The analysis of 2 × 1 and 2 × 2 contingency tables: an historical review

This paper describes the historical development of analytic techniques for frequency data presented as 2 x 1 or 2 x 2 contingency tables. The issues raised include: the need for a continuity correction when estimating the exceedance probability of a discrete statistic; the vulnerability of such statistics to a conservative bias when used in hypothesis testing; and the different statistical models that may underlie contingency tables. In the case of 2 x 1 contingency tables the recommended technique is the binomial test with a modified decision procedure for hypothesis testing. In the case of 2 x 2 contingency tables there is a single statistic approximating the chi-square distribution which can be used to test the hypothesis of an association between the two relevant variables and which in most practical situations is robust with respect to the occurrence of small expected cell frequencies.