Bartlett’s test can be used to verify that assumption. This test uses the following null and alternative hypotheses: H 0: The variance among each group is equal. H A: At least one group has a variance that is not equal to the rest. The test statistic follows a Chi-Square distribution with k-1 degrees of freedom where k is the number of groups.
The first one (Lehman, O'Rourke, Hatcher, & Stepanski, 2013) indicates explicitly that homogeneity of variance is an assumption for paired samples t-test (page 45). The second one (McDonald, 2014
To check homogeneity of variances, there are 3 famous tests: Levene's test, Brown-Forsythe test and Bartlett's test. Bartlett's test is not robust with respect to the normality, in the sense that
Levene’s test example in Python. In order to see Levene’s test in practice and its application in Python, we will use the mentioned in one of the previous sections. First, import the required dependencies: Then read the .csv file provided into a Pandas DataFrame and print first few rows: And you should get:
Both tests require the homogeneity (of variances) assumption: the population variances of the dependent variable must be equal within all groups. However, you don't always need this assumption: you don't need to meet the homogeneity assumption if the groups you're comparing have roughly equal sample sizes;
An F -test ( Snedecor and Cochran, 1983) is used to test if the variances of two populations are equal. This test can be a two-tailed test or a one-tailed test. The two-tailed version tests against the alternative that the variances are not equal. The one-tailed version only tests in one direction, that is the variance from the first population
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how to test homogeneity of variance
