#### 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