One-Way Within-Subjects Design - Analysis of Variance Designs - page 269

has not been met, then you should use one of the corrections automatically
provided by SPSS.
The Mauchly test, evaluated against a chi square distribution, was sta-
tistically significant, W (9)

05. This indicates that we have
violated the assumption of sphericity. Mauchly's W is evaluated with 9
df because there are ten pairwise comparisons of the correlations (five
levels taken two at a time allows for ten combinations) and the degrees of
freedom are computed as the number of comparisons minus one.
Given a violation of sphericity, we would use one of the available
corrections shown under the heading of Epsilon in Figure 10.12. The two
most commonly used corrections are Greenhouse-Geisser and the Huynh-
Feldt , probably because the lower bound correction is considered by many
to be too conservative. All three corrections work by multiplying the
degrees of freedom for the F ratio by the respective epsilon value shown
in the table and evaluating the significance of F against these adjusted
degrees of freedom.

= 0 . 036, p <.

10.12.3 EVALUATING THE EFFECT OF THE WITHIN-SUBJECTS VARIABLE
Figure 10.13 displays the summary table for the within-subjects vari-
ance. With a significant sphericity test, we use the Greenhouse-Geisser
adjustment. Note that multiplying the Greenhouse-Geisser Epsilon value
shown in Figure 10.12 of 0.488 by the degrees of freedom for Sphericity
Assumed, we obtain the degrees of freedom shown in Figure 10.13. Thus,
(4) (0 657. This results in a more

stringent test of significance because we have fewer degrees of freedom
(less power) in evaluating the F ratio.
There are two sources of within-subjects variance that may be seen
in Figure 10.13, one for the independent variable of prepost and one for
the within-subjects error (which is the Treatment

. 488) = 1 . 951 and (28)(0 . 488) = 13 .

×

Subjects interaction).
Note that SPSS ties the error variance directly to the effect by specifying
Error(PREPOST) in its label; technically, the full label for this error term

The effect of the
within subjects
variable is statistically
significant based on
the Greenhouse-
Geisser correction.

Tests of Within-Subjects Effects

Measure: MEASURE_1

Type III Sum
of Squares

SS

Source df Mean Square Sig.

F

A

Sphericity Assumed
Greenhouse-Geisser
Huynh-Feldt
Lower-bound
Sphericity Assumed
Greenhouse-Geisser
Huynh-Feldt
Lower-bound

PREPOST

4
1.951
2.695
1.000
28
13.657
18.865
7.000

30.963
63.483
45.955
123.850
1.663
3.409
2.467
6.650

.000
.000
.000
.003

123.850
123.850
123.850
123.850

18.624
18.624
18.624
18.624

SS

A×S

Error(PREPOST)

46.550
46.550
46.550
46.550

Figure 10.13 Omnibus ANOVA for within-subjects effects.