# Chi-square, expected counts & Fischer exact test

#### Trolle

##### New Member
Sitting here with a stat book and some questions are popping up.

Chi-square assumes that expected counts are greater than 5. However, in larger tables it is allowed to have up to 20% of expected counts less than 5. What is this 20% of? Is it of the cells in the matrix. For example, in a 2x4 table I have 8 cells. Of these 8 cells 1 may have expected counts less than 5 (20% of 8)? Or, am I misunderstanding the assumption?

If I do end up breaking these assumptions I can progress to Fischer's exact test. Is that correctly understood?

#### lancearmstrong1313

##### New Member
20% of the total cells. So if you have 8 total cells then you could have 1 cell (12.5%) with an expected count less than 5.

Regardless if the assumptions for Chi-Square are met, you can always use Fisher's Exact test - in fact I would probably recommend using it instead of Chi-Square. The only thing is that if you have a large dataset it can take a long time for SAS (or whatever program you are using) to compute the actual p-value (Chi-Square is not exact so its computation time is not as long).