Type I error and power of the rank transform analysis of covariance (ANCOVA) in a 3 x 4 factorial layout
The purpose of this dissertation was to compare the Type I error and power properties of the rank transform (RT) analysis of covariance (ANCOVA) with the parametric ANCOVA in a 3 x 4 factorial layout using Monte Carlo techniques. With all parametric assumptions valid, i.e., N$\sim$iid(0,1), the simulation results demonstrated that the RT ANCOVA test failed as a test for interaction due to severe Type I error inflation. The Type I error inflations associated with the RT were most pronounced when both main effects were nonnull and the interaction null. Further, Type I error inflations became progressively worse as the variate/covariate correlation and/or sample size increased. For example, with an effect size of 0.8, n = 10 observations per cell, and nominal alpha ($\alpha$) = 0.05, the Type I error rates were: 0.065 with r = 0.0; 0.066 with r = 0.3; 0.078 with r = 0.6; and 0.155 with r = 0.9. Moreover, with n = 30, the Type I error rates were: 0.123 with r = 0.0; 0.134 with r = 0.3; 0.167 with r = 0.6; and 0.443 with r = 0.9, ceteris paribus. Furthermore, Type I error inflations were even worse for nonnormal conditional distributions possessing positive kurtosis. Type I error inflations were also noted with one main effect and interaction nonnull, and the remaining main effect null. The RT ANCOVA was robust with respect to Type I error if and only if one main effect was nonnull, however. Also associated with the RT procedure was a loss of power. Power losses were more pronounced for smaller sample sizes and conditional nonnormality. As above, the stronger the variate/covariate correlation, the larger the power loss. Under conditional normality, and with respect to the robustness of the test for parallelism, the parametric ANCOVA procedure generated reasonable Type I error rates, whereas the RT became ultra-conservative as the strength of the variate/covariate correlation and/or sample size increased. Otherwise, both procedures displayed erratic Type I error rates when conditional normality was violated. The degree of inflation or conservatism for both procedures was contingent on the set of parameters being simulated.
|Year of publication:||
|Authors:||Headrick, Todd C|
Wayne State University
|Type of publication:||Other|
ETD Collection for Wayne State University
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