STATISTICAL ASPECTS OF SAFETY OF COSMETICS 151 dividuals from the defined population, who are then assigned a number [rom 1 to 4000. From a table of random numbers, 2000 numbers are selected to represent the individuals assigned the new product, and the remainder are given the old. Then if the new product is no more ir- ritating than the old, one would expect to see no more than 4 to 5 cases in each group of 2000 persons. In the procedure iust described the persons included in the study have had to be informed that they were testing a (new) product, although they may not have been told anything else. A test situation of this kind frequently has psychogenic effects and can in itself produce adverse reactions, thus increasing the irritation rate for both products. Un- [ortunately, there is no way of separating the psychogenically induced response from the response actually due to the product's composition. In order to overcome the possibility of confusion of "true" Kith psychogenically induced reactions, there has been devised a procedure known as the "paired-comparisons" method. In general, this technique results in each individual being treated with each of the products simul- taneously, or, if this is not possible, then in some random alternation. If the product is a deodorant, the individual is given, e.g., t•'o jars, marked in some way so that he can distinguish between them. The marks, however, do not indicate which product is which. He is in- structed to use one on the right armpit and the other on the left armpit. If the product is a shaving lotion, then the instructions would be to use the two bottles in some randomly selected order of weeks. When paired-comparisons are used, it is also desirable that the alloca- tion of use of the two products be made in such manner that the new product, if it is a deodorant, be used on the right armpit by some and on the left armpit by others. In fact quite a number of variations in patterns of usage may be introduced, depending upon the relevance of such patterns to the problem of irritation. The advantage of the paired comparison method is that it is possible to separate reactions of a psychogenically-induced nature. In these cases, the usual response will be irritation resulting from use of both products. Some of these may not be psychogenically-induced, and these individuals may be sensitive either to some agent common to both new and old formulations as a result of other physiological or mechanical reasons. This poses no problem since the inclusion of either type con- [uses the picture, and the method helps to remove this confusion. For each of the procedures stated above there has been the require- ment that the individuals comprising the sample be ignorant of the

152 JOURNAL OF THE SOCIETY OF COSMETIC CHEMISTS nature of the product or products assigned for use by them. This is a single-blind technique, and it is the only one possible for designs in which the presence or absence of irritation is reported by the members of the sample without evaluation by a physician. An added advantage of the paired-comparison method is that it makes it possible to reduce the sample size•n the example used here from 4000 to 2000--since each individual acts as his own control. Put in other words, one obtains the same amount of information for half the cost. It is possible that, as a result of either of the above procedures, no cases of irritation will be noted. How can this situation be interpreted ? In the light of the question posed previously, it can be said with reason- able certainty that the risk of irritation due to the new or the old product is less than the maximum tolerable by the manufacturer. This is directly in line with the producer's concern. The actual incidence of irritation in the population of consumers is irrelevant to his problem. Moreover, to get such information, unless the incidence rate was in fact quite large, would be so costly that it would not be practicable. It is suggested that one or the other of the mentioned procedures be carried out prior to the "test-marketing" of the product. This implies that the source of the sample be entirely outside the plant, i.e., that plant employees not be used. It is further suggested that each member of the sample be personally seen by a competent dermatologist so that evalua- tion of the presence or absence of irritation is made independently of the respondents. If this is done, than a further refinement of the blind- procedure is possible--the double-blind--where the evaluating physician is not aware of which product--old or new--has been used at which location or time. If, as there seems to be reason to believe for some products, the irrita- tion potential is small, it may be very difficult or impossibly expensive to determine the incidence of irritation. However, it is also possible that the use of the ratio of complaints to units sold will dilute the incidence as suggested. SUMMARY It appears that the approach described in this paper is the most reason- able. It provides the best information considering the cost involved, since it expressly takes into consideration the greatest risk the cosmetic producer can afford. In addition it yields some information not only about those who may go to the trouble of making a complaint but those who experience irritation and make no complaint. It provides the best