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Example 9
here has been employed by Bentler and Woodward (1979) and others. Another
approach, by Sörbom (1978), is demonstrated in Example 16. The Sörbom method is
more general. It allows testing other assumptions of analysis of covariance and permits
relaxing some of them as well. The Sörbom approach is comparatively complicated
because of its generality. By contrast, the method demonstrated in this example makes
the usual assumptions of analysis of covariance, except for the assumption that
covariates are measured without error. The virtue of the method is its comparative
simplicity.
The present example employs two treatment groups and a single covariate. It may
be generalized to any number of treatment groups and any number of covariates.
Sörbom (1978) used the data that we will be using in this example and Example 16.
The analysis closely follows Sörbom’s example.
About the Data
Olsson (1973) administered a battery of eight tests to 213 eleven-year-old students on
two occasions. We will employ two of the eight tests, Synonyms and Opposites, in this
example. Between the two administrations of the test battery, 108 of the students (the
experimental group) received training that was intended to improve performance on the
tests. The other 105 students (the control group) did not receive any special training.
As a result of taking two tests on two occasions, each of the 213 students obtained four
test scores. A fifth, dichotomous variable was created to indicate membership in the
experimental or control group. Altogether, the following variables are used in this
example:
Variable Description
pre_syn Pretest scores on the Synonyms test.
pre_opp Pretest scores on the Opposites test.
post_syn Posttest scores on the Synonyms test.
post_opp Posttest scores on the Opposites test.
treatment
A dichotomous variable taking on the value 1 for students who
received the special training, and 0 for those who did not. This
variable was created especially for the analyses in this example.