I am comparing the response to a drug under five different conditions. The textbook instruction is to perform a one-way ANOVA followed by a post hoc test if necessary.
The P value from an ANOVA is borderline (0.056), however, my data does not fit the criteria for an ANOVA, as the within-group variation varies greatly between groups. Is it acceptable to perform a post hoc test (in my case, t-tests with a multiple comparison adjustment such as Benjamini-Hockberg would seem appropriate) without doing an ANOVA? If so, why does anyone bother with ANOVAs in the age of computers, when multiple corrected tests can be performed so easily?