If you turn to a basic textbook on biostatistics you will probably "nd that the "rst one or two chapters discuss how to present and summarize data (descriptive statistics), while the remaining 10}30 chapters discuss how to draw inferences (statistical inference). The part of the chapter that deals with measures of location will describe the mean, median and mode, and, if quantitative data are already introduced, the proportion. If the book has a slant towards epidemiology, then there will be a more extensive discussion of measures of risk and relative risk. To quote one textbook, &statistical inference . . . . is to many people the more exciting part of statistics'. Dr. Feinstein shows in his article that there is a lot more that can be said on the subject of choosing a summary measure to compare two groups than is found in the customary textbook, and that the topic contains its own intellectual challenges and excitement. For this he deserves thanks.
Besides giving a general overview of measures of contrast, one of the central points of philosophy of this article concerns the concept of &quantitative signi"cance'. In our training as biostatisticians, many of us adopt "rst the critical and wide-reaching notion of statistical signi"cance as an aid to protect us from the tricks that chance can play on us, and then as we mature, we learn to add to the demands of statistical signi"cance the need also for clinical signi"cance, that the di!erences we observe are consonant with having some clinical impact. However, here Dr. Feinstein talks of another type of signi"cance, &quantitative', which seems to be neither statistical nor clinical. Indeed, just before the Discussion and Conclusions, Dr. Feinstein clearly separates quantitative from clinical signi"cance: &. . . quantitative signi,cance should be judged by its own standards, whereas judgements about populational signi,cance or clinical importance will require a separate set of standards'.
Although I cannot "nd in the article any attempt to de"ne formally what is meant by quantitative signi"cance, I understand the di!erence between quantitative and statistical signi"cance to be the following. Statistical signi"cance is judged operationally by the comparison of two sampling distributions, for example, of two sample means. If these sampling distributions are su$ciently separated, then we have statistical signi"cance. Quantitative signi"cance is the same concept applied to the population distributions.
The di$culty is in deciding how much separation of the population distributions is required to declare quantitative signi"cance. Dr. Feinstein quotes the work of Cohen on the e!ect size and his own work with Burnand et al. as attempts at drawing closer to some sensible criteria of quantitative signi"cance, and makes further comparisons in his paper here with criteria for minimally useful proportions of explained variance and minimally useful correlation coe$cients.
One might add to these the use of the probability that a (randomly chosen) patient given the experimental treatment will have a better result than a (randomly chosen) patient receiving the