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Is there still a place for Pearson's chi‐squared test and Fisher's exact test in surgical research?

Fisher first described his exact test for 2 ¥ 2 tables of frequencies in 1925. He used it to analyse a ‘thought’ experiment that originated in the claim by a colleague, Dr Muriel Bristol, that she could tell by taste whether milk or tea had been added first to a teacup. She was told in advance that there would be four cups to which tea was added first, four to which milk was. Thus, both the column and the row marginal totals were fixed in advance – so-called double conditioning. The test involves listing all possible permutations of the entries in a 2 ¥ 2 table, with the proviso that the column and row totals remain constant (see Appendix 1). In passing, it should be said that Yates’ correction for continuity to the Pearson’s chi-squared test, which he described in 1934 as an approximation to the Fisher’s test, is irrelevant nowadays because of the ubiquity and power of personal computers. So, too, are Cochran’s rules for preferring the Fisher’s test to Pearson’s chi-squared if n < 40 or the smallest expected frequency is <5. Both these tests are popular with surgical investigators, as judged by the number of articles in four ‘general’ surgical journals with Impact Factors ranging from 1.34 to 7.90 – ANZ Journal of Surgery, British Journal of Surgery, Annals of Surgery, and Surgery – in which they were used (Table 2A). Researchers in disciplines such as physiology, pharmacology, clinical chemistry and even internal medicine usually measure the outcomes of their studies on continuous scales – as concentrations, pressures, rates and so forth. However, surgeons and surgical researchers usually express the outcomes of their studies on categorical scales. These scales may be unordered (for such variables as sex, state of origin and type of hip prosthesis) or ordered (for such variables as the stages of malignant tumours, socioeconomic status and age-group). Whether the categories are unordered or ordered, the results can usually be presented in the form of tables of frequencies. These are called r ¥ c or two-way tables, where r refers to rows and c to columns (and sometimes to the number of rows and columns). The simplest is the 2 ¥ 1 table, or single binomial. A more familiar form is the 2 ¥ 2 table, or contingency table. I have previously addressed the matter of how best to evaluate 2 ¥ 2 tables. In what follows, I shall describe 2 ¥ 1 tables and their analysis. Then, I shall remind readers of how best to analyse 2 ¥ 2 tables that consist of two independent binomials, deal with 2 ¥ c tables in which the columns are either unordered or ordered and, finally, with more complex r ¥ c tables. Table 1 A stereotype 2 ¥ 2 table of frequencies