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Statistics education has unique challenges, and many students experience a great deal of anxiety when faced with statistical concepts and mathematical calculations. Though a great deal of research has explored personality risk factors for generalized anxiety in clinical domains, comparatively few studies have examined the relationship between individual differences and domain-specific anxiety in statistics and mathematics classrooms. An interesting finding of the present research was that concern over mistakes and doubts about action (facets of perfectionism) predicted specific classroom-related fears (e.g., test anxiety), yet did not strongly relate to negative attitudes (e.g., attitudes about the value of statistics overall). Our approach applies common rigorous methods in personality science (e.g., basic psychometric soundness, quantitative analysis that accounts for familywise error rates, pre-registration, and open data) to a core topic of importance to educational research (i.e., classroom anxiety). We believe this cross-disciplinary approach is an important strength. Further, we believe that our research can open a dialogue about important personality variables that can impede learning in the classroom. In this way, we hope that our research can help teachers identify students in need of support by revealing personality variables that tend to co-occur with statistics anxiety.

A short-form statistics anxiety scale was found to have 6 factors.

Perfectionism and anxiety sensitivity positively correlated with math and statistics anxiety.

Self-efficacy negatively correlated with math and statistics anxiety.

Results held when controlling for gender, university program, and education level.

S

We focus on two sub-dimensions of perfectionism from

A meta-analysis of 7 studies (

Statistics anxiety is a multifaceted construct that can be split into “anxiety” and “attitudes” towards statistics (

There is little research that specifically discusses self-efficacy, anxiety sensitivity, concern over mistakes and/or doubts about actions and their associations with

Students in arts programs experience higher levels of math anxiety relative to students in science programs (

Graduate students are more than six times as likely to experience mental health problems—including anxiety—than the general population (

Finally, women tend to score higher than men on traits corresponding with negative emotionality, such as neuroticism (

Statistics/math anxiety is an important topic to study because it has known negative effects on performance and engagement in statistics classrooms (

We examined self-efficacy, anxiety sensitivity, concern over mistakes, doubts about actions, and their relationship to math/statistics anxiety among post-secondary university students when controlling for degree programs, gender, and graduate student status. Our analysis plan and hypotheses were pre-registered (see

Power analyses suggested that a sample size of 319 is sufficient to detect correlations of .20 or larger, assuming an alpha of .05 and 95% power. This effect size was estimated by averaging the relationships between all STARS subscales and facets of perfectionism across three studies (

Participants were current undergraduate or graduate students recruited online. We collected data from two populations—undergraduate students at Dalhousie University through the SONA system (the online psychology participant pool), and graduate students from Prolific (an online survey company). Prolific participants sign up voluntarily for the website and it is advertised via word of mouth and social media. On January 13, 2022, there were 6768 graduate students in Prolific’s pool, and the top 3 majors were Psychology (12%), Engineering (11%) and Computer Science (7%).

There were no inclusion or exclusion criteria for the SONA sample other than being a current undergraduate student at Dalhousie University. For the Prolific sample, current graduate students were eligible to participate. The SONA sample was recruited using ads posted online through Dalhousie University’s Department of Psychology Participant Pool website. The Prolific sample was recruited using internal advertisement on the Prolific website. Only registered users on the Prolific website who met the screening criteria (current graduate students) could see the ad for the study.

Our initial sample consisted of 506 participants (

After exclusions, ages ranged from 16 years old to 53 years old (^{1}

Three participants’ gender were coded as “nonbinary”. To avoid excluding their data on equity/diversity grounds, each was arbitrarily assigned as “woman” for analyses involving gender, making the variable “man vs. not man”.

Ethnicities were White (76.6%), Asian (9.2%), Middle Eastern (5.6%), Hispanic/Latinx (2.9%), Black (2.0%) and Other (3.8%). SONA and Prolific samples are heterogeneous populations, which necessitates including sample as a covariate.Prolific users were administered a screening survey when they first signed up as a participant with the service. Among other things, the survey asked users “Are you currently a student?” (yes/no) and “Which level of education are you currently in?” Only participants who answered “yes” to the student status question and one of “Graduate degree (MA/MSc/MPhil/other)” or “Doctorate degree (PhD/other)” were considered eligible for our study. The SONA participant pool comprised current undergraduate psychology students.

Participants answered a demographics questionnaire following consent, asking about age, ethnicity, statistics course experience, education level, and university program (i.e., arts, science, other^{2}

In our original pre-registered plan, we were going to dichotomize programs into “arts vs. science.” However, many participants were in programs that did not cleanly fit into this dichotomy (e.g., Medicine, Engineering, Health). Thus, we added the “other” category, to avoid throwing out too much data.

). We expected all SONA participants would be undergraduates and all Prolific participants would be graduate students, but this was added as a double-check of screening.We measured self-efficacy with the 8-item New General Self-Efficacy Scale (NGSE;

We measured anxiety sensitivity with the 18-item Anxiety Sensitivity Index-3 (ASI-3;

Perfectionism was measured with short-form subscales from the Frost Multidimensional Perfectionism Scale (FMPS;

The Statistics Anxiety Rating Scale (STARS;

Item | Worth | Test | Help | Self-Concept | Teachers | Interpretation |
---|---|---|---|---|---|---|

16. I’m never going to use statistics so why should I have to take it? | -.004 | -.01 | -.05 | .02 | .005 | |

13. I don’t see why I have to fill my head with statistics. It will have no use in my career. | .04 | .02 | .06 | -.03 | -.04 | |

9. I feel statistics is a waste. | -.11 | .002 | .11 | .07 | .17 | |

4. Doing an examination in a statistics course. | -.01 | -.01 | .02 | .02 | -.01 | |

5. Walking into the room to take a statistics test. | -.03 | .05 | -.08 | .009 | -.01 | |

1. Studying for an examination in a statistics course. | .05 | .04 | .13 | -.008 | .18 | |

2. Going to ask my statistics teacher for individual help with material I am having difficulty understanding. | .01 | .01 | -.02 | .02 | -.04 | |

7. Asking one of my teachers for help in understanding a printout. | -.04 | -.02 | .06 | -.03 | .10 | |

12. I don’t have enough brains to get through statistics. | -.02 | .03 | -.009 | .02 | -.02 | |

11. I can’t even understand secondary school maths; how can I possibly do statistics? | .10 | -.03 | .05 | .04 | .04 | |

15. Statistics teachers task so fast you cannot logically follow them. | -.02 | .02 | 0 | -.05 | .006 | |

14. Statistics teachers speak a different language. | .04 | -.008 | .04 | .20 | 0 | |

10. Statistics teachers are so abstract they seem inhuman. | .16 | -.06 | -.009 | .04 | .05 | |

8. Trying to understand the statistical analyses described in the abstract of a journal. | -.003 | -.02 | .04 | -.03 | .003 | |

6. Interpreting the meaning of a probability value once I have found it. | .04 | .14 | -.03 | .03 | .09 | |

3. Doing the coursework for a statistics course. | -.02 | .26 | .04 | .27 | -.05 |

We measured math anxiety with the Abbreviated Math Anxiety Scale (AMAS; ^{3}

Our pre-registered plan indicated using a single total score for math anxiety. However, prior factor analytic work suggests a 2-factor model (i.e., learning and evaluation math anxiety), with two highly-correlated factors (

Predictors & Outcomes | r^{a} (95% CI^{b}) |
p_{holm}^{c} |
r*^{d} (95% CI) |
p_{holm} |
---|---|---|---|---|

Self-Efficacy | ||||

Test and Class Anxiety | -0.15 [-0.24, -0.06] | .009** | -0.12 [-0.22, -0.03] | .093 |

Interpretation Anxiety | -0.20 [-0.29, -0.11] | < .001*** | -0.18 [-0.27, -0.09] | .002** |

Fear of Asking for Help | -0.28 [-0.37, -0.19] | < .001*** | -0.24 [-0.34, -0.15] | < .001*** |

Worth of Statistics | -0.12 [-0.21, -0.03] | .066 | -0.09 [-0.18, 0.01] | .340 |

Fear of Statistics Teachers | -0.16 [-0.25, -0.07] | .006** | -0.13 [-0.22, -0.03] | .086 |

Computational Self-Concept | -0.29 [-0.37, -0.20] | < .001*** | -0.24 [-0.34, -0.15] | < .001*** |

Math Anxiety | -0.23 [-0.31, -0.14] | < .001*** | -0.20 [-0.30, -0.10] | .001** |

Anxiety Sensitivity | ||||

Test and Class Anxiety | 0.24 [0.15, 0.33] | < .001*** | 0.24 [0.15, 0.32] | < .001*** |

Interpretation Anxiety | 0.27 [0.18, 0.35] | < .001*** | 0.27 [0.18, 0.35] | < .001*** |

Fear of Asking for Help | 0.32 [0.23, 0.40] | < .001*** | 0.29 [0.21, 0.37] | < .001*** |

Worth of Statistics | 0.11 [0.02, 0.20] | .080 | 0.11 [0.01, 0.21] | .263 |

Fear of Statistics Teachers | 0.15 [0.06, 0.24] | .009** | 0.14 [0.04, 0.23] | .048* |

Computational Self-Concept | 0.25 [0.16, 0.34] | < .001*** | 0.24 [0.15, 0.33] | < .001*** |

Math Anxiety | 0.35 [0.26, 0.43] | < .001*** | 0.35 [0.26, 0.44] | < .001*** |

Concern Over Mistakes | ||||

Test and Class Anxiety | 0.28 [0.19, 0.36] | < .001*** | 0.23 [0.14, 0.32] | < .001*** |

Interpretation Anxiety | 0.28 [0.19, 0.36] | < .001*** | 0.25 [0.15, 0.34] | < .001*** |

Fear of Asking for Help | 0.40 [0.32, 0.47] | < .001*** | 0.36 [0.27, 0.44] | < .001*** |

Worth of Statistics | 0.06 [-0.03, 0.15] | .388 | 0.05 [-0.04, 0.14] | .494 |

Fear of Statistics Teachers | 0.10 [0.01, 0.19] | .133 | 0.08 [-0.02, 0.17] | .480 |

Computational Self-Concept | 0.20 [0.11, 0.28] | < .001*** | 0.18 [0.09, 0.27] | .001** |

Math Anxiety | 0.38 [0.29, 0.45] | < .001*** | 0.35 [0.26, 0.43] | < .001*** |

Doubts About Actions | ||||

Test and Class Anxiety | 0.25 [0.16, 0.34] | < .001*** | 0.23 [0.14, 0.33] | < .001*** |

Interpretation Anxiety | 0.26 [0.17, 0.34] | < .001*** | 0.24 [0.15, 0.33] | < .001*** |

Fear of Asking for Help | 0.31 [0.22, 0.39] | < .001*** | 0.28 [0.19, 0.37] | < .001*** |

Worth of Statistics | 0.01 [-0.08, 0.11] | .728 | -0.01 [-0.09, 0.08] | .832 |

Fear of Statistics Teachers | 0.10 [0.01, 0.19] | .133 | 0.07 [-0.02, 0.16] | .390 |

Computational Self-Concept | 0.22 [0.13, 0.30] | < .001*** | 0.18 [0.10, 0.27] | .001** |

Math Anxiety | 0.36 [0.28, 0.44] | < .001*** | 0.35 [0.26, 0.43] | < .001*** |

^{a}Pearson correlation coefficient. ^{b}Confidence interval. ^{c}^{d}Standardized regression coefficient after adjusting for covariates.

*

The study was reviewed by Dalhousie University's Social Sciences and Humanities Research Ethics Board (#2020-5290). Participants were compensated with 0.5 credit points towards an eligible course (SONA) or £2.50 (Prolific). SONA participants could indicate “observer” status, meaning they may complete the study and receive compensation, but we would destroy their data and not use it for research. All questions had a “prefer not to answer” option, which was counted as missing data. After reading a consent form, participants took part in a cross-sectional survey using SurveyMonkey, where they answered each of the questionnaires specified above. Completing questionnaires took ~20 minutes. Upon completion, participants were debriefed and compensated.

Our confirmatory hypotheses and data analyses were pre-registered, with a time-stamped plan located in the

Scripts used for our primary data analyses can be located in the

We conducted an exploratory factor analysis on the abbreviated STARS. We used maximum likelihood estimation for the extraction of factors, oblimin rotation^{4}

We prefer an oblimin rotation to a varimax rotation because factor analysis data we relied on when selecting the highest factor loadings for the short form scale indicated correlated factors (

Parallel analysis suggested six factors; according to our preregistered plan, this was the decision criterion for determining the number of factors to retain. The abbreviated STARS follows the six-factor structure of

Model | RMSEA | TLI |
---|---|---|

1 Factor | 0.19 | 0.44 |

2 Factor | 0.15 | 0.64 |

3 Factor | 0.71 | 0.14 |

4 Factor | 0.82 | 0.11 |

5 Factor | 0.08 | 0.90 |

6 Factor | 0.04 | 0.97 |

We calculated Pearson correlations between our predictors and math/statistics anxiety measures. Afterward, we controlled for gender, university program, and education level/sample (i.e., SONA/undergraduate vs. Prolific/graduate) by including these three variables as covariates in multiple regression. We adjusted

Prior to adjustment for covariates, self-efficacy was significantly negatively correlated with math anxiety and all statistics anxiety subscales except for worth of statistics. After controlling for gender, university program, and education level/sample (i.e., SONA vs. Prolific), self-efficacy’s relationships became non-significant with test and class anxiety (p_{holm} = .093) and fear of statistics teachers (p_{holm} = .086); however, the other relationships remained statistically significant with mostly similar effect sizes. Effect sizes ranged from -.12 to -.29 in bivariate correlations and from -.09 to -.24 after adding covariates.

Anxiety sensitivity was positively correlated with math anxiety and each statistics anxiety subscale except for worth of statistics (p_{holm} = .08). Relationships remained statistically significant after controlling for gender, university program, and education level. Effect sizes ranged from .11 to .35 in both the bivariate correlations and after adding covariates.

The pattern for both perfectionism variables was similar. Both concern over mistakes and doubts about actions were positively correlated with math anxiety and 4 of 6 statistics anxiety subscales before and after adding covariates. Standardized regression coefficients adjusting for covariates ranged from .05 to .36 for concern over mistakes and from -.01 to .35 for doubts about actions.

Supplementary relationships between covariates and math/statistics anxiety and data visualizations are located in the

We generally found support for our hypotheses: Self-efficacy, anxiety sensitivity, and perfectionism were correlated with both statistics/math anxiety. The strongest relationships tended to be with items conceptually related to anxiety. The weakest relationships tended to be with the worth of statistics and fear of statistics subscales. These subscales tended to include items that lacked an anxious affect component (e.g.,

Effect sizes for self-efficacy’s significant relationships to math/statistics anxiety ranged from -.09 to -.24 after covariate adjustment, and there were non-significant associations with the test and class anxiety, worth of statistics, and fear of statistics teachers subscales. Self-efficacy may correlate more strongly with depression than with anxiety or attitudes towards statistics. Interventions that focus on developing and maintaining self-efficacy might modestly protect against at-risk students’ math/statistics anxiety, but the small relationships suggest relying on self-efficacy interventions alone would be insufficient.

As in many other domains (

The two dimensions of self-critical perfectionism we measured (i.e., doubts about actions, concern over mistakes) showed a similar pattern. Both dimensions positively correlated with math anxiety, test and class anxiety, interpretation anxiety, and fear of asking for help and computational self-concept but generally did not associate with the factors more closely associated with attitudes towards statistics (i.e., the remaining two STARS factors). Self-critical perfectionists may experience anxiety towards statistics, but not necessarily negative feelings towards statistics as a discipline. The correlations with statistics anxiety are consistent with prior studies (

None of our predictors were significantly correlated with the worth of statistics subscale. Though anxiety sensitivity was the only predictor we examined that was significantly related to fear of statistics teachers after covariate adjustment, its effect size was very close in magnitude to self-efficacy (-.13 vs. .14). Thus, the results for this measure provide only weak evidence of a relationship. The item wording for the fear of statistics teachers subscale focuses on perceptions of how confusing instructors are, rather than fear, so the weak evidence may be because this subscale lacks content validity.

Exploratory analyses suggest that students in arts programs have higher statistics anxiety, consistent with humanities students having a higher aversion towards math than science students (

These results should reasonably generalize to other university students in comparable universities with undergraduate or graduate programs; however, it should be noted that these samples are not representative nor randomly sampled. Procedures are straightforward, and unlikely to vary if changed from online to pen-and-paper. We do not necessarily expect generalization to other perfectionism subscales (e.g., other-oriented perfectionism). We do not expect results for self-efficacy to apply across every type of domain-specific self-efficacy (e.g., physical self-efficacy). However, results do appear to generalize across two quantitative domains (math and statistics). Results are likely contingent on the content of introductory statistics curriculums at this point in history.

Within

Further research on math/statistics anxiety protective and risk factors with a broader undergraduate sample can add to this study’s findings. The cross-sectional design of our study means we are examining behaviours and feelings at a specific time. Thus, findings may not represent individuals’ true feelings over time. Conducting cross-sectional correlational analyses, while able to establish the presence of relationships, means we cannot infer causality. Future research might use longitudinal methods.

While our study provides useful psychometric data for an abbreviated version of the STARS, we inadvertently excluded an item on the computational self-concept subscale because of an administrative error. With only two items, findings for computational self-concept are less trustworthy. Selecting the top three factor loadings from

Not all students are the same—they differ in experience, demographic characteristics, and personality. We found that individual differences in students predicted variation in statistics/math anxiety. Self-efficacy was modestly correlated with anxiety in the statistics classroom; as students’ self-confidence increases, their anxiety tends to decrease. Anxiety sensitivity intensified statistics anxiety through over-focus on the physical, cognitive, and social symptoms of anxiety. The perfectionism facets we studied focus on rigid black and white thinking (concern over mistakes) and perseveration (doubts about actions). Statistics education inevitably results in mistakes and uncertainty—which can be intolerable for perfectionistic people, resulting in greater anxiety. Demographically, women who are undergraduates in arts programs tended to experience the most fear in statistics classrooms. Nonetheless, the results for personality also held after controlling for gender, program, and graduate student status. Overall, our research suggests the importance of considering the unique personality and individual differences of our student population when teaching.

Shazia Kashif is thanked for her research assistance with some of the data analysis.

Research funded by a 2020 Social Sciences and Humanities Explore Grant (internal grant at Dalhousie University). This work was supported by a Social Sciences and Humanities Research Council Explore Grant [#39167], Halifax, Nova Scotia.

This study was reviewed by the Social Sciences and Humanities Research Ethics Board at Dalhousie University (REB# 2020-5290).

This paper was modified from Nicholas McCaughey’s honours thesis, which had the same title “The Association of Self-Efficacy, Anxiety Sensitivity, and Self-Critical Perfectionism with Statistics and Math Anxiety.” The honours thesis was not published and served as the first draft of the present manuscript.

For this article, data is freely available (

For this article, the following Supplementary Materials are available (for access see

Preregistration: A time-stamped data analysis plan and power analysis registered prior to accessing the data.

OSF Page: This page contains the raw data, data management plan, analysis scripts, codebook, all questionnaire materials, and supplementary analyses. Supplementary analyses include violin plots examining differences across faculty, a bivariate correlation matrix, scatterplots, and re-analyses using the 3-factor subscales of the Anxiety Sensitivity Index 3.

The authors have declared that no competing interests exist.