Interpretation of Computer OutputTo see whether the data meets the necessary assumptions for ANOVA the plots shown in
Figures 8.15 a and b should be inspected first. A general linear trend is indicated in the
first plot and there is no discernible pattern to the scatter of points in the second plot so
the assumptions appear to have been met.
Looking at the first section of output in Figure 8.14, summary information on the
variables entered in the model is printed. You should look at the number of observations
and the levels of the class variable to check that the model has been specified as you
intended.
The next section of output presents results of the analysis of variance in the form of an
ANOVA table. You should first examine the degrees of freedom to check they are
correct. Under the column heading Source there are three row headings, Model, Error and
Corrected Total. The total variation attributable to all the independent variables in the
model, (in this case there is only one independent variable, Religion) is given as the
Model sums of squares (10.5833333). In this case, the model sums of squares is the same
as the sums of squares for Religion (in the next section) and accounts for the variability
among the sample means of the three religious groups. The sums of squares for error and
corrected sums of squares are also printed. These correspond with the values in the
worked example. A test of overall model fit which in this case is also a test of the null
hypothesis that the Religion means are equal is provided by the F-statistic, F=0.79, and
the associated p-value of 0.4671. This probability is compared to the selected alpha level
of 5 per cent, and in this example there is insufficient evidence to reject the null
hypothesis, and we conclude that the mean attribution scores for the three religious
groups are not significantly different—the same conclusion that we arrived at in the
worked example. Note that in the SAS output the exact probability of the obtained F-
statistic is printed, however, when reporting the results authors usually give a 5 per cent
or a 1 per cent level. Additional information in the output includes R-Square, a measure
of variation in the data attributable to group differences here only 6.9 per cent of the
variance in attribution scores is accounted for by Religion. The coefficient of variation,
CV statistic, is a unitless measure of variation (Root MSE/Response variable mean)×100.
For interpretation of Root MSE see section 8.2, interpretation of computer output for
linear regression.
The SAS output gives both Type I and Type III sums of squares. Type I SS takes
account of the order in which the effects (independent variables) are added to the
statistical model. The Type III SS is adjusted for all other effects in the statistical model
(order is unimportant). Generally Type III sums of squares should be used. A detailed
explanation about the types of sums of squares is given in the text SAS System for Linear
Models (SAS Institute, 1991).
A priori and post hoc Multiple Comparison ProceduresOnce a significant F-statistic has been found, the nature of the differences among the
means should be investigated. In this example a preplanned hypothesis test was not
specified and so an a priori comparison would not be used. Similarly, the F-statistic is not
Inferences involving continuous data 323