J. Soc. Cosmetic Chemists, 19, 95-107 (Feb. 5, 1968) Easy Statistical and Plant Data Tests for Laboratory W. M. WOODING, B.Ch.E* Presented May 2, 7967, New York City Synopsis--Rank tests and other nonparametric procedures can be used to take advantage of the objectivity available to an experimenter by application of statistical methods to his data. Three welLknown rank tests are described and examples of their use are given. Hopefully, this presentation will stimulate cosmetic chemists and others to a wider use of statistics when studying the results of experimental or observational procedures. INTRODUCTION This paper is presented to encourage wider use of simple sta- tistical procedures by chemists and others who deal with numerical data. All of the tests discussed are found in the literature, and it is hoped that the examples given here will be sufficiently interesting to persuade the reader to investigate similar tests and use them. The tests described are known as "non-parametric," which implies that the nature of the underlying statistical distribution has no influence upon the validity of the procedures. This property is possessed by many similar tests given in the references to this paper. A second property of nonparametric tests is simplicity. They usually require nothing but pencil, paper, and a few minutes of time. Some of them may occasionally be applied mentally to the data with no computational work at all. All three specimen tests described here were designed to determine whether pairs of variables which are numerically different are, in fact, * Carter Products Research, Carter-Wallace, Inc., Half Acre Road, Cranbury, N.J. 08512. 95

JOURNAL OF THE SOCIETY OF COSMETIC CHEMISTS really different, or whether repetition of the experiment would be likely to show no difference at all, or even a reversal of the original magnitudes. For example, one may have two sets of viscosity measurements, one for an old lotion formula and one for a new composition. The data may sug- gest that the new formula has a lower viscosity than the old one. The difference between the two averages may be so large as to produce great conviction that it is real rather than the result of sampling or testing variation on the other hand, the difference may be small, and may leave doubt in the investigator's mind. Even in the first case, however, it may be that an objective way of verifying the apparent difference would be more convincing to the investigator himself or to others than a simple presentation of the results supported by a professional opinion. If this is the case, these tests should be found useful and interesting. The use of statistics is not necessary to conduct investigative tech- nical or scientific work. Obviously, many great discoveries have been made without the benefit of a knowledge of such procedures. These tools are now available, however, and provide valuable supplements to professional experience and skill. In addition, in many cases they will allow a reduction in the amount of routine work necessary to arrive at a decisive conclusion, and they always provide a more objective basis for a statement of opinion. The experimenter unfamiliar with statistical procedures should follow the directions given here and in the references quite literally. It is possible to break the rules, but statistics is full of traps for the unwary. On the other hand, application of the tests as described is not difficult, and is unlikely to lead to serious misunderstanding of the results. Much of the content of this presentation is very detailed, elementary and "cookbook" statistics. If the reader is already well-versed in the application of statistical methods and experimental designs to investiga- tive work, this presentation will probably represent familiar material. It has been the writer's experience, however, that most statistical litera- ture is so surrounded by mathematical abstractions, and appears so rarely outside of the statistical journals and texts, that many if not a majority of workers in an applied field may have become reluctant to try them. WILCOXON Two-SAMPLE RANK SUM TEST This test is intended for use in comparing two independent sets of data to determine the probability that their average values would be the same in the long run, if the experiments were repeated an indefinite