# Will the small proportion ruin the ability of chi-square test? [duplicate]

Let me raise an example to be clear: say I have a 2*2 contingency table as follows:

5 10

10000 10000

I assume it satisfies the assumptions of chi-square test. But the proportion ~ 0.05% is very small. Will it cause a problem? E.g. the effect size can be small I suspect.

• What are the assumptions to which you refer and what exactly do you mean by "effective size"? I suspect your question has been addressed already in many threads on this site: please see stats.stackexchange.com/search?q=chi+square+test+assumption+5.
– whuber
Aug 28, 2018 at 17:54
• The assumption includes independence and min frequency of 5 for each cell. For effect size, a classical one for chi square test is Cramer's V score. Aug 28, 2018 at 18:19
• A minimum frequency of 5 in each cell is not an assumption of the chi-squared test. A standard rule of thumb is that the p-value is reliable provided the expected frequencies in a large proportion of cells are at least 5. That is something you can find in the link I provided earlier.
– whuber
Aug 28, 2018 at 18:38
• My mistake. But my example still satisfies the expected frequency requirements. Is it appropriate to do a chi square test? Aug 28, 2018 at 19:07
• Look to the duplicates to confirm you are correct in that supposition. They are clear about this.
– whuber
Aug 28, 2018 at 19:10