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7.8 HYPOTHESIS TESTING: THE RATIO OF TWO POPULATION VARIANCES 271
for example, that the SAS system uses a folded F-test procedure. MINITAB uses two different
tests. The first is an F-test under the assumption of normality, and the other is a modified
Levene’s test (1) that is used when normality cannot be assumed. SPSS uses an unmodified
Levene’s test (2). Regardless of the options, these tests are generally considered superior
to the variance ratio test that is presented in Example 7.8.1. Discussion of the mathematics
behind these tests is beyond the scope of this book, but an example is given to illustrate
these procedures, since results from these tests are often provided automatically as outputs
when a computer program is used to carry out a t-test.
EXAMPLE 7.8.2
Using the data from Example 7.3.2, we are interested in testing whether the assumption
of the equality of variances can be assumed prior to performing a t-test. For ease of discussion,
the data are reproduced below (Table 7.8.1):
TABLE 7.8.1 Pressures (mm Hg) Under the Pelvis During Static Conditions for
Example 7.3.2
Control 131 115 124 131 122 117 88 114 150 169
SCI 60 150 130 180 163 130 121 119 130 148
Partial outputs for MINITAB, SAS, and SPSS are shown in Figure 7.8.2. Regardless of
the test or program that is used, we fail to reject the null hypothesis of equal variances
1H 0 : s 2 1 = s 2 2 2 because all p values 0.05. We may now proceed with a t-test under
the assumption of equal variances.
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MINITAB Output
F-Test
Test Statistic 0.46
P-Value 0.263
Levene’s Test
Test Statistic 0.49
P-Value 0.495
SPSS Output
Levene’s Test for
Equality of Variances
F
Sig.
.664 .482
SAS Output
Equality of Variances
Variable Method Num DF Den DF F Value Pr F
pressure Folded F 9 9 2.17 0.2626
FIGURE 7.8.2 Partial MINITAB, SPSS, and SAS outputs for testing the equality of two
population variances.