A microarray study aims at having a high probability of declaring genes to be differentially expressed if they are truly expressed, while keeping the probability of making false declarations of expression acceptably low. Thus, in formal terms, well‐designed microarray studies will have high power while controlling type I error risk. Achieving this objective is the purpose of this paper. Here, we discuss conceptual issues and present computational methods for statistical power and sample size in microarray studies, taking account of the multiple testing that is generic to these studies. The discussion encompasses choices of experimental design and replication for a study. Practical examples are used to demonstrate the methods. The examples show forcefully that replication of a microarray experiment can yield large increases in statistical power. The paper refers to cDNA arrays in the discussion and illustrations but the proposed methodology is equally applicable to expression data from oligonucleotide arrays. Copyright © 2002 John Wiley & Sons, Ltd.