# Fisher and chi-squared assumptions/limitations not met

Fisher exact test is said to be used with a total sample (n) < 1000, whereas chi-squared test should be used when each category (/cell in a contingency table) >=5. What if you have an mxn contingency table where the total sample size > 1000 but some of the cells have 0 or 1 sample size?

• The rule of thumb $\ge 5$ applies to expected frequencies. It's widely considered very conservative, and I could cite authorities for $\ge 1$ as a fairly safe rule of thumb. But it's always good advice to watch out when you have very small expected frequencies. For 0 or 1 "sample size" here, read "observed frequency"? – Nick Cox May 20 '16 at 16:26
• Correct Nick; sample sizes here I was always referring to observed frequencies. – dter May 20 '16 at 16:34
• I'd take a step back and consider whether a hypothesis of no association between variables makes sense any way. When some categories in a large sample are very rare, it's often a sign that you are a long way from independence of rows and columns. That's certainly not a rule as small frequencies can be expected under independence, but I've often seen it in practice. – Nick Cox May 20 '16 at 16:37