Multiple Comparison Procedures - Analysis of Variance Designs - page 154

This is the probability of
the F ratio occurring by
chance alone.

A

ANOVA

satscore

Sum of
Squares Sig.

df Mean Square F

Between Groups
Within Groups
Total

230497.1 4 57624.286 43.467 .000

39771.429 30 1325.714

270268.6 34

SS
quadratic,
and cubic
components.

A linear,

B

ANOVA

satscore

This is the
probability of
the differences
occurring by
chance alone
for linear,
quadratic,
and cubic.

Sum of
Squares
230497.143
219520.000
10977.143
7546.939
3430.204
3430.000
.204
39771.429
270268.571

df Mean Square F Sig.

Between Groups (Combined)

4
1
3
1
2
1
1
30
34

57624.286
219520.000
3659.048
7546.939
1715.102
3430.000
.204
1325.714

43.467
165.586
2.760
5.693
1.294
2.587
.000

.000
.000
.059
.024
.289
.118
.990

Linear Term Contrast

Deviation

Quadratic Term Contrast

Deviation

Cubic Term Contrast

Deviation

Within Groups
Total

Contrast

SS S/A

Figure 7.23 A shows omnibus ANOVA discussed in Chapter 6 and shown in Fig-
ure 6.8. B shows output for the trend analysis we just performed.

7.24 OUTPUT FOR POLYNOMIAL CONTRASTS
(TREND ANALYSIS) IN SPSS

Recall that we already performed the omnibus ANOVA in the context
of Chapter 6. We reproduce the summary table for that analysis in
Figure 7.23A so that you can see what the polynomial contrast analysis
has accomplished. Figure 7.23B displays the results of the trend analysis
that we just performed.
Note first the sum of squares for Between Groups from the earlier
analysis in Figure 7.23A. It has a value of 230497.143. This value represents
the effect of the independent variable of study time. In the trend analysis
that we just performed, we see that sum of squares for the BetweenGroups
(Combined) also has a value of 230497.143. The reason for why these two
values is the same is that they represent the same entity - the overall
between-groups variance is the composite of all the polynomial trends;
that is, the sum of all the polynomial sums of squares is equal to the
between-groups sum of squares.
Our trend analysis has partitioned the between-groups sum of squares
(230497.143) into its polynomial portions or contrasts. The summary