Network Models to Organize a Dispersed Literature: The Case of Misunderstanding Analysis of Covariance

Abstract

Introduction Analysis of covariance (ANCOVA) remains a widely misunderstood approach for dealing with group differences on potential covariates (Miller & Chapman, 2001). This misunderstanding of the ANCOVA has a long history and its discussion is dispersed across fields and journals, making it difficult to obtain a systematic overview. Here we present a network method to organize the results of a literature search conducted by 44 Master's students as part of the 2016 University of Amsterdam course "Good Research Practices". The ANCOVA Pitfall Dora wants to assess whether, in her own university, men earn more than women. She has access to the salaries of a subset of researchers, and, as expected, men earn significantly more than women (p < .005). But wait! The men in her sample are also older than the women, and this confounds the results: perhaps the salary difference is due to age rather than gender. To address this confound and "control for" age, Dora includes age as a covariate in an ANCOVA. This procedure is tempting but statistically problematic. The ANCOVA is easier to interpret correctly when age influences salary but does not differ across the groups. As explained in Miller and Chapman (2001; but see chapter 10 in Judd, McClelland, & Ryan, 2011, and Field, 2013, pp. 484-486), when groups differ on a covariate (e.g., age), removing the variance associated with the covariate also removes the shared variance associated with the group (e.g., gender). As a result, the grouping variable loses some of its representativeness. This occurs mostly when groups are pre-existing and are not obtained by random assignment (Jamieson, 2004). As an example, assume one has access to the height of several mountain peaks in the Himalayas and the Pyrenees (Cohen & Cohen, 1983). One may test whether the mountain ranges differ in height and it may be tempting to include air pressure as a covariate; after all, air pressure differs across the

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