For example, i know a traditional table would be something like male / female and yes / no.
I have conducted a survey on opinions of animal research. One of my questions is "do you have ethical misgivings" which is a yes or no response. I would like to compare responses of six different job types, to see if there is a statistically significant difference among those job types as to whether they have ethical misgivings. Is this 6 x 2 permittable in a Chi squared test?
To take it further, say I again want to compare the same job categories with a nominal outcome with 4 levels (Likert scale), would a 6 x 4 table be permitted? I have a small sample size (n=81), and I have tried Ordinal Regression though fail the assumptions. This is a simple project and I would just like some basic comparisons. I am using SPSS.
Thanks so much
Best Answer
There's no specific upper limit to size of table in a chi-squared test of independence or homogeneity of proportions. Theoretically a table may be as large as you like though software may impose restrictions on what size it will deal with (typically these limits would be very large though; it would be a surprise to see modern software fail to deal with a table with several million elements in it. As a test I just now tried a big one in R -- it managed a table with a hundred million cells just fine).
However, if many of the expected counts are low there can be a problem with the chi-squared approximation to the distribution of the statistic under the null hypothesis.