Psychological theories are statements of constraint. The role of hypothesis testing in psychology is to test whether specific theoretical constraints hold in data. Bayesian statistics is well suited to the task of finding supporting evidence for constraint, because it allows for comparing evidence for 2 hypotheses against each another. One issue…

The purpose of the recently proposed "p[subscript rep]" statistic is to estimate the probability of concurrence, that is, the probability that a replicate experiment yields an effect of the same sign (Killeen, 2005a). The influential journal "Psychological Science" endorses "p[subscript rep]" and recommends its use…

In this article, the authors have 2 aims. First, hierarchical, nonhierarchical, and nonstandard log-linear models are defined. Second, application scenarios are presented for nonhierarchical and nonstandard models, with illustrations of where these scenarios can occur. Parameters can be interpreted in regard to their formal meaning and in regard…

Most psychology journals now require authors to report a sample value of effect size along with hypothesis testing results. The sample effect size value can be misleading because it contains sampling error. Authors often incorrectly interpret the sample effect size as if it were the population effect size. A simple solution to this problem is to…

Standard least squares analysis of variance methods suffer from poor power under arbitrarily small departures from normality and fail to control the probability of a Type I error when standard assumptions are violated. This article describes a framework for robust estimation and testing that uses trimmed means with an approximate degrees of…

Underpowered studies persist in the psychological literature. This article examines reasons for their persistence and the effects on efforts to create a cumulative science. The "curse of multiplicities" plays a central role in the presentation. Most psychologists realize that testing multiple hypotheses in a single study affects the Type I error…

Latent class analysis (LCA) provides a means of identifying a mixture of subgroups in a population measured by multiple categorical indicators. Latent transition analysis (LTA) is a type of LCA that facilitates addressing research questions concerning stage-sequential change over time in longitudinal data. Both approaches have been used with…

For comparing nested covariance structure models, the standard procedure is the likelihood ratio test of the difference in fit, where the null hypothesis is that the models fit identically in the population. A procedure for determining statistical power of this test is presented where effect size is based on a specified difference in overall fit…