the null hypothesis (the "expected values") being low. The usual rule for deciding whether the chi-squared approximation is good enough is that the chi-squared test is not suitable when the expected values in any of the cells of a contingency table are below 5, or below 10 when there is only one degree of freedom (this rule is now known to be overly conservative). In fact, for small, sparse, or unbalanced data, the exact and asymptotic p-values can be quite different and may lead to opposite conclusions concerning the hypothesis of interest. In contrast the Fisher exact test is, as its name states, exact as long as the experimental procedure keeps the row and column totals fixed, and it can therefore be used regardless of the sample characteristics. It becomes difficult to calculate with large samples or well-balanced tables, but fortunately these are exactly the conditions where the chi-squared test is appropriate. For hand calculations, the test is feasible only in the case of a 2 × 2 contingency table. However the principle of the test can be extended to the general case of an m × n table, and some statistical packages provide a calculation (sometimes using a Monte Carlo method to obtain an approximation) for the more general case. The test can also be used to quantify the overlap between two sets. For example, in enrichment analyses in statistical genetics one set of genes may be annotated for a given phenotype and the user may be interested in testing the overlap of their own set with those. In this case a 2 × 2 contingency table may be generated and Fisher's exact test applied through identifying Genes that are provided in both lists Genes that are provided in the first list and not the second Genes that are provided in the second list and not the first Genes that are not provided in either list The test assumes genes in either list are taken from a broader set of genes (e.g. all remaining genes). A p-value may then be calculated, summarizing the significance of the overlap between the two lists. Example For example, a sample of teenagers might be divided into male and female on one hand and those who are and are not currently studying for a statistics exam on the other. For example, we hypothesize that the proportion of studying students is higher among the women