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

Valued by statisticians, enforced by editors, and confused by many authors, standard errors (SEs) and confidence intervals (CIs) remain a controversial issue in the psychological literature. This is especially true for the proper use of CIs 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 CI construction, in an attempt to encourage students and researchers in cognitive psychology to use CIs in their reports and presentations. Focusing on a simple but prevalent case of statistical inference, the comparison of two sample means, we describe possible CIs for between- and within-subjects designs. In addition, we give hands-on examples of how to compute these CIs and discuss their relation to classical t-tests.