# 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, α = alpha, β = 1 - power and t_{v,p} is a Student t quantile with v degrees of freedom and probability p. n is rounded up to the closest integer.