826 JOURNAL OF THE SOCIETY OF COSMETIC CHEMISTS itself is not plotted, since this is better illustrated in the plot of its interaction. It will be noted that Fig. 7 (which is a plot of means of the original data with a straight line visually fitted to them) bears out the conclusions as to linearity of the concentration effect suggested by the analysis of Table IV Analysis of Variance Source of Variation DF SS MS F • P Among concentrations (A) Linear (A1) 1 Quadratic (Aq) 1 Cubic (Ac) 1 Between patch types (confounded with blocks) Between observation times (C) Concentration linear X patch type (AiB) Concentration quadratic X patch type (AqB) Concentration cubic X patch type Concentration linear X observation time (A1C) Concentration quadratic X observa- tion time (AqC) Concentration cubic X observation time (A•C) Patch type X observation time (BC) Concentration linear X patch observa- tion time (A1BC) Concentration quadratic X patch X observation time (AqBC) Concentration cubic X patch X observation time (A•BC) Among replicates Between blocks (within replicates) Within blocks Total among blocks Residual (error) Total 33.00 33.00 8.28 0.01 0.02 0.02 1 ... 0.20 0.20 1 ... 1 25.52 25.52 6.35 0.03 1 5.71 5.71 1.42 .. 1 0.19 0.19 1 .. 1 0.51 0.51 1 .. 1 5.11 5.11 1.27 .. 1 4.69 4.69 1.17 .. 1 0.81 0.81 1 .. 1 22.69 22.69 5.64 0.05 5 1 9.20 9.20 2.29 •-•0.1 1 9.18 9.18 2.28 NO. 15 1 1.63 1.63 ...... 1• 118.46 ......... 2 129.54 64.77 2.83 ... 1 3.52 3.52 1 ... 2 45.80 22.90 ...... X 178.86 ......... • 112.66 4.02 ...... 47 409.98 ......... Notes: Definitions of column head symbols' DF = degrees of freedom, SS = sum of squares of deviations from the mean, MS = mean square, F' = value obtained in F test of significance, and P = probability of the observed difference having occurred by chance.

STATISTICAL EVALUATION OF CUTANEOUS IRRITANTS / / / / / / ¾' / / / so ø I I I I I 0 507 i 1695 2 2 386 0•/• •O/o 2Olo 4Olo •n Concen•rol,on + I Figure 7. Variable A. Plot of concentration effect. (Log linear portion significant at 0.01 level.) No significant curvature 827 variance. Because of the significant linear effect and the nonsignif- icance of higher effects, the visual fitting with a straight line was justified. Note, however, that the "linearity" is based upon logarithmic spacing of the four concentrations, with -+-1 added to keep all values positive. DISCUSSION AND CONCLUSIONS These experiments demonstrate three points which the authors believe are of great importance in irritation testing, and perhaps for patch testing in general, in addition to the specifics connected with the particular variables used. These are the following: (1) It appears possible with a properly designed experiment to obtain meaningful estimates of irritation on a scale of 0 to 4, to less than the nearest 0.50 scale unit. (2) Differences among subjects and among repetitions of experi- ments have always been regarded as a source of difficulty in irritation testing. This work demonstrates that it is possible, by using very well- known and commonly-used statistical techniques, to isolate completely the first of these sources of variation and to prevent their interference with differences sought among various experimental conditions. (3) The use of common multi-factor experimental techniques to- gether with appropriate statistical analyses appears practical and useful in studying patch test data.