How are the critical values for Dunnett's and Tukey's multiple comparison tests computed?

 Prism (up to version 5) does not compute critical values for the Dunnett or Tukey tests, but rather uses values tabulated by others.

It is possible, but difficult, to compute these values and we are considering do so in the future (to allow computation at more significance levels). These references explain how:

Calculation of critical values for Dunnett and Tamhane's step-up multiple test procedure
Authors: Kwong K.S.1; Liu W.
Source: Statistics and Probability Letters, Volume 49, Number 4, 1 October 2000 , pp. 411-416(6)

Computation of the distribution of the maximum studentized range statistic with application to multiple significance testing of simple effects
Authors: Margaret Diponzio; Copenhaver; Burt Holland
Journal of Statistical Computation and Simulation, 1563-5163, Volume 30, Issue 1, 1988, Pages 1 – 15

 C code for the Tukey values can be found here. 

The R command ptukey computes the probability for any values. For example, if q=3.1, and there are 5 values in each group, and the overall ANOVA has 16 degrees of freedom (residual), calculate the adjusted P value using the command below (if the two groups had different number of values, enter their harmonic mean)

 1 - ptukey(3.1,5,16)

The command qtukey similarly computes the critical values corresponding to any probability. As far as I can see, there is no similar command for the Dunnett probabilities. 

Fortran code to calculate critical values for the Dunnett test calculation can be found  at the online site for the Book by Hsu referenced below (click on the link for Fortran code, and then the link for  the qmcv procedure).