Limitations of the application of fourfold table analysis to hospital data

J Berkson - Biometrics Bulletin, 1946 - JSTOR
J Berkson
Biometrics Bulletin, 1946JSTOR
In the biologic laboratory we have a method in table 1-b. The entries, a, b, с and d are of
procedure for determining the effect of an manipulated arithmetically to determine agent or
process that may be considered typ-whether there is any correlation between A ical. It
consists in dividing a group of animals and B. A considerable number of indices into two
cohorts, one considered the" experi-have been elaborated to measure this correlamental
group," the other the" control." On tion. Pearson has given the formula for calthe …
In the biologic laboratory we have a method in table 1-b. The entries, a, b, с and d are of procedure for determining the effect of an manipulated arithmetically to determine agent or process that may be considered typ-whether there is any correlation between A ical. It consists in dividing a group of animals and B. A considerable number of indices into two cohorts, one considered the" experi-have been elaborated to measure this correlamental group," the other the" control." On tion. Pearson has given the formula for calthe experimental group some variable is culating the product-moment correlation cobrought to play; the control is left alone. efficient from a fourfold table on the assump-The results are set up as in table 1-a. If the tion that the distribution of both variâtes is results show that the ratio a: a-\-b is different normal; Yule has an index of association for from the ratio c: c-\-d, it is considered demon-the fourfold table; there are the chi-square strated that the process brought to bear on test and others. In essence, however, all these the experimental group has had a significant indices measure in different ways whether effect. and how much, in comparison with the varia-A similar method is prevalent in statistical tion of random sampling, the ratio a: a+ b practice, which I venture to think has come differs from the ratio c: c+ d. If the difference into authority because of its apparent equiva-departs significantly from zero, there is said lence to the experimental procedure. In Bio-t0 be correlation, and the correlation is the metrika it is referred to as the fourfold table greater the greater the difference, and it is used as a paradigm of statistical Now there is a distinction between the analysis. The usual arrangement is that given method as used in the laboratory and as* This paper was presented in somewhat different form at a meeting of the American Statistical
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