Final answer:
Welch's correction adjusts for unequal variances in two group comparisons, while Games-Howell corrects for unequal variances and unequal sample sizes in multiple group comparisons.
Step-by-step explanation:
The difference between Welch's correction and Games-Howell post-hoc test is that Welch's correction corrects for unequal variances when comparing two means, while the Games-Howell test corrects for both unequal variances and unequal sample sizes when comparing multiple means. Essentially, Welch's is an adaptation of the t-test for scenarios where two groups have unequal variances. Games-Howell is a post-hoc analysis used after a one-way ANOVA when both assumptions of equal variances and equal sample sizes are violated. It applies a modified significance level to compensate for these issues.