Nonparallel Slopes Using Analysis of Covariance for Body Size Adjustment May Reflect Inappropriate Modeling

Abstract

One advantage, yet unreported, of allometric modeling over simple analysis of covariance (ANCOVA), is that the former is theoretically less likely to violate the parallel slopes assumption, particularly when body size is the covariate. To explain in a tutorial format, we used real data to describe gender differences in a maximal machine lift (ML) using body mass (BM) as the covariate in 705 active duty servicemembers. Traditional ANCOVA revealed that slopes were different, t(701) = 2.44, p = .015, thereby precluding quantification of the BM-adjusted gender difference. Using the theoretically more appropriate allometric approach, slopes were not different, t(701) = 0.30, p = .76. We then could compare men to women, finding that men were 74.5% stronger than women in BM-adjusted ML -- a finding more interpretable and defensible than that based on the nonparallel slopes situation. We recommend that for ANCOVA with body size as the covariate and a physiologic outcome variable as the dependent variable, allometric modeling at least be considered.