Imagine we conduct a one-way independent ANOVA with four levels on our independent variable and obtain a significant result. Given that we had equal sample sizes, we did not make any predictions about which groups would differ before the experiment and we want guaranteed control over the Type I error rate, which would be the best test to investigate which groups differ?
A)Hochberg's GT2
B)Helmert
C)Orthogonal contrasts
D)Bonferroni

Question

Quizplus · Accepted Answer

Given that we did not have any specific prediction about which groups would differ, Bonferroni correction would be the best choice. Bonferroni test is one of the most conservative post-hoc tests which adjusts the p-values for multiple comparisons by dividing the alpha level by the number of tests performed. This test ensures control over Type I error rate when multiple comparisons are being made. However, it may be less powerful compared to other post-hoc tests. Hochberg's GT2 and Orthogonal contrasts are more powerful post-hoc tests but are not as conservative as Bonferroni. Helmert test is not a post-hoc test but rather a test of linear trend in the data.

Imagine We Conduct a One-Way Independent ANOVA with Four Levels