(Sigma Squared) .(Sigma) S.S. ?,::X •- (Chi Squared) ': ?•?{) O (rho) -, STATISTICAL METHODS IN THE COSMETIC INDUSTRY SYMBOLS USED Any individual result or series of results. Probability that an event will occur. Probability that an event will not occur (q = p -- 1). Variance (,'= sum of squares of deviations from the mean/degrees of freedom). Degrees of freedom. The sum of a series of results. Thus 27x is the sum of all the results x• + x• q- x• q- .... The number of results in a series. The mean of a series of results x•,•,• ..... The mean of a series of results y •,•_, 3, ß ß ß ß Estimated standard deviation (square root of the variance). Estimated standard deviation of the mean of a series, often called "Standard Error" (a,, = a/x/n). Deviation. Difference between a result x and the mean of the series •. Student's t. The deviation divided by its estimated standard error (t = dx/n/rr). Sum of Squares Correction Term. Mean Square. The ratio between two variances, the larger estimate of variance being the numerator. Factorial (thus 4! is factorial 4 = 4 X 3 x 2 x 1). The sum of squares of a number of variables which vary normally and independently about zero with unit variance. Frequency expected. Frequency observed. Correlation coefficient. Spearman's ranking coefficient. Coefficient of Concordance. Average frequency. Base of natural logarithms (e = 2.71828). Greater than , smaller than (A is greater than B: A B). 233

JOURNAL OF THE SOCIETY OF COSMETIC CHEMISTS Values of t required by the Examples Given Degrees of Probability Freedom 0.8 0-7 0-1 0.05 0.01 I 3 0-277 0.424 2.353 3.182 5-841 5 0-267 0.408 2.015 2.571 4-032 I0 0.260 0.397 1.812 2.228 3.169 11 1-796 2.201 3.106 15 1-753 2.131 ' ' Values of F required l•y the Examples Given N• is degrees of freedom of larger variance. Ns is degrees of freedom of smaller variance. p = 0.20 • = 0.001 '•'-'-• N• 4 5 2 10 1.8 . 1.8 14.9 15 1-7 1-7 11.3 18 1-67 1.64 10.4 19 1.66 1-63 10.2 Values of X 3 required by the Examples Given Degrees of Probability Freedom 0.2 0.1 0.02 0.01 1 1.642 i 2-706 5.412 6:635 2 3.219 I 4-665 7.824 9.210 4 5.989 7.779 I 1.668 13.277 Value of r required by .Example Given Degrees of Probability Freedom 0-01 0-001 2 0.990 I .- 0-999 VARIANCE There are several ways in which the .variability of a set of results ca'• be expressed, of which the more useful are the range and the vananc The ran e of a series of results is the difference between the highest and th•'• lowest restfit of the series. ' The variance is the sum of the squares of the de•ation of each individ½•'"•)•( result from the arithmetical mean of the series divided by the numbe results in the series when there are 30 or more results, divided by one le•'•:}• than the number of results when the series consists of less than 30 resul•2:•