Sample sizes set on the basis of desired power and expected effect size are often too small to yield a confidence interval narrow enough to provide a precise estimate of a population value.
Formulae are presented to achieve a confidence interval of desired width for four common statistical tests: finding the population value of a correlation coefficient (Pearson r), the mean difference between two populations (independent- and dependent-samples t tests), and the difference between proportions for two populations (chi-square for contingency tables).
Use of the formulae is discussed in the context of the two goals of research: (a) determining whether an effect exists and (b) determining how large the effect is. In addition, calculating the sample size needed to find a confidence interval that captures the smallest benefit of clinical importance is addressed.
Eric W. Corty, PhD, is Professor of Psychology, Penn State Erie, The Behrend College, Erie, Pennsylvania.
Robert W. Corty, AB, is Undergraduate Student, Harvard College, Cambridge, Massachusetts.
Accepted for publication November 2, 2010.
We thank Mike Chmielewski, MA, Doctoral Candidate, University of Iowa; Sara Douglas, PhD, Associate Professor, Frances Payne Bolton School of Nursing, Case Western Reserve University; and Kenny Sher, PhD, Professor of Psychology, University of Missouri at Columbia, for comments on a draft of this article.
Corresponding author: Eric W. Corty, PhD, Penn State Erie, The Behrend College, 4701 College Drive, Erie, PA 16563 (firstname.lastname@example.org).