Cell values in Chi-square and Fisher's Exact test

#1
Hi, I'm deciding on which test to use to calculate the sample size in g*power. I'm confused about the cell value requirement of the chi-square test of independence. It says that each cell must be at least 5. If it has less than that Fisher's exact test must be used. My study is a 4x8 test of independence. I don't have the data yet so I don't know what the distributions will be like. Each cell might have more than 5 or may even have 0. However, Fisher's exact should only have 2 options (which mine have 4 and 8). So I'm really confused about which test to use. Thanks in advance!
 

Karabiner

TS Contributor
#2
It says that each cell must be at least 5.
No. The EXPECTED number of observations must be >= 5. It depends on the null
hypothesis, and your assumptions, and/or the study design (e.g. experimental study
with groups of equal size).

For example, if one has 2 x 4 table, including a binary outcome with expected probabilites
0.5 / 0.5, and four experimental groups with proportions 0.25 / 0.25 / 0.25 / 0.25, and a
null hypothesis of independence between group and outcome, then the expected proportion
in each cell would be 0.25 * 0.5 = 0.125. Now it is easy to calculate the total number
of observations required in order to achieve >=5 expected frequencies in each cell.

With kind regards

Karabiner
 
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