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My table of chi-square test for homogeneity has 3x5 cells, 3 samples to a likert scale item. Most cells in the table have a frequency count of less than two, so it is recommended to discard the column of which contains a cell with frequency of less than two. How will this affect my hypothesis if I discard the entire column just because a cell has a value of less than 2 or 0?

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1) Likert scale items are ordered. Chi-square ignores the information in that ordering. You're tossing away a lot of your power against interesting alternatives.

You would probably benefit from investigating some of the potential alternatives to straight homogeneity when you have ordered categories.

2) the usual requirement (which is usually too stringent in any case) isn't for a minimum observed count, it's for a minimum expected count

3) don't discard your valuable data, you have so little of it:

a) (not great, but better): you can combine it with an adjacent category (another small one if possible)

b) even better still, you can simulate from the distribution of the chi-square with the same margins, and with a large enough simulation, get accurate p-values. This is available right in the regular chisq.test command in R, for example (or you could do an 'exact' test, whether based off the chi-square statistic or the fisher test. )

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Use fisher's exact test instead which gives a more accurate p value than the chi squared for low sample populations hyper-geometric distributions (finite distribution parameters).

This link below tell of HYPGEOMDIST which is a pretty powerful excel function that should get you started.

http://www.real-statistics.com/binomial-and-related-distributions/hypergeometric-distribution/

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