The followup multiple comparison tests that Prism offer differ a depend on which kind of ANOVA you are using, so there are separate instructions for oneway ANOVA, twoway ANOVA, and threeway ANOVA. Note that the multiple comparisons choices are on two tabs of each ANOVA dialog:
•The Multiple Comparisons tab is where you set your goal, and this is quite different for each kind of ANOVA.
•The Options tab is where you choose the test you want to use, and these choices are similar for the three kinds of ANOVA and this page provides an overview that pertains to all three kinds of ANOVA.
The Options tab of all three ANOVA dialogs offers three big choices, corresponding to the three headings below, and additional choices within.
The choices for multiple comparisons that Prism makes available to you depends on three questions:
•Your goal. Which comparisons do you want to make? Answer this question, based on your experimental goals, on the multiple comparisons tab of the oneway ANOVA dialog.
•Do you want to include confidence intervals with your results? Not all multiple comparisons tests can compute confidence intervals. Answer this question, which is a personal preference not really linked to particular experimental designs, on the options tab of the oneway ANOVA dialog.
•Nonparametric?
Goal 
Report CI as well as significance? 
Method 
Compare every mean to every other mean 
Yes 
Tukey (recommended) 
No 
HolmSidak (preferred) 

Compare every mean to a control mean 
Yes 

No 

Compare selected pairs of means (up to 40) 
Yes 

No 

Linear trend? Do column mean correlate with column order? 
No 
Test for linear trend. Only available with oneway ANOVA. 
If you do oneway ANOVA and choose to not assume equal SDs in all the populations, Prism performs alternative forms of ANOVA, also alternative multiple comparisons tests.
Prism offers three methods to control the false discovery rate. All decide which (if any) comparisons to label as "discoveries" and do so in a way that controls the false discovery rate to be less than a value Q you enter.
When you choose to control the False discovery rate, Prism first computes an exact P value for each comparison. For regular ANOVA, it uses the Fishers LSD method. For nonparametric ANOVA, it uses Dunn's method without correcting for multiple comparisons. For oneway ANOVA without assuming equal variances, it uses the Welch t test. Then it takes this set of P value, and uses the method to control the false discovery rate that you chose and reports which comparisons are large enough (which P values are small enough) to be tagged as "discoveries".
For regular (parametric) ANOVA, Prism computes these with the Fisher LSD test. For oneway ANOVA without assuming equal variances, it computes P values using the Welch t test instead.
With nonparametric ANOVA, Prism uses uncorrected Dunn's test which does not correct for multiplicity.
These P values, which do not account for multiple comparisons, will be smaller than multiplicity adjusted P values. If you report these P values, explain that they are not adjusted for multiple comparisons.