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Should we use a chi-square test for homogeneity?
Use the chi-square test for homogeneity to determine whether observed sample frequencies differ significantly from expected frequencies specified in the null hypothesis.
What is homogeneity of data?
This term is used in statistics in its ordinary sense, but most frequently occurs in connection with samples from different populations which may or may not be identical. If the populations are identical they are said to be homogeneous, and by extension, the sample data are also said to be homogeneous.
When to use the two proportion test of homogeneity?
The test of homogeneity expands the test for a difference in two population proportions, which is the two-proportion Z-test we learned in Inference for Two Proportions. We use the two-proportion Z-test when the response variable has only two outcome categories and we are comparing two populations (or two subgroups.)
How is the null hypothesis used in the test of homogeneity?
In the test of homogeneity, we select random samples from each subgroup or population separately and collect data on a single categorical variable. The null hypothesis says that the distribution of the categorical variable is the same for each subgroup or population. Both tests use the same chi-square test statistic.
How to calculate degree of homogeneity in chi square?
(We ignore the totals, as always.) For chi-square tests based on two-way tables (both the test of independence and the test of homogeneity), the degrees of freedom are ( r − 1) ( c − 1), where r is the number of rows and c is the number of columns in the two-way table (not counting row and column totals).
Is the proportion with a given response the same in all populations?
In other words, the proportion with a given response is the same in all of the populations, and this is true for all response categories. The alternative hypothesis says that the distributions differ. Note: Homogeneous means the same in structure or composition.