ANOVA Assumptions - Analysis of Variance Designs - page 81

Distribution analysis of: GAFscore

The UNIVARIATE Procedure
Variable: GAFscore ( GAFscore )
therapy = 1

The normality
assumptions are
not violated; the
probabilities (Sig.)
are

Tests for Normality
Statistic Test

Shapiro-Wilk
Kolmogorov-Smirnov
Cramer-von Mises
Anderson-Darling

p Value

> .05.

W
D
W-Sq
A-Sq

0.961611
0.180245
0.027473
0.186637

Pr < W
Pr > D
Pr > W-Sq
Pr > A-Sq

0.8192
>0.1500
>0.2500
>0.2500

Figure 5.37 Output for the normality tests.

The results of our analysis are presented in Figure 5.37. The Shapiro-
Wilk and the Kolmogorov-Smirnov tests show results identical to those of
SPSS;theothertwoarenotcomputedbySPSS.Ascanbeseeninthe pValue
column, all four tests have indicated that the distribution of the scores in
therapy group 1 does not depart from what would be expected of scores
that were distributed normally. That said, we would not encourage you to
claim that the five scores are distributed in a normal or any other manner,
as five scores are far too few to use as a base for any such conclusions.

5.6.5 SAS HOMOGENEITY OF VARIANCE ANALYSIS
To assess the Assumption of homogeneity of variance, from the main
menu select Analyze ➜ ANOVA ➜ One-Way ANOVA .Inthe Task Roles
window, drag GAFscore to the icon for Dependent variables and drag
therapy to the icon for Independent variable . This is shown in Figure 5.38.
Select Tests in the navigation panel to be presented with the screen
shown in Figure 5.39. Select Welch's variance-weighted ANOVA ,thetest
we would prefer using to evaluate group differences (instead of the Fisher
F ratio) if the assumption of equal variances is rejected. SAS Enterprise
Guide provides three tests of homogeneity of variance ( Bartlett's test ,the
Brown Forsyth test, and Levene's test); choose all three and click Run .
Figure 5.40 displays the results of the tests of homogeneity of variance.
The Levene test was statistically significant in the SPSS analysis ( p

=

. = .

0627). This is because
SPSS has computed the variability around the mean by using absolute
differences between the scores and the mean, a traditional way to perform
the calculation. In the One-Way ANOVA procedure, SAS uses the squared
deviations around the mean, and this produces somewhat different results.
The other tests of homogeneity all return statistically significant results
consistent with SPSS, and we conclude on that basis that the data do
not meet the assumption of homogeneity of variance. Based on that
conclusion, we would use the Welch variance-weighted ANOVA in place
of the Fisher F ratio.

025) but shows a nonsignificant result here ( p