Stress Level vs. GPA

A statistics project asking whether self-reported stress level has a real effect on GPA, a one-way ANOVA across 2,000 students that says yes, and not in the direction you'd expect.

Statistics
ANOVA
Rguroo

View on GitHub

Overview

A statistics group project with Jimmy Chen, Parmida Jannesari, Tong Chhin, and Brian Diaz: does self-reported stress level (Low, Moderate, High) have a statistically significant effect on GPA, across 2,000 university students from a Kaggle lifestyle survey?

Method

A one-way ANOVA on GPA ~ Stress_Level, after checking all three assumptions (independence, normality via QQ-plot, equal variance via residuals-vs-fitted) held. All three groups were unbalanced by design: 297 Low, 674 Moderate, 1,029 High, since it's a voluntary-response survey, not a random sample.

Results

F = 434.888 on df (2, 1997), p ≈ 0, so the null (equal means) gets rejected outright. A Tukey HSD post-hoc test found all three pairwise differences significant at 95% confidence, and the direction runs opposite to the obvious guess: mean GPA was highest for the High-stress group (3.26), then Moderate (3.02), then Low (2.82).

Stress Level vs GPA ANOVA method diagram: from the raw survey dataset through assumption checks, the one-way ANOVA F-test, Tukey HSD post-hoc comparisons, to the result that high-stress students had the highest mean GPA. — Tap the diagram to open it full size.

Caveats

It's an observational study, so this is association, not causation, and the report calls out real confounders that weren't measured: major/course difficulty, work hours, sleep quality. It's also a voluntary-response sample, so the finding describes these 2,000 students, not university students generally.