Thought I had my head around this but have just done some reading and am now not so sure.
So chi squared is said to be an “estimation” and Fishers exact should be used for small numbers (??)
One source I read said “less than 5” (but surely any study with less than 5 is underpowered?). but then the online calculator I use with a 2 x 2 contingency test says “only use Chi-squared if instructed to”
So if I have a sample size of 100 (total sample size – 50 in each group) – should I be using a chi-squared test or a fishers exact? p value comes out very similair but want to know what i am doing is correct
And additional to that – you can use percentages/proportions for chi squared but not fishers exact..correct?
I am no statistical expert.. but I think I can see where you are going a bit wrong..
‘less than 5’ does not refer to the total sample size at all. What it refers to is the ‘EXPECTED FREQUENCY’ within the chi-square contingency table. For each cell within the table, there is an OBSERVED frequency and an EXPECTED frequency. The observed one is the result obtained, e.g. from a questionnaire – ie the observed result. The expected frequency is the number that is expected in that cell if the null hypothesis is true (ie assumes there is no difference between the variables of interest). If more than a certain number of cells within the contingency table have an expected frequency of less than 5, then the more accurate way of calculating the p value is via the Fishers Exact test. SPSS normally tells you when this is applicable. I suggest you read a text book that explains the Chi-Square test.
There is no reason not to use Fisher’s exact test. The test gives the exact (as you’d think from the name) p-value. The Pearson chi-square tends to be a little too low, and if you do Yates’s correction, it’s a little too high.
In the old days, Fisher’s exact test was hard, especially with larger samples, but now we have computers so we don’t care.