Confidence intervals for two sample means: Calculation, interpretation, and a few simple rules

Abstract

Valued by statisticians, enforced by editors, and confused by many authors, standard errors (SEs) and confidence intervals (C/s) remain a controversial issue in the psychological literature. This is especially true for the proper use of C/s for within-subjects designs, even though several recent publications elaborated on possible solutions for this case. The present paper presents a short and straightforward introduction to the basic principles of C/construction, in an attempt to encourage students and researchers in cognitive psychology to use C/s in their reports and presentations. Focusing on a simple but prevalent case of statistical inference, the comparison of two sample means, we describe possible C/s for between- and within-subjects designs. In addition, we give hands-on examples of how to compute these C/s and discuss their relation to classical f-tests.