Page 172 - Applied Statistics Using SPSS, STATISTICA, MATLAB and R

152 4 Parametric Tests of Hypotheses

− q 1 α s p < ( xa + a + a x )
−
2
n 1 1 2 x +L k k 4.37
q s
−
− (a µ + a µ +L + a µ k ) < 1 α p .
2
k
1
1
2
n

A popular test available in SPSS and STATISTICA, based on the result 4.37, is
the Scheffé test. This test assesses simultaneously all possible pair-wise
combinations of means with the aim of detecting homogeneous groups of classes.

Example 4.15
Q: Perform a one-way ANOVA on the Breast Tissue dataset, with post-hoc
Scheffé test if applicable, using variable PA500. Discuss the results.
A: Using the goodness of fit tests to be described in the following chapter, it is
possible to show that variable PA500 distribution can be well approximated by the
normal distribution in the six classes of breast tissue. Levene’s test and one-way
ANOVA test results are displayed in Tables 4.14 and 4.15.

Table 4.14. Levene’s test results obtained with SPSS for the breast tissue problem
(variable PA500).
Levene Statistic df1 df2 Sig.
1.747 5 100 0.131

Table 4.15. One-way ANOVA test results obtained with SPSS for the breast tissue
problem (variable PA500).
Sum of df Mean Square F Sig.
Squares
Between 0.301 5 6.018E-02 31.135 0.000
Groups
Within 0.193 100 1.933E-03
Groups

Total 0.494 105

We see in Table 4.14 that the hypothesis of homogeneity of variances is not
rejected at a 5% level. Therefore, the assumptions for applying the ANOVA test
are fulfilled.
Table 4.15 justifies the rejection of the null hypothesis with high significance
( p < 0.01). This result entitles us to proceed to a post-hoc comparison using the
Scheffé test, whose results are displayed in Table 4.16. We see that the following
groups of classes were found as distinct at a 5% significance level: