﻿ Sample size for paired t test

# Sample size for paired t test

Menu location: Analysis_Sample Size_Paired t.

This function gives you the minimum number of pairs of subjects needed to detect a true difference DELTA in population means with power POWER and two sided type I error probability ALPHA (Dupont, 1990; Pearson and Hartley, 1970).

Information required

• POWER:  probability of detecting a true effect

• ALPHA : probability of detecting a false effect (two sided: double this if you need one sided)

• DELTA : difference in population means

• SD : estimated standard deviation of paired response differences

Practical issues

• Usual values for POWER are 80%, 85% and 90%; try several in order to explore/scope.

• 5% is the usual choice for ALPHA.

• SD is usually estimated from previous studies.

• If possible, choose a range of mean differences that you want have the statistical power to detect.

Technical validation

The estimated sample size n is calculated as the solution of:

- where d = delta/sd, a = alpha, b = 1 - power and tv,p is a Student t quantile with v degrees of freedom and probability p. n is rounded up to the closest integer.