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Example
9
An Alternative to Analysis of
Covariance
Introduction
This example demonstrates a simple alternative to an analysis of covariance that does
not require perfectly reliable covariates. A better, but more complicated, alternative
will be demonstrated in Example 16.
Analysis of Covariance and Its Alternative
Analysis of covariance is a technique that is frequently used in experimental and
quasi-experimental studies to reduce the effect of pre-existing differences among
treatment groups. Even when random assignment to treatment groups has eliminated
the possibility of systematic pretreatment differences among groups, analysis of
covariance can pay off in increased precision in evaluating treatment effects.
The usefulness of analysis of covariance is compromised by the assumption that
each covariate be measured without error. The method makes other assumptions as
well, but the assumption of perfectly reliable covariates has received particular
attention (for example, Cook and Campbell, 1979). In part, this is because the effects
of violating the assumption can be so bad. Using unreliable covariates can lead to the
erroneous conclusion that a treatment has an effect when it doesn’t or that a treatment
has no effect when it really does. Unreliable covariates can even make a treatment
look like it does harm when it is actually beneficial. At the same time, unfortunately,
the assumption of perfectly reliable covariates is typically impossible to meet.
The present example demonstrates an alternative to analysis of covariance in
which no variable has to be measured without error. The method to be demonstrated