## Bonferroni correction for power analysis with more than two groups

I'm trying to find a textbook reference for the following procedure written explicitly in the context of power analysis.  Please let me know if you know (k u e k a w a AT gmail com).

When there are more than two conditions in the experiment design, the alpha level, one of the parameters that go into power analysis, can be divided by the number of contrasts.  If there are three groups (control, treatment 1, treatment 2), there are three contrast points:

C vs T1, C vs T2, and T1 vs T2.

The typical alpha level is 0.5, so you can do:

0.5 / 3 = 0.16

and use that in the power analysis software.

If only two contrasts are important for your purpose:

0.5 / 2 = 0.25

Reference:

page 24 of

https://medschool.vanderbilt.edu/cqs/files/cqs/media/2010Ayumi.pdf

Bonferroni correction:

https://en.wikipedia.org/wiki/Bonferroni_correction

## SAS Proc POWER examples

Comparison of two independent groups:

proc power;
twosamplemeans test=diff
groupmeans = 0 | .2
stddev = 1
npergroup = .
power = .8;
run;

Comparison of dependent data (paired)

proc power;
pairedmeans test=diff
meandiff = .2
corr = 0.5
stddev = 1
npairs = .
power = .8;
run;

Comparison of proportions

proc power;
twosamplefreq test=pchi
groupproportions = (.65 .70)
nullproportiondiff = 0
power = .80
npergroup =.;
run;