Unit Summary 

Reading Assignment
An Introduction to Statistical Methods and Data Analysis, chapter 7.3.
Ftest to Compare Two Population Variances
To compare the variances of two quantitative variables, the hypotheses of interest are:
H_{o}: _{1}^{2}  _{2}^{2} = 0
H_{a}: _{1}^{2}  _{2}^{2} 0
For onetailed tests, you can follow section 7.3 of our textbook to set up the corresponding hypotheses and perform the test.
One of the major applications of a test to compare two population variances is for checking the equal variances assumption if you want to use the pooled variances ttest. In other situations, such as quality control problems, you may want to choose the process with smaller variances in the two processes of interest.
The Minitab command to use is homogeneity of variance test:
Stat > ANOVA > Homogeneity of Variance
An Example to Compare Two Population Variances
Using the data in the package time given in Lesson 10, we want to check whether it is reasonable to assume that the two machines have equal population variances. Recall that the data are given as:
New Machine Old Machine 42.1 41.3 42.4 43.2 41.8 42.7 43.8 42.5 43.1 44.0 41.0 41.8 42.8 42.3 42.7 43.6 43.3 43.5 41.7 44.1 = 42.14, s_{1} = 0.683 = 43.23, s_{2} = 0.750
Enter the package time for both machines into one column and name it "package time" with the type of machine indicated in another column named "machine."
The Minitab printout for the test for equal variances is as follows:
Homogeneity of Variance
Response package time Factors machine ConfLv1 95.0000 Bonferroni confidence intervals for standard deviations
Lower Sigma Upper N Factor Levels 0.447064 0.683455 1.37624 10 new 0.490520 0.749889 1.51002 10 old FTest (normal distribution)
Test Statistic : 1.204 PValue : 0.787 Levene's Test (any continuous distribution)
Test Statistic : 0.024 PValue : 0.879
How do we interpret the Minitab output?
Minitab gives us both the results for the Ftest (assuming that the two populations follow a normal distribution) and the Levene's test. The hypotheses are:
H_{o}: _{1}^{2}  _{2}^{2} = 0
H_{a}: _{1}^{2}  _{2}^{2} 0In this example, the pvalue for both the Ftest and the Levene's test is very large (larger than 0.1). We don't need to check whether the two populations are normal and we can conclude that we cannot reject the null hypothesis. If there is a discrepancy between the Ftest and the Levene's test, you need to check whether the normal assumption holds before you can use the Ftest since the Ftest is very sensitive to departure from the normal assumption.