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scores. If we wish to perform a multiple comparisons test to examine the
mean differences of the groups, this test must be performed on the
adjusted
and not the observed means. Furthermore, if we wish to present the group
means on which the comparison was based, we must report the
adjusted
rather than the observed means.
16.5 ASSUMPTIONS OF ANCOVA
ANCOVA is subject to all of the assumptions underlying ANOVA. These
are as follows:
Normal distribution of the dependent variable.
Independence of variance estimates.
Homogeneity of variance.
Random sampling.
These assumptions have been discussed in Chapter 5. In addition, there are
two additional assumptions that are important to meet when performing
an ANCOVA:
Linearity of regression.
Homogeneity of regression.
16.5.1 LINEARITY OF REGRESSION
We discussed in Section 16.4.1 that, based on the sample as a whole, the
scores on the covariate are used in a linear regression procedure to pre-
dict the scores of the dependent variable. In order to properly interpret
the results of the regression procedure, it is assumed that the relation-
ship between the two variables is linear. Technically, the linear regression
procedure evaluates the predictability of the dependent measure based
on a linear model incorporating the covariate; if the dependent variable
and the covariate are not related linearly (even if they are strongly related
in a more complex way), the linear regression procedure will return an
outcome of “no viable prediction.”
The most common way to determine if the data meet this linearity
assumption is to graph the data in a scatterplot. The
y
axis of such a plot
represents the dependent variable and the
x
axis represents the covariate.
Each data point represents the coordinate of these two for each case. For
example, consider the simplified data set shown in the first four columns
in Table 16.1.
Although there are two different groups represented in the data file
as shown in the first column of Table 16.1, the linearity of regression
assumption is evaluated on the sample as a whole. Thus, regardless of
group membership, Case 1 scored a 1 on the dependent variable and a 1
on the covariate, Case 2 scored a 2 on the dependent variable and a 5 on
the covariate, and so on.
