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Independent Samples T Test Sharon Pruitt

Independent Samples t-Test Analysis--Sharon Pruitt An independent samples t-test was conducted to examine whether district enrollment differed significantly between Region 1 and Region 5. Prior to conducting the analysis, assumptions for normality and homogeneity of variance were assessed. Visual inspection of histograms indicated that enrollment for Region 5 approximated normal distribution while Region 1 displayed some positive skewness due to larger districts. However, given the sample size, the t-test was considered robust to this violation. Homogeneity of variance was assessed using Levene's Test, which was statistically significant, F(1. 93) = 6.71, p = .011, indicating unequal variances. As a result, the Welch t-test was used for interpretation. Results indicated a statistically significant difference in enrollment between Region 1 and Region 5, t(77.27) = 2.83, p = .006. Districts in Region 1 (M = 2353.75, SD = 4005.16) had significantly higher enrollment than districts in Region 5 (M=987.83, SD = 490.23). Because the p-value is less than .05, I reject the null hypothesis. Effect size analysis revealed Cohen's d of 0.39, indicating a small to moderate practical effect. This suggests that while the difference in enrollment is statistically significant, the magnitude of the difference is modest.