Statistical Analysis for Education and Psychology Researchers

2 12 16.7500000 2.95803989

5 12 17.5833333 2.15146180

General Linear Models Procedure

Dependent Variable: ATTRIB1

Parameter Estimate T for H0: Parameter=0 Pr>|T| std Error of Estimate

0–1 2.66666667 2.86 0.0097 0.93244005

5–2 0.83333333 0.89 0.3821 0.93244005

Figure 8.19: Output for 2×2 Factorial

ANOVA on the data shown in Table

8.14

Interpretation of Computer Output

The ANOVA results section of the output is interpreted in the usual way (see
interpretation of One-way unrelated ANOVA). When interpreting main effects and
interactions a quick approximation of the importance of these effects is indicated by the
relative size of the sums of squares. In this example the variable sex has by far the largest
sums of squares. The F-ratios should be inspected for significance and main effects
should always be examined first followed by lower- to higher-order interactions. Here
there is a significant main effect for sex, F=8.18; df 1,20; p<0.05, but no significant
effect for religion.
The interaction term signifies dependence and therefore has no sensible meaning
without first considering the main effects. In this example interactions effects are small
and none significant, only the results of main effects should therefore be reported. Should
the interaction have been significant, the main effects would have to be interpreted with
caution.
The next section of output contains information about means and can be used for
plotting simple effects (effect of one variable at one level of the other). These plots can
be very informative when there is a significant interaction. We can conclude from the
ANOVA table that there is a significant difference in the mean attribution scores for
males and females and this difference does not appear to depend upon religion. The final
section of this output relates to the preplanned hypothesis tests and estimates of the
differences in mean attribution scores between males and females and between the
Christians and Sikhs. The results indicate that whereas there is a significant difference
between males and females, there is no significant difference between the religious
groups.

8.10 Split-Plot ANOVA

When to Use

The split-plot design is quite common in educational and psychological research. Split-
plot ANOVA should be considered when measures on a response variable are
continuous, when two independent groups of subjects are given two or more tests

Inferences involving continuous data 337