10.1 CHI-SQUARE: TESTS OFINDEPENDENCE ANDHOMOGENEITYPart 2: Tests of Homogeneity
Tests of Homogeneity Homogeneous: of the same structure or composed of similar parts When we perform a test of homogeneity, we use a contingency table and the chi-square distribution to determine whether several populations share the same proportions of distinct categories. A test of homogeneity tests the claim that different populations share the same proportions of specified characteristics.
How to Test for Homogeneity of Populations Note: when we reject the null hypothesis, we do not know which proportions differ among the populations, we only know that the populations differ in some of the proportions sharing a characteristic.
Example: Test for HomogeneityTim is doing a research project involving petpreferences among students at his college. He tookrandom samples of 300 female and 250 male students.Each sample member responded to the survey question“If you could own only one pet, what kind would youchoose?” The possible responses were: “dog,” “cat,”“other pet,”“no pet.” The results of the study follow. Pet PreferenceDoes the same proportion of males as females prefereach type of pet? Use a 1% level of significance. We’llanswer this question in several steps