A researcher compares three teaching methods on final exam scores (Method A: n=18, Method B: n=42, Method C: n=30). A one-way ANOVA in SPSS is significant. Relevant SPSS output is summarized below.
Test of Homogeneity of Variances (Levene): F(2, 87) = 5.42, p = .006 ANOVA: F(2, 87) = 6.90, p = .002
Post Hoc (selected rows): Games-Howell pairwise p-values: A vs B: p = .18 A vs C: p = .003 B vs C: p < .001
Tukey HSD pairwise p-values: A vs B: p = .12 A vs C: p = .041 B vs C: p = .049
Which option is the BEST answer regarding (1) the appropriate post-hoc test to report and (2) the pattern of significant differences?
Report Tukey HSD because the omnibus ANOVA is significant; conclude all three methods differ because Tukey gives p < .05 for A–C and B–C and the omnibus test was significant.
Report Games-Howell because Levene’s test is significant (homogeneity violated) with unequal group sizes; conclude Method C differs from both A and B, while A and B do not differ significantly.
Report Bonferroni-corrected independent-samples t-tests because Levene’s test is significant; conclude only A differs from C because B–C is likely a false positive due to unequal n.
Report Fisher’s LSD because the omnibus ANOVA is significant; conclude A differs from B, but neither differs from C because Games-Howell is overly conservative.