Analysis of Covariance and Randomized Block Design with Heterogeneous Slopes |
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| Authors: | Alan J Klockars S Natasha Beretvas |
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| Institution: | 1. University of Washington;2. University of Washington;3. S. Natasha Beretvas is now at the University of Texas at Austin |
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| Abstract: | The authors compared the Type I error rate and the power to detect differences in slopes and additive treatment effects of analysis of covariance (ANCOVA) and randomized block (RB) designs with a Monte Carlo simulation. For testing differences in slopes, 3 methods were compared: the test of slopes from ANCOVA, the omnibus Block × Treatment interaction, and the linear component of the Block × Treatment interaction of RB. In the test for adjusted means, 2 variations of both ANCOVA and RB were used. The power of the omnibus test of the interaction decreased dramatically as the number of blocks used increased and was always considerably smaller than the specific test of differences in slopes found in ANCOVA. Tests for means when there were concomitant differences in slopes showed that only ANCOVA uniformly controlled Type I error under all configurations of design variables. The most powerful option in almost all simulations for tests of both slopes and means was ANCOVA. |
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| Keywords: | ANCOVA randomized block Type I error |
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