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http://www.microbiologybytes.com/maths/1011-21.html

Pearson's Chi-Square test Assumptions:

The chi-square test is a non-parametric test which assumes that the data analyzed:

1. Consist of nominal or ordinal variables.
2. Consist of entire populations or be randomly sampled from the population.
3. No single data point should be zero (if so, use Fisher's exact test - below).
4. All the objects counted should be independent of one another.
5. 80% of the expected frequencies should be 5 or more (if not, try aggregating groups or use Fisher's exact test for small sample sizes).

If you use the chi-square test under other circumstances, the results will be meaningless!

IMPORTANT:

• Note that acceptance or rejection of the null hypothesis can only be interpreted strictly in terms of the question asked, e.g. "There is a difference between the groups" or "There is no difference between the groups" and NOT EXTRAPOLATED to "There is a difference between the groups because...

Fisher's exact test is an alternative to c² for testing the hypothesis that there is a statistically significant difference between two groups. It has the advantage that it does not make any approximations (Fisher's exact test), and so is suitable for small sample sizes.

Assumptions of Fisher's exact test:

Fisher's exact test is a non-parametric test which assumes that the data analyzed:

1. Consist of nominal or ordinal variables.
2. Consist of entire populations or be randomly sampled from the population, as in all significance tests.
3. Independent observations: It is assumed that the value of the first unit sampled has no effect on the value of the second unit. Pooling data from before-after tests or matched samples would violate this assumption.
4. Mutual exclusivity: A given case may fall in only one class.