Calculating sample size needed if statistical differences are analyzed by independent t-test

To determine the number of subjects in a study with two groups (an experimental group and a control group) where the main outcome is a continuous variable (one generating a mean for each group), you need to be able to estimate the following:

  • Mean outcome for group 1
  • Mean outcome for group 2
  • Standard deviation for both groups

This sheet assumes that you want an 80% chance of being able to detect the difference (beta = 0.20).  Use the following formula to calculate d (the effect size index):

 

d = (mean for group 1 – mean for group 2)/standard deviation

 

So if the mean for group 1 is 50 and the mean for group 2 is 10, and the standard deviation is 30, then d = (50 – 10)/30 = 1.33.  The sample size would be close to 10.

 

For a two-tailed test, the sample sizes per group (not for the whole study) are as follows:

d:         .10       .20       .30       .40       .50       .60       .70       .80       .90       1.20     1.40

Size:    1571    393      175      99        64        54        33        26        17        12        9