MEASUREMENTS ON HUMAN HAIR 393 •vhere rr is the common standard deviation of each of the before and after treatment means, and n (40) is the number of observations used to calculate the means. In our ease, rr will be given by the square root of the residual mean square calculated in Step 2 of the analysis of variance. We will have the following: O'm, for shampoo A -- 35.2 x 1.41 6.32 = 7.85 for shampoo B = 32.1 x 1.41 6.32 = 7.16 If desired, these numbers can be used to esti•nate confidence level litnits (q- L) for the differences, i.e., +L = t x O'm. The residual variance used to calculate the standard errors has 74 degrees of freedom. The correspond- ing value for t for the 95 per cent confidence level is 2.0, hence +Lx = ---2. x 7.85 = -T-15.7 -----LB = +2. X 7.16 = -----14.3 and the changes in combing forces for shampoos can be expressed as follows: Change in PCF shampoo A = -21.2 q- 15.7 g Change in PCF shampoo B = 1.3 --- 14.3 g Step c. In order to calculate the significance of the difference between the two average differences for each shampoo we perform a t test. The value for t is given as follows: Dx - DB nt X n2 t= O'e '• n• + n2 in which o'e is the combined standard deviation obtained by combining and O',•b. According to the expression o-e • = o',• 2 x df•. + o',•b 2X dfb ---- 1151.7 df•. + dfb --2 O'c = 33.9 where the degrees of freedom = 74. Also, n• = n• = 40. The calculated value of t equals 2.97. The value of t found on a t-table for the 99 per cent Con- fidence level is 2.6. The difference between changes in PCL produced by shampoos A and B is thus shown to be significant at the 99 per cent con- fidence level.

394 JOURNAL OF THE SOCIETY OF COSMETIC CHEMISTS In the present example, the analysis of variance would have been sufficient to demonstrate the superiority of shampoo A over B, because it showed that shampoo A had a significant effect while shampoo B did not. In other cases, however, if both products are shown to have a significant effect, the calcula- tions under steps a to c leading to the t-test are required in order to prove the superiority of a product over the other one. APPLICATIONS Effect of commercial hair products on combability. Table VI shows the ef- fect of a selection of commercial products on the combability of originally un- treated human hair. It can be noticed from the table that most types of hair products, if formulated correctly, can improve the combability of human hair. Effect of quaternary ammonium compounds on wet combability. The effect of quaternary ammonium compounds on the combability of human hair is well known (6). Figure 5 shows the effect of increasing amounts of dodecyl- trimethylammonium chloride sorpted by bleached hair on its combability. The hair was bleached for 60 min using a commercial lightening product. It was then treated by immersing it in 0.05 g/100 g aqueous solutions of the quaternary for 0, 1, 5, 60, and 19.0 min at room temperature and then rinsing for 20 sec under running deionized water. The amount of quaternary on the hair was determined by extraction with chloroform and further analysis using the method of G. V. Scott (7). Table VII shows similar data for a set of quaternary ammonium compounds (8). The two levels of uptake were pro- T,able VI Effect of Commercial Hair Products on Cmnbability Per Cent Change in Peak Combing Force Product Wet Dry Regular shampoo Conditioning shampoo A Conditioning shampoo B Leave-in creme rinse Rinse-off creme rinse Semipermanent dye product Oxidation dye product A Oxidation dye product 13 Oxidation dye product 13 plus a r•nse-off creme rinse Lightener (15-min treatment) Lightener (60-rain treatment) Lightener (60-rain treatment) plus ,a conditioner Conditioning setting lotion q- 4.% -- 19.% -- 23.% -- 27.% -- 57.% + 31.% -- 40.% -- 72.% -- 69.% -- 48.% -- 3S.% -- 34.% -- 55.% -- 15.% q-741.% q- 47.% -- 65.% -- 25.% q-265.% + 20.% q-760.% +110.% q- 180.% -- 20.% -- 63.% -- 72.%