The Difference between Statistical Hypotheses and Scientific Hypotheses

Abstract

When a professional stacistician runs a statistical test he is usually concerned only with the mathematical properties of certain sets of numbers, but when a scientist runs a stztistical test he is usually crying to understand some namral phenomenon. The hypotheses the statistician tests exist in a world of black and white, where the alternatives are clear, simple, and few in number, whereas the scientist works in a vast gray area in which the alternative hypotheses are often confusing, complex, and limited in number only by the scientist's ingenuity. The present paper is concerned with just one feature of this distinction, namely, that when a statistician rejects the null hypothesis at a certain level of confidence, say .05, he may then be fairly well assured (p = .95) that the alternative statistical hypothesis is correct. However, when a scientist runs the same rest, using the same numbers, rejecting the same null hypothesis, he cannot in general conclude with p = .95 that his scientific hypothesis is correct. In assessing the probability of his hypothesis he is also obliged to consider the probability char the statistical model he assumed for purposes of the test is really applicable. The staciscician can say if the distribution is normal, or zf we assume the parent ppulation is distributed exponentially. These ifs cost the statistician nothing, but they can prove to be quite a burden on the poor E whose numbers represent controlled observations nor just symbols written on paper. The scientist also has che burden of judging whether his hypothesis has a greater probability of being correct than other hypotheses that could also explain his data. The stacistician is confronted with just two hypotheses, and the decision which he makes is only between these two. Suppose he has two samples and is concerned with whether the two means differ. The observed difference can be attributed either to random variation (the null hypothesis) or to the alternative hypochesis that the samples have been drawn from two populations with different means. Ordinarily these two alternatives exhaust the statistician's universe. The scientist, on the other hand, being ultimately concerned with the nature of natural phenomena, has only started his work when he rejects the null hypothesis. An example may help to illustrate these rwo points.