RES 6003 Module 3 Group Comparison Report Example

Comparing Groups of Nursing Graduates: An Independent-Samples t Test of Exit Examination Scores by Licensure Result and a One-Way ANOVA of Nursing GPA by Weekly Work Hours

Student Name

American College of Education

RES6003: Applied Statistics

Module 3 Assignment

Instructor Name

October 26, 2026

Introduction

Our nursing program's earlier reports first described its 186 recent graduates and then tested the program's 88.7% first-attempt licensure pass rate against its target. This report compares groups within the same graduates. Two questions come from the program's faculty. First, did graduates who failed the licensure examination score lower on the exit examination than those who passed, and by how much? Second, does nursing GPA differ among students who worked 10 or fewer hours a week, 11 to 20 hours or more than 20 hours during the program? The first question calls for a test comparing two group means; the second, with three groups, calls for a one-way analysis of variance.

Question 1: Exit Scores by Licensure Result

The 165 graduates who passed the licensure examination had a mean exit score of 949.0 (SD = 69.3), and the 21 who failed had a mean of 903.7 (SD = 69.9). The null hypothesis states that the two groups' population means are equal, and the two-sided alternative states that they differ, tested at α = .05.

An independent-samples t test assumes independent observations, roughly normal scores within each group and, in its Student form, equal population variances. Independence holds, since each graduate appears once. Skewness was near zero in the passing group (0.02) and modest in the failing group (0.43), and with 21 cases in the smaller group the test is reasonably robust to that degree of departure. Levene's test found no evidence of unequal variances, F(1, 184) = 0.01, p = .93.

Results of the t Test

Graduates who passed scored significantly higher on the exit examination than those who failed, t(184) = 2.82, p = .005. The mean difference was 45.3 points, 95% CI [13.6, 77.0], and Cohen's d was 0.65, a medium-to-large effect by conventional benchmarks (Cohen, 1992). Because the groups were so unequal in size, 165 against 21, I also ran Welch's t test, which does not assume equal variances. Delacre et al. (2017) argued that Welch's version should be the default, since it loses little when variances are equal and protects against error when they are not. Welch's test gave the same conclusion, t(25.3) = 2.80, p = .010. The difference is real and sizable, but the wide interval, from about 14 to 77 points, shows that 21 failures pin down its size only loosely.

Question 2: Nursing GPA by Work Hours

By weekly work hours, mean nursing GPA was 3.26 (SD = 0.27, n = 59) in the lightest group, up to 10 hours; 3.24 (SD = 0.32, n = 70) in the middle group, 11 to 20 hours; and 3.05 (SD = 0.33, n = 57) in the heaviest group, above 20 hours. The null hypothesis states that all three population means are equal; the alternative states that at least one differs.

One-way ANOVA shares the t test's assumptions of independence, normality within groups and equal variances. Group skewness ranged from 0.00 to -0.56, mild enough for the F test with groups of 57 to 70. Levene's test did not indicate unequal variances, F(2, 183) = 1.11, p = .33, so the standard F test was appropriate.

Results of the ANOVA

Nursing GPA differed significantly across the three work-hour groups, F(2, 183) = 8.07, p < .001, η² = .08. Work-hour group thus accounted for about 8% of the variation in GPA, a moderate effect for a single grouping variable. A significant F test shows only that the means are not all equal; it does not say which groups differ. To find out, I compared each pair of groups using the pooled error term and a Bonferroni adjustment, which multiplies each p value by the number of comparisons, three, to hold the overall Type I error rate near .05.

Graduates working more than 20 hours had a lower mean GPA than those working 10 or fewer hours, a difference of 0.20 points, adjusted p = .001, d = 0.66, and lower than those working 11 to 20 hours, a difference of 0.19 points, adjusted p = .002, d = 0.61. The two lower-hour groups did not differ, a difference of 0.02 points, adjusted p > .99. The pattern is a threshold rather than a steady decline: GPA held steady up to 20 hours a week and dropped beyond that point.

Why Not Several t Tests?

A reader might ask why the three work-hour groups were not simply compared with three separate t tests. Each test run at α = .05 carries its own 5% risk of a false positive, so three unadjusted tests push the probability that one or more of them errs to about 14%. The ANOVA tests the overall question once at the chosen level, and the follow-up comparisons are run only because that overall test was significant, with the Bonferroni adjustment keeping their combined error rate in check. Tukey's honestly significant difference test would have been a reasonable alternative and, with three groups, would have led to the same conclusions.

Effect Sizes and Practical Meaning

Lakens (2013) urged researchers to report an effect size with every test, since later studies and reviews depend on them, and both tests here show why. A p value of .005 for the exit score difference says the difference is unlikely to be zero; Cohen's d of 0.65 says it is large enough to matter. For GPA, a drop of 0.2 grade points is the difference between a B-plus and a B average, and in a program that dismisses students below 2.40 it shifts more of the heavy workers toward the danger zone. Neither effect is trivial, and neither is so large that it determines outcomes for individual students.

Cautions in Interpretation

Both comparisons are observational, so neither shows cause. Students who failed licensure scored lower on the exit examination, but the exit examination did not cause the failure; both probably reflect the same gaps in preparation. Students who worked more than 20 hours had lower GPAs, but they may differ from other students in family responsibilities, finances or prior schooling, any of which could depress grades independently of work. A further caution concerns the remediation course: Module 1 showed that students who took it had lower exit scores, so any later comparison of remediated and non-remediated students must account for who was sent to remediation in the first place.

Implications for the Program

The results suggest two practical steps. The exit examination's ability to separate passing from failing graduates supports using it as an early signal, though the overlap between groups, with standard deviations near 70 points around means 45 points apart, means it should flag students for support rather than predict individual results. And the GPA threshold above 20 work hours a week suggests that advising, scholarship support or flexible clinical scheduling aimed at heavy workers could help, a hypothesis the program could test directly. A useful next step would be to record why students work long hours, so that support can be matched to the reason, whether family income, child care or the cost of the program itself.

Conclusion

Graduates who passed licensure outscored those who failed on the exit examination by about 45 points, t(184) = 2.82, p = .005, d = 0.65, and nursing GPA was lower in the heaviest work group than in either other group, F(2, 183) = 8.07, p < .001, η² = .08. Module 4 examines these relationships as continuous associations through correlation, regression and a test of independence.

References

Cohen, J. (1992). A power primer. Psychological Bulletin, 112(1), 155-159. https://doi.org/10.1037/0033-2909.112.1.155

Delacre, M., Lakens, D., & Leys, C. (2017). Why psychologists should by default use Welch's t-test instead of Student's t-test. International Review of Social Psychology, 30(1), 92-101. https://doi.org/10.5334/irsp.82

Lakens, D. (2013). Calculating and reporting effect sizes to facilitate cumulative science: A practical primer for t-tests and ANOVAs. Frontiers in Psychology, 4, Article 863. https://doi.org/10.3389/fpsyg.2013.00863