Author: Amira Mandour
Biostatistician | Clinical Trials & Statistical Modeling
Expert
This study explores how excitement toward studying statistics, along with age and gender, relates to students’ attitude toward the subject. The attitude measure is represented on a four-point ordinal scale, ranging from “The WORST” to “THE BEST”.
Given the ordered nature of the outcome, an Ordinal Logistic Regression (OLR) model is used to analyze the relationship between predictors and the ordinal response.
Objective:
Primary Objective:To determine the relationship between students’ excitement toward studying statistics and their attitude using ordinal logistic regression.
Secondary Objectives:To evaluate the effects of age and sex on students’ attitudes toward statistics.
To check whether the proportional odds assumption holds for the model.
Ordinal logistic regression was fitted using the Proportional Odds Model via the clm() function from the ordinal package in R. The model estimates the log-odds of being in a higher attitude category versus all lower categories.
Model comparison:A null model (intercept only) and a full model (including predictors) were fitted.
A likelihood ratio test (anova(modelnull, model1)) was used to assess whether the predictors significantly improved model fit.
Model fit statistics:AIC and log-likelihood were examined for overall model fit.
Nagelkerke (Cragg & Uhler) pseudo R² was calculated using the nagelkerke() function from the rcompanion package to quantify the proportion of variance explained by the model.
Proportional odds assumption:
Evaluated using the nominal_test(model1) function from the ordinal package; no significant violations were observed.
Model diagnostics included:Proportional odds assumption test, evaluated using the nominal_test() function from the ordinal package; no significant violations were observed.
Goodness of fit via pseudo R² measures.
Odds ratios and 95% confidence intervals for interpretability.
Significance was evaluated at α = 0.05.
Descriptive Analysis and Rationale for Modeling:
Table 1 presents participants’ demographic and motivational characteristics by attitude toward studying statistics, measured on a four-level Likert scale (“The WORST” to “THE BEST”). Participants’ attitudes tended to improve with younger age, although the differences were not statistically significant (mean age 21.2 years in the “THE BEST” group vs. 26.5 years in “The WORST” group; p = 0.30). Sex distribution was similar across attitude categories (p = 0.14).
In contrast, students’ excitement toward statistics increased with better attitudes, with a mean score of 2.65 in the “THE BEST” group versus 2.32 in “The WORST” group, a statistically significant difference (p = 0.017).
These findings suggest that while age and sex are not strongly associated with attitude, higher excitement toward statistics is linked to more positive attitudes, supporting the use of ordinal logistic regression to quantify the relationship between excitement and attitude while adjusting for demographic factors.
| Variable | Attitude Category | p-value2 | |||
|---|---|---|---|---|---|
| The WORST (n=13)1 | Bad (n=14)1 | Okay (n=31)1 | THE BEST (n=37)1 | ||
| Age (years) | 26.54 ± 12.29 | 23.86 ± 4.29 | 22.16 ± 3.13 | 21.24 ± 1.83 | 0.3 |
| Sex | 0.14 | ||||
| Male | 6 (46%) | 5 (36%) | 7 (23%) | 18 (49%) | |
| Female | 7 (54%) | 9 (64%) | 24 (77%) | 19 (51%) | |
| Excitement Toward Statistics | 2.32 ± 0.34 | 2.40 ± 0.33 | 2.52 ± 0.41 | 2.65 ± 0.38 | 0.017 |
| 1 Mean ± SD; n (%) | |||||
| 2 Kruskal-Wallis rank sum test; Fisher’s exact test | |||||
Examining the Determinants of Students’ Attitudes Toward Studying Statistics: The Role of Age, Sex, and Excitement:
Figure 1 illustrates the distribution of students’ ages across the four attitude categories toward studying statistics, from “The WORST” to “THE BEST.”
The boxplots show a slight trend where younger students tend to report more favorable attitudes, as indicated by the lower ages in the higher attitude categories. However, the difference in age between attitude groups was not statistically significant (p = 0.30).
This suggests that, within this sample, age may have a minor influence on attitude, but it does not appear to be a strong determinant of students’ perceptions toward learning statistics.
Figure 2 shows the distribution of sex across different attitude categories toward studying statistics.
The stacked bar plot represents the proportion of males and females within each attitude group, from “The WORST” to “THE BEST.”
Overall, the proportions of females appear relatively higher than males across categories, but the difference was not statistically significant (p = 0.14).
This suggests that sex does not strongly influence students’ attitudes toward learning statistics in this sample.
Figure 3 presents the relationship between students’ excitement toward statistics and their attitudes toward studying the subject.
The plot shows that as excitement scores increase, students tend to report more favorable attitudes — progressing from “The WORST” toward “THE BEST.”
The red points mark the mean excitement levels within each attitude category, which follow a clear upward trend.
This pattern indicates that greater enthusiasm for statistics is associated with more positive attitudes, and the difference in excitement levels across attitude groups was statistically significant (p = 0.017). Overall, the figure suggests that excitement plays a key motivational role in shaping students’ perceptions toward learning statistics.
Figure 4 illustrates how students’ attitudes toward studying statistics vary with both age and excitement toward the subject.
In the left panel, attitude levels tend to improve modestly among younger students, indicating that younger participants generally express more favorable attitudes toward statistics compared with older peers, although the difference was not statistically significant (p = 0.30). In contrast, the right panel shows a clear positive association between excitement and attitude, students with higher excitement scores consistently report more positive attitudes (p = 0.017).
Taken together, these findings suggest that enthusiasm for statistics is a stronger determinant of positive attitudes than age, emphasizing the motivational aspect of students’ perceptions toward learning the subject.
Figure 5 displays the relationship between students’
excitement toward statistics and their attitudes
toward studying the subject, stratified by sex.
Across both males and females, higher excitement scores are associated
with more favorable attitudes (ranging from “The WORST” to
“THE BEST”). The pattern suggests that excitement may be a key
predictor of positive attitudes.
Results:
Model Summary
An ordinal logistic regression was fitted to examine how excitement, age, and sex relate to students’ attitudes toward studying statistics. The dependent variable, attitude toward statistics (Attitude), was measured on a four-point ordinal scale ranging from “The WORST” to “THE BEST.”
| Characteristic | OR1 | 95% CI1 | p-value |
|---|---|---|---|
| Age (years) | 0.88 | 0.79, 0.95 | 0.006 |
| Sex | |||
| Male | — | — | |
| Female | 0.69 | 0.30, 1.54 | 0.4 |
| Excitement Score | 3.97 | 1.41, 12.3 | 0.012 |
| Model Fit: AIC = 237.12, LogLik = -112.56, Pseudo R² = 0.2 | |||
| 1 OR = Odds Ratio, CI = Confidence Interval | |||
The findings suggest that excitement toward studying statistics is a key predictor of students’ attitudes toward the subject. Specifically, students who report higher excitement levels are significantly more likely to view statistics positively. This aligns with educational psychology theories that link emotional engagement with improved academic perceptions and outcomes.
Age showed a small but significant negative effect, suggesting that younger students tend to have more favorable attitudes toward statistics. This could reflect differences in exposure, confidence, or adaptability to new learning methods.
No significant gender difference was observed, indicating that male and female students generally share similar attitudes once excitement and age are accounted for.
The model demonstrated a moderate fit to the data, with a log-likelihood of −112.56 and an Akaike Information Criterion (AIC) of 237.12. The model’s pseudo R² value of 0.20 indicates that approximately 20% of the variability in the ordered response categories was explained by the predictors included in the model.
This suggests that Age, Sex, and Excitement collectively have a meaningful, though not exhaustive, influence on the outcome variable.
The proportional odds assumption was evaluated using the nominal_test() function from the ordinal package. The test showed no evidence of non-proportionality for any predictor, as relaxing the proportional odds constraint did not improve model fit. This indicates that the assumption was met and that the effects of Age, Sex, and Excitement can be interpreted as consistent across all thresholds of the outcome.
Conclusion
This study demonstrates that excitement is a significant determinant of positive attitudes toward statistics, independent of age and sex. Efforts to enhance excitement and engagement in statistics courses — such as active learning, applied examples, and data visualization — could foster better attitudes and possibly improve learning outcomes.