A variety of methods for computing factor scores can be found in the psychological literature. These methods grew out of a historic debate regarding the indeterminate nature of the common factor model. Unfortunately, most researchers are unaware of the indeterminacy issue and the problems associated with a number of the factor scoring procedures. This article reviews the history and nature of factor score indeterminacy. Novel computer programs for assessing the degree of indeterminacy in a given analysis, as well as for computing and evaluating different types of factor scores, are then presented and demonstrated using data from the Wechsler Intelligence Scale for Children-Third Edition. It is argued that factor score indeterminacy should be routinely assessed and reported as part of any exploratory factor analysis and that factor scores should be thoroughly evaluated before they are reported or used in subsequent statistical analyses.

All too often researchers perform a Multivariate Analysis of Variance (MANOVA) on their data and then fail to fully recognize the true multivariate nature of their effects. The most common error is to follow the MANOVA with univariate analyses of the dependent variables. One reason for the occurrence of such errors is the lack of clear pedagogical materials for identifying and testing the multivariate effects from the analysis. The current paper consequently reviews the fundamental differences between MANOVA and univariate Analysis of Variance and then presents a coherent set of methods for plumbing the multivariate nature of a given data set. A completely worked example using genuine data is given along with estimates of effect sizes and confidence intervals, and an example results section following the technical writing style of the American Psychological Association is presented. A number of issues regarding the current methods are also discussed.

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Traditional indices of effect size are designed to answer questions about average group differences, associations between variables, and relative risk. For many researchers, an additional, important question is, “How many people in my study behaved or responded in a manner consistent with theoretical expectation?” We show how the answer to this question can be computed and reported as a straightforward percentage for a wide variety of study designs. This percentage essentially treats persons as an effect size, and it can easily be understood by scientists, professionals, and laypersons alike. For instance, imagine that in addition to d or η2, a researcher reports that 80% of participants matched theoretical expectation. No statistical training is required to understand the basic meaning of this percentage. By analyzing recently published studies, we show how computing this percentage can reveal novel patterns within data that provide insights for extending and developing the theory under investigation.

An alternative strategy for computing factor scores was introduced and compared to a popular contemporary scoring procedure. The new strategy involved unit-weighted composites of the standardized items that possessed salient factor score coefficients. Within the context of a sampling model, this strategy was shown to be superior to the common method of computing factor scores by unit-weighting and summing the standardized items with salient factor structure coefficients. Specifically, the new strategy produced factor scores that (a) captured a greater proportion of the true score variance of the factors, (b) were less confounded by true scores from factors other than those they were supposed to be estimates of, and (c) were less correlated with one another when the underlying factor structure was truly orthogonal. The implications of these findings were discussed within the context of two general applications of factor analysis, and practical recommendations were offered.