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# Analysis of Covariance

I've decided to
present the statistical model for the Analysis of Covariance design
in regression analysis notation. The model shown here is for a case where there is a
single covariate and a treated and control group. We use a dummy
variables in specifying this model. We use the dummy variable Z_{i} to
represent the treatment group. The beta values (**b**'s) are
the parameters we are estimating. The value **b**_{0}
represents the intercept. In this model, it is the predicted posttest value for the
control group for a given X value (and, when X=0, it is the intercept for the control
group regression line). Why? Because a control group case has a Z=0 and since the Z
variable is multiplied with **b**_{2}, that whole
term would drop out.

The data matrix that is entered into this analysis would consist of three columns and as many rows as you have participants: the posttest data, one column of 0's or 1's to indicate which treatment group the participant is in, and the covariate score.

This model assumes that the data in the two groups are well described by straight lines that have the same slope. If this does not appear to be the case, you have to modify the model appropriately.

Copyright ©2006, William M.K. Trochim, All Rights Reserved

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Last Revised: 10/20/2006