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Unformatted text preview: Math 208 - ANCOVA 1 Analysis Of Covariance The Analysis of Covariance model (ANCOVA) are similar to the CRB design and other blocking designs like latin squares in that they are intended to re- duce the amount of error variability in the data by using an additional variable believed to be related to the response variable. In the case of ANCOVA, the variable in question is quantitative. Suppose there are 3 types of rehabilitation methods used on people who have undergone knee surgery. We want to know if there is a difference in the amount of time required in rehabilitation between the 3 methods. Suppose further that it is known that the weight of an individual also affects the amount of time needed for rehab. One option seems to be to create blocks for different weight ranges. The disadvantage of this is that the blocks are not homogenous, only nearly homogenous, as it might be difficult to find triples of people of exactly the same weight, and thus would need an interval of weights. ANCOVA avoids this design issue. 1.1 Concomitant/Covariate Variables The quantitative variables added to an ANOVA model are called concomitant variables. They are also called covariates. 1.1.1 Choice of Covariates Its clear that the covariate should have some relationship with the response. Otherwise, you are only throwing away degrees of freedom which could otherwise be going to estimate σ 2 (which would increase confidence interval sizes, etc) without actually decreasing the experimental error variance. Examples of covariates that are commonly used on human studies are prestudy attitudes, age, socioeconomic status, and aptitude. If we were interested in comparing different marketing strategies, and each store was an experimental...
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