ANTIPERSPIRANT RESULTS 169 lower in variance than CHGBAS and 17% lower than POSTRT. The variance of either POSTRT or CHGBAS ranged from approximate equality to almost double the ANCOVA variance over the 70 studies. Our conclusion is that the ANCOVA method guarantees maximum precision for any given test and justifies the use of baseline measurement. The amount of baseline correction needed was found to vary from study to study. The typical difference between POSTRT and CHGBAS comparisons of treatment pairs was +5% percent reduction, which is large when related to differences commonly seen among commercial products. In general, the ANCOVA result was numerically between the POSTRT and CHGBAS results, sometimes agreeing more with one method or the other, the typical difference being about + 2.5% sweat reduction from either POSTRT or CHGBAS. Averaged over all studies, the differences among the three methods was essentially zero, empirically confirming that all three methods were mutually unbiased. Two critical assumptions of the ANCOVA analysis are (a) that the regression line is linear and (b) that slopes are equal across treatment groups within a study. Through examination of many antiperspirancy studies, we have found no evidence that would refute either assumption. In this work, we transformed sweat rates to their logarithms prior to data analysis, as was so convincingly advocated by Wooding (5). Our data diagnostics have confirmed the need for log transformation to achieve the normal error distribution essential for valid normal-theory statistical testing. The arithmetic handling of sweat rates or their ratios in statistical analyses will lead to misleading results and should be avoided. Our mathematical model was based on the fact that the experimental design has two sizes of experimental units, subjects and axillae. This model was slightly more complex than the one suggested by Wooding and Finklestein (6) and allowed for proper testing of the sides by treatment interaction. We found this interaction effect to be nonexistent, leading to a simpler statistical model and analysis, which will be later described. We have had extensive experience with multitreatment studies of three to seven treat- ments for comparing many developmental products and/or competitive products in a single test. For these studies, we recommend a round robin design in which all treat- ment pairs are allocated equally among test subjects. We present a simple model and analysis for this test design. The ANCOVA method has been found to be appropriate for analysis of multitreatment studies. Other findings were related to variants of the test protocol and their repeated-measures characteristics. Baseline results taken on adjacent days were observed to be highly correlated and thus did not appreciably increase baseline precision, leading to a recom- mendation of a single baseline per study. Similarly, the two sweat measurements taken during a test day were shown to be highly correlated and did not greatly increase measurement precision. However, the duplicates were found to be useful diagnostics to identify questionable data. The panel size required to declare specific numerical differences between treatments as statistically significant is also explored. The panel size is a function of the test variation level, the size of the difference between treatments, and the levels of efficacy of the two treatments. The panel size is also dependent on test design in multiple treatment studies. A sample size table is presented for the two treatment cases.

170 JOURNAL OF THE SOCIETY OF COSMETIC CHEMISTS We may summarize our conclusions as follows: (1) Baseline data, when available, should be utilized in the analysis to increase precision of the treatment effects. Baseline information is also useful for determining when a given subject is responding in an atypical manner. (2) Analysis of covariance is the recommended statistical procedure for incorporation of baseline data. It will give equal or better precision versus the competitive analysis based on simple change from baseline. (3) Logarithmic transformation of sweat rates is necessary to ensure that the assumptions of variance homogeneity and distribution normality are met. (4) Although repeated measurements do not greatly improve precision, they can be useful in data-checking. (5) The above conclusions apply to multitreatment studies (three or more treatments). DETAILED DISCUSSION In this section we present our results in detail after a review of statistical methodology presented by earlier writers. We first consider the analysis of post-treatment data alone and derive a simple model for the analysis of this data. We then discuss two methods of utilizing baseline data and compare the precision of all three methods based on analysis of past clinical studies. The final sections discuss other repeated-measures aspects of these studies and the required panel size. An outline for this section is as follows: ß Overview of current data analysis practice ß The need for the log transform of sweat measurements ß The POSTRT model for analyzing post-treatment data alone ß Design and analysis of multitreatment studies ß Results of POSTRT analysis on past studies ß A simpler POSTRT model ß The use of baseline data--the CHGBAS and ANCOVA models ß Comparison of the three analysis methods ß Multiple baselines and readings--Are they necessary? ß Determination of panel size ß Use of the SAS statistical package CURRENT PRACTICE•VERVIEW The "gravimetric" method for conducting antiperspirant efficacy studies was described by Majors and Wild (4). Current experimental design philosophy is based on the fact that, in the general population, average sweat rates from the right axilla are greater than those on the left axilla. Therefore, each pair of treatments is assigned such that an equal number of human subjects have a specified treatment on right and left axillae. The allocation of treatments to axillae within a panel of human subjects is made by random assignment. Test results are usually reported in terms of percent sweat reduction (PCTRED) of one treatment relative to another. For any two treatments, this is calculated as: