Cochran (1952): none of the expected cell frequencies should be less than one. No more than 20 % of the expected cell frequencies should be less than 5. Cochran, W. G. (1952). The chi-square goodness-of-fit test. Annals of Mathematical Statistics, 23, 315-345. The test statistics is approximately Chi-squared, under the assumption that all expected cell frequencies are at least 1.5, in which case this approximation is satisfactory. Morris H. DeGroot Probability and Statistics. Addison Wesley. Application of the chi-square formula. Let O be the observed value of each cell in a table. Let E be the expected value calculated in the previous step. For each cell, subtract E from O, then square the result and then divide by E. Do this for every cell and sum all the results. This is the chi-square value for the table. If Yates' correction for continuity is to be applied, due to cell counts below 5, the calculation is the same except for each cell, subtract an additional .5 from the difference of O - E, prior to squaring and then dividing by E. This reduces the size of the calculated chi-square value, making a finding of significance less likely -- a penalty deemed appropriate for tables with low counts in some cells.