Context: I have a sample with N=707
Respondents had to first choose what was their telecomunications service provider:
Variable 2: Brand: At&T, Comcast, Verizon, Vodafone
Afterwards respondents were randomly assigned to each group were exposed to a specific stimuli according to the group.
Variable 1: Groups: 1,2,3,4,5,6,7
I want to check if the brands distributions between the groups are statisticall significant ot not?
I was checking the Chi-Square test of homogeneity (2xC), what would be the equivalent test for conducting with polytomous variables with more than 3 levels?
Dear Andre,
The direct analog of the chi-square test of homogeneity is the chi-square test for contingency tables. But I think, that you can not apply this method because there are two independent factors that have an affect on your observations. I suggest you to use 1-way within subjects ANOVA or 2-way between subjects ANOVA for your purpose. You can read about these tests in a book of B. Tabachnik "Using multivariate statistics".
If you want to see if there is an association between Brand and Group, the chi-square test of association is appropriate. It works for R x C tables.
There are caveats for using the test when there are low "expected" counts in the table.
This is the same test as chi-square test of homogeneity, and chi-square test of independence. Just different names.
Another name for it is the Chi-square test of association.
Many people use the rule of thumb that the Chi-square approximation is good enough if all expected frequencies are 5 or greater. But for tables larger than 2 x 2, that rule of thumb is conservative. A better rule is that the approximation is good if "[n]o more than 20% of the expected counts are less than 5 and all individual expected counts are 1 or greater" (Yates, Moore & McCabe, 1999, p. 734). For more info, see this summary on my website:
- https://sites.google.com/a/lakeheadu.ca/bweaver/Home/statistics/notes/chisqr_assumptions
HTH.
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