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.