Psychology ETDs

Publication Date

Fall 11-15-2018


The analysis of covariance (ANCOVA) is a statistical technique originally developed by Fisher (1932) to increase the precision of the estimate of a treatment effect in experimental data. It is used when researchers have both qualitative and quantitative predictors of a continuous outcome. ANCOVA’s most basic assumptions are similar to those of analysis of variance (ANOVA) and other related linear models, but also include an additional assumption regarding the regression line relating the outcome and the covariate. This assumption, referred to as homogeneity of regression, requires that the within-group regression slopes be the same for all groups. Typically, one also assumes that the covariate is a fixed effect, but some methodologists question this practice. Consequences of either employing a model allowing for heterogeneity of regression (an ANCOHET model) or presuming that the covariate is random can be dealt with fairly easily if both do not occur simultaneously. However, a problem arises when one simultaneously encounters both a random covariate and heterogeneity of regression: the interaction between the random covariate and the fixed factor of treatment will affect the apparent evidence for the main effect of treatment. The current study investigated the utility of different methods of testing for the main effect of treatment in the presence of heterogeneity of regression with a random covariate. Using a Monte Carlo simulation, a 2x3x5x2x3 design manipulated the number of groups, sample size per group, extent of heterogeneity of regression, presence of a group effect, and test location to investigate this issue. For each combination of these factors, different types of tests of the group effect were conducted, as explained in the Method section. Two error terms, the mean square for the interaction and an average of the mean square error for an ANCOHET model and the interaction mean square, performed poorly across all simulations for all metrics. On the other hand, the ANCOHET and ANCOVA error terms produced Type I error rates, power, confidence interval coverage rates and widths, as well as average standard errors under low and medium levels of heterogeneity of regression that were acceptable. When heterogeneity of regression was high or extreme, the ANCOHET approach underestimated the true standard error, whereas the ANCOVA error term did not. Using an approach to increase the ANCOHET standard error based on Chen (2006) did not result in a large enough increase to make up for this underestimation. In conclusion, with the low and moderate levels of heterogeneity of regression typically reported in the literature the ANCOHET test of the group effect can be recommended even with a random covariate. Under large or extreme levels of heterogeneity of regression, an error term from a standard ANCOVA should instead be used.

Degree Name


Level of Degree


Department Name


First Committee Member (Chair)

Timothy E. Goldsmith

Second Committee Member

Harold D. Delaney

Third Committee Member

Davood Tofighi

Fourth Committee Member

Li Li




Analysis of Covariance, Heterogeneity of Regression, Random Covariate

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Psychology Commons