistics overlap to a certain extent. Moreover, it appears that mathematics anxiety is transferred to statistics courses (Onwuegbuzie & Wilson, 2003). However, sex also affected one component of statistics attitudes, namely, the subjectively perceived difficulty of statistics. Especially female students seem to have the impression that they do not come with enough mathematics training to do well in statistics classes (Rodarte-Luna & Sherry, 2008), although in the present study Swiss J. Psychol. 71 (3) © 2012 Verlag Hans Huber, Hogrefe AG, Bern

sex and mathematics achievement were independent. This independence is in line with recent meta-analyses showing that there is no gender gap in mathematics performance (Lindberg, Hyde, Petersen, & Linn, 2010). In addition, Schram (1996) demonstrated in her meta-analysis that women actually outperformed men in statistics achievement, although the effect was small (Cohen’s d = .08) and studies were heterogeneous. Nevertheless, there appears to be a lack of statistical self-efficacy especially in women – and the resulting negative attitude toward statistics may keep many female students away from engaging in research work or pursuing an academic career (Zeidner, 1991). This problem may be prevalent in psychology, where the majority of students is female. In line with previous studies, attitudes toward statistics strongly affected statistics achievement (Cashin & Elmore, 2005; Fitzgerald et al., 1996; Onwuegbuzie, 2003; Zeidner, 1991). More specifically, both Affect and Cognitive Competence exerted strong effects on statistics test performance, implying that those with more positive feelings toward statistics and those feeling more competent in statistics showed higher statistics achievement. Unlike previous studies, there was a strong negative net suppression effect (Krus & Wilkinson, 1986) of Difficulty, which was positively correlated with statistics test performance, but received a negative regression weight in the multivariate analysis. Thus, it is not the perceived Difficulty per se (which was positively associated with statistics achievement), but its measure that multivariately suppressed criterion-irrelevant variance in Affect and Cognitive Competence, thus enhancing their effects on statistics achievement. Where to go from here? A number of authors have made suggestions concerning how to improve statistics attitudes and, hence, statistics achievement (Pan & Tang, 2005). I propose a different avenue of research that draws on the relation between subjective and objective statistics achievement. Compared to other research domains addressing subjective and objective perspectives on performance (see Mascherek & Zimprich, 2011; Zimprich, Martin, & Kliegel, 2003), the link between attitudes toward statistics and statistics achievement is relatively strong. In addition, Hilton et al. (2004) demonstrated that attitudes toward statistics change over time. So, if individual changes in attitudes toward statistics and individual changes in statistics achievement were strongly correlated, this would be evidence for the importance of students’ attitudes toward statistics. Methodologically, this could be examined using latent change models (e.g., Zimprich et al., 2003).

Acknowledgments Daniel Zimprich is now at the University of Ulm, Germany. The author would like to thank Anna Mascherek for assisting in collecting the data and, of course, the psychology students who participated in the study.


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Daniel Zimprich Department of Developmental Psychology Institute of Psychology and Education University of Ulm Albert-Einstein-Allee 47 D-89081 Ulm Germany [email protected] Swiss J. Psychol. 71 (3) © 2012 Verlag Hans Huber, Hogrefe AG, Bern