Experimental design question

The Dunnett test is characterized by a particular minimum critical t-value (t), specificed for a given number of treatments (k) and degrees of freedom (nk-k, where n is the number of replicates, for a balanced experiment). If you hold n constant, how does t change as a function of k when k becomes large? Either a closed form equation (if there is one), or else a big table of Dunnett critical values on which I can do a regression would be fine. I’m looking for a bigger table than I can find through a google search or in a statistics textbook. I’ve tried using the standard table from statistics textbooks and it’s not detailed enough for me to really see the behavior at large k.

The basic issue here is I want to plot exactly how the critical value changes, for comparisons against a single control group, as you add more and more ‘test’ groups.

http://www.stat.ufl.edu/~winner/tables/dunnett-2side.pdf

http://www.psychology.gatech.edu/psyc6019lab/Tables/Dunnett.pdf

How to go larger ?

  1. One reason its not published is that your statistics package has it inbuilt.

So you might be able to find a function eg, dunnet_critical_value(n,alpha,t) …

  1. If you don’t have the function to calculate it, why bother going to look up the formula ?

graph the curve for n from 3 to 12…

What shape is that curve ? extrapolate the curve to 15, 20… you can see the value stops changing much … so doubling the number of groups doesn’t change it too much?

Interpretation: law of large numbers kicking in… its really a numerical statement of whats happening until you have large numbers…