USING CONFIDENCE-INTERVALS IN WITHIN-SUBJECT DESIGNS

We argue that to best comprehend many data sets, plotting judiciously selected sample statistics with associated confidence intervals can us efully supplement, or even replace, standard hypothesis-testing proced ures. We note that most social science statistics textbooks limit disc ussion of confidence intervals to their use in between-subject designs . Our central purpose in this article is to describe how to compute an analogous confidence interval that can be used in within-subject desi gns. This confidence interval rests on the reasoning that because betw een-subject variance typically plays no role in statistical analyses o f within-subject designs, it can legitimately be ignored; hence, an ap propriate confidence interval can be based on the standard within-subj ect error term-that is, on the variability due to the subject x condit ion interaction. Computation of such a confidence interval is simple a nd is embodied in Equation 2 on p. 482 of this article. This confidenc e interval has two useful properties. First, it is based on the same e rror term as is the corresponding analysis of variance, and hence lead s to comparable conclusions. Second, it is related by a known factor ( square root 2) to a confidence interval of the difference between samp le means; accordingly, it can be used to infer the faith one can put i n some pattern of sample means as a reflection of the underlying patte rn of population means. These two properties correspond to analogous p roperties of the more widely used between-subject confidence interval.