The Purpose of Chi-Square Homogeneity Test
Chi-Square Homogeneity Test
The purpose of a chi-square homogeneity test is to compare the distributions of a variable of two or more populations. As a special case, it can be used to decide whether a difference exists among two or more population proportions. For a chi-square homogeneity test, the null hypothesis is that the distributions of the variable are the same for all the populations, and the alternative hypothesis is that the distributions of the variable are not all the same (i.e., the distributions differ for at least two of the populations). When the populations under consideration have the same distribution for a variable, they are said to be homogeneous with respect to the variable; otherwise, they are said to be non-homogeneous with respect to the variable. Using this terminology, we can state the null and alternative hypotheses for a chi-square homogeneity test simply as follows:
H0: The populations are homogeneous with respect to the variable.
Ha: The populations are non-homogeneous with respect to the variable.
The assumptions for use of the chi-square homogeneity test are simple random samples, independent samples, and the same two expected-frequency assumptions required for performing a chi-square independence test. Although the context of and assumptions for the chi-square homogeneity test differ from those of the chi-square independence test, the steps for carrying out the two tests are the same. In particular, the test statistics for the two tests are identical. As with a chi-square independence test, the observed frequencies for a chi-square homogeneity test are arranged in a contingency table. Moreover, the expected frequencies are computed in the same way.
A special use of the chi-square homogeneity test is for comparing several population proportions. The population proportion is the proportion of an entire population that has a specified attribute. In these circumstances, the variable has two possible values, namely, “the
The purpose of a chi-square homogeneity test is to compare the distributions of a variable of two or more populations. As a special case, it can be used to decide whether a difference exists among two or more population proportions. For a chi-square homogeneity test, the null hypothesis is that the distributions of the variable are the same for all the populations, and the alternative hypothesis is that the distributions of the variable are not all the same (i.e., the distributions differ for at least two of the populations). When the populations under consideration have the same distribution for a variable, they are said to be homogeneous with respect to the variable; otherwise, they are said to be non-homogeneous with respect to the variable. Using this terminology, we can state the null and alternative hypotheses for a chi-square homogeneity test simply as follows:
H0: The populations are homogeneous with respect to the variable.
Ha: The populations are non-homogeneous with respect to the variable.
The assumptions for use of the chi-square homogeneity test are simple random samples, independent samples, and the same two expected-frequency assumptions required for performing a chi-square independence test. Although the context of and assumptions for the chi-square homogeneity test differ from those of the chi-square independence test, the steps for carrying out the two tests are the same. In particular, the test statistics for the two tests are identical. As with a chi-square independence test, the observed frequencies for a chi-square homogeneity test are arranged in a contingency table. Moreover, the expected frequencies are computed in the same way.
A special use of the chi-square homogeneity test is for comparing several population proportions. The population proportion is the proportion of an entire population that has a specified attribute. In these circumstances, the variable has two possible values, namely, “the