A non-profit wants to know whether sending a communication improves constituent retention, and is it worth sending an expensive print piece over a free email? The communication can be sent by email, snail mail, or not at all (i.e., three treatments). The expected retention rate after a year in the untreated group is 93%. Any measurable difference in retention (0.5 percentage points or greater) would justify the costs of the snail mail.
How would I calculate the sample size?
If there were only two treatments (snail mail and no mail), I would do this:
/* Is the improvement at least 1 percentage point? */
proc power;
twosamplefreq groupproportions=(0.93 0.940) test=pchi power=0.80 npergroup=. sides=1; /* npergroup=7514 */
quit;
Should I use LOGISTIC?
In R it seems I would want pwr.chisq.test.
