Using generalized linear models (GLMs) to model errors in motor performance

Because of differences in design factors, experiments in human motor performance sometimes produce a wide range in variability or consistency in a subject's individual errors. These differences in variation often lead to heterogeneity in the variance-covariance matrices between group factors, which prohibits the use of repeated-measures (RM) ANOVA or MANOVA techniques to analyze the error data. Provided certain conditions are met, however, each subject's individual errors can be collapsed into the summary error measures, constant error (CE) and variable error (VE), which can still provide a more than adequate description of the subjects' performance. This article proposes the appropriate conditions and the corresponding generalized linear models (GLMs) with which a subject's individual errors, recorded in short-term motor memory research, can be combined into the summary measures, CE and VE, which can be analyzed subsequently as the dependent variables in the experimental design. The CE scores can be modeled using GLMs without requiring the assumption of homogeneity of variances. Similarly, the VE scores can be modeled as a GLM, using a log-linear regression model that assumes a gamma distribution, rather than using a traditional analysis of variance (ANOV A) model that assumes an inappropriate normal error distribution for these scores. An example reveals that the analysis of VE scores, unlike the analysis of CE scores, is able to differentiate between group practice methods. These differences tend to be underestimated by traditional ANOVA methods, however. Differences between the ANOV A and GLM analyses of the VE scores are further clarified by simulation. Based on differences like those observed in the example, when simulated VE scores were analyzed, assuming both a normal and a gamma distribution, the power of the gamma tests was found to be superior to the normal analyses in all but a small range of cases, in which such differences were found to be negligible. Hence, it is only by declaring the VE scores to have a GLM with a gamma distribution that the anticipated group practice differences can be properly identified.