Token swap test of significance for serial medical data bases

Established tests of statistical significance are based upon the concept that observed data are drawn randomly from a larger, perhaps infinite source population. The significance value, p, is the probability that the observations are drawn from a source population satisfying the null hypothesis; if p is small enough (less than 5 percent, 1 percent, etc.), then the null hypothesis is rejected. Serial medical data bases, such as a hospital clinic intake or autopsy case accessions, often do not have an identifiable source population from which they are randomly drawn. In an effort to make a reasonable interpretation of these less-than-ideal data, this report introduces a "token swap" test of significance, in which the usual paradigm of repeated drawing from a source population is replaced by a paradigm or misclassification within the observed data themselves. The token swap test consists of rearranging the data into a balanced distribution, and determining the disparity between the observed and the balanced distribution of data. In a two-by-two contingency table, patients are represented as "tokens" distributed into four "cells." Significance is determined by the proportion of "token swaps" that are able to transform the balanced table into the observed table. The token swap test was applied to three series of autopsy observations, and gave results roughly comparable to the corresponding (two-tail) chi-square and one-tail Fisher exact tests. The token swap test of significance may be a useful alternative to classic statistical tests when the limiting assumptions of a retrospective, serial medical data base are present.