Sample size determination in replication attempts: The standard normal z test

In the light of evidence suggesting that replication attempts are often markedly deficient in power, a case can be made for a more rigorous approach to sample size determination in such studies. A method is proposed which uses information provided by the original experiment to arrive at a distribution of probable effect sizes. The sample size to be employed in a replication attempt is that which supplies an expected power of the desired amount over the distribution of probable effect sizes. To facilitate the application of the method, formulae arc developed which provide a rapid, straightforward means of establishing the appropriate sample size when the significance test employed is the standard normal z test. Examples of sample size determination using the formulae are presented for replication studies investigating the difference between two means, the difference between two correlations, and the difference between two proportions.