Toby Mordkoff, University of Iowa
ABSTRACT: All statistical inferences, including those concerning population effect size, are some kind of best guess. Being a guess of some sort, they can be (in fact: always are) wrong to a certain degree. The construction of a confidence interval is one of the best ways to warn yourself and others as to possible size of the error. (Until recently, the value of confidence intervals was one of the few things that Bayesians and null-hypo testers seemed to agree on.) The construction of a confidence interval for a mean or mean difference (i.e., a non-standardized effect) is relatively simple and familiar to most people. The simplicity comes from the use of the central t distribution, which is symmetrical. In contrast, the construction of a confidence interval for any standardized measure (from Cohen's d to eta-squared) is much more complicated, because a noncentral t or F distribution must be used. Even worse: there are an infinite number of noncentral distributions, so their values cannot be tabled; they must be calculated as needed. Fortunately, in the last 20 years, advances in computer speed have allowed for the rapid calculation of values from noncentral distributions using desk-top PCs and several good freeware programs exist. In this talk, I will first define noncentral t and F distributions and then explain why these must be used when constructing confidence intervals for population effect size. I will also demonstrate how to get the key values (which is what used to be impractical) using Steiger's NDC.exe (www.statpower.new/software.html). Finally, I will provide the equations for converting the output from programs like NDC.exe into various, popular measures of effect size, as well as make some suggestions as to which should be used for various purposes.