ISSUES IN BIOMEDICAL STATISTICS: STATISTICAL INFERENCE

The first step in making inferences under the frequentist system of statistical logic is to propose a null hypothesis. An experiment is then performed, or a set of observations made. The resulting data are subjected to statistical analysis to determine whether the null hypothesis should be rejected or not. If it is, then some alternative hypothesis must have been entertained. In biomedical work, the alternative hypothesis should usually be non‐specific and it follows that the statistical test of the null hypothesis should be interpreted in a two‐sided fashion. The decision to reject or accept statistical null hypotheses, whether on the basis of a P value or confidence intervals, is probabilistic in nature and always attended by the risk of error. It is argued that, in biomedical research, it is the risk of making false‐positive statistical inferences (Type I error) that should be most closely controlled. The risks of Type I error cannot be considered in isolation from the model of inference under which the null hypothesis is tested. That which forms the basis for using the classical t, F and χ2 tests is the population model, in which the inference is referred to a defined population that has been randomly sampled and which conforms to a specified frequency distribution. Under this model, serious errors in statistical inference can occur if the actual distributions of the populations do not conform to those specified by theory. More importantly, the population model is inappropriate to most biomedical research, in which treatment groups are created by randomization but not by random sampling. When this is so, the randomization model of inference should be adopted, under which inferences apply only to the actual experiment performed and under which the appropriate statistical tests are those based on permutation. Under this model, permutation tests are free of assumptions about distributions, and the risk of Type I error is determined exactly. The randomization model of inference is commended, and permutation tests, to biomedical investigators.