SOME RAPID APPROXIMATE STATISTICAL PROCEDURES

Abstract

The last twenty years have seen a great increase in the use of statistical methods in various branches of science and technology. One of the obstacles to the more widespread use of these methods is the complex and laborious nature of the computations which are often required in order to make use of the customary textbook methods. It is not always realized that rapid approximate methods are available for many situations.4 Such approximate methods, however, sacrifice some of the information contained in the data. The purpose here is to describe a few of these methods which have been used by experimentalists in biological and physical research. Signi$canceof Differences. Many experiments are designed to test whether one category differs from another in regard to some measurable quantity. These categories may be, for example: the tensile strength of two types of metal or plastic; the effect of a proposed drug or treatment compared with one now in use; or the comparison of the effect of two fertilizer mixtures on the yield of a certain crop. In all such cases the logic underlying the experiment is usually the same. The assumption is made that the two categories (materials, drugs, or fertilizers) do not differ. An experiment is performed leading to a set of replicated measurements under each category. A statistical constant is calculated from the results, and the probability of obtaining a value as large or larger than that obtained is used as a guide in accepting or rejecting the original assumption. If this probability is sufkiently small, the hypothesis that the two materials are the same is abandoned and a decision is reached that they are different. The particular probability level a t which the hypothesis is abandoned is, of course, a matter of choice, and is determined in part by the seriousness of the consequences should a wrong decision be made, the time and expense involved in the experiments, etc. Efficient statistical tests are described in current textbooks, but these tests often require considerable computation. The tests to be described here are quite simple but often adequate for the purpose in view. Tests Based on Rank Vumbers. An example from entomological work will serve to illustrate these methods. Two household fly sprays had been tested on houseflies, and the tests were replicated eight times for each material. The results obtained, expressed as per cent mortality of the houseflies, are shown in TABLE 1. The average per cent mortality for sample A is 67.7 per cent, while for sample B it is 61.7 per cent. The question to be decided is whether these results indicate a superiority of sample A over sample B? or whether the results are merely due to chance fluctuations and would not hold true in the long run. We may assign rank numbers 1 to 16 to the 16 results in order of magni-