Combability Measurements on Human Hair

Mario L. Garcia; Jose Diaz

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MEASUREMENTS ON HUMAN HAIR Table I Combability Results on Bleached Hair Before and After the Use of a Semipermanent Dye Product A 387 Wet Measurements 70øF) Peak Combing Load (G) Before Treatment (BT) After Treatment (AT) Swatch Run Number Average Run Number Average Per cent Number 1 2 3 Column 1 2 3 Column Change 1 700. 1050. 1160. 970. 980. 820. 320. 707. --27.1 2 1500. 1125. 925. 1183. 366. 360. 664. 463. --60,9 3 525. 690. 1000. 738. 664. 422. 460. 515. --30.2 4 1200. 1175. 1210. 1195. 650. 900. 616. 722. --39.6 5 850. 1950. 825. 1208. 436. 500. 480. 472. --60.9 6 1845. 1425. 1550. 1607. 440. 350. 530. 440. --72.7 Average BT = 1150, average AT = 553. Per cent change = (55•50!150') X 100 = --52. per cent. Dry Measurements (65 per cent RH, 70 øF) Peak Combing Load (G) Before Treatment After Treatment Swatch Run Number Colnmn Run Number Average Per cent Number 1 2 3 Average 1 2 3 Column Change 1 800. 530. 784. 705. 236. 258. 220. 238. --66.3 2 416. 390. 304. 370. 200. 247. 140. 196. --47.0 3 500. 340. 275. 372. 263. 19 •. 140. 200. --46.2 4 48S. 365. 399. 417. 275. 310. 255. 280. --32.9 5 1180. 800. 500. 827. 400. 210. 370. 327. --39.5 6 620. 550. 650. 607. ]87. 155. 25,6. 200. --32.9 Average BT = 550, average AT = 240. (240. -- 550.• Per cent change: •, •. ] X 100 = --56 per cent. because they are more readily calculated, the use of PCL values is recom- mended. The computations are best illustrated by considering examples. Example I The data, which appears in Table I are typical and correspond to an experi- ment that was done for the purpose of determining the effect of an experi- mental semipermanent dye product on the wet and dry comb ability of bleached hair.

388 JOURNAL OF TIlE SOCIETY OF COSMETIC CHEMISTS The columns with headings Run 1-3 contain the PCL values for each of the 3 replicate runs that were recorded for each swatch. The average column consists of the averages of the runs for each swatch. The average before treatment (BT) and average after treatment (AT) values are the averages of the average values appearing in the average col- umns. The per cent change in PCL is calculated using the expression ( Average PCL AT - Average PCL BT ) x 100 = per cent change in PCL Average PCL BT If average combing loads are measured instead of peak combining loads, the data are treated in an identical manner. the results of the above set of measurements are summarized as follows. Effect of experimental direct dye base on combability: average per cent change in dry PCL .... 56. per cent average per cent change in wet PCL .... 52. per cent. The percent change columns on the right hand side of Table I give the per cent changes for the individual swatches. We have chosen not to use these numbers, i.e., their averages, to calculate the total per cent change in PCL, due to the treatment. These m•mbers, however, give, on inspection, a practical indication of the reproducibility of the experiment and/or treatment effects. Example II In most cases, combability measurements involve the comparison of the e.%cts on combability of two or more products. Even when this is not the case, a product whose effect .on combability has been previously measured, is normally included in the experiments. This is recommended because it serves as an internal standard which will detect any bias in the results due to differences in the hair. Hair from the same source should always be used in any comparative study. A comparison between products can be done by measuring the effect on combability of each product individually as in example I and then comparing the average per cent changes. If the effects on comb'ability of t•vo products are sufficiently different, that is, of the order of (per cent change PCL) Product A- (per cent change PCL) Product B • 20 per cent, and if the per cent change in PCL for most of the replicate swatches is uniform, the validity of the observed difference frequently can be decided by simple inspection of the data. If there is any doubt and/or the data are going to be used as part of documentation supporting claims for a product, the statistical significance of the differences must always be established. This is best accomplished by doing an analysis of variance on the data (4). Such an analysis is illustrated as follows with data that were used to com- pare the effect of shampoo A (Table II) to that o.f shampoo B (Table III) on the combability of dry human hair. As can be seen in the Tables, 8

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MEASUREMENTS ON HUMAN ttAIR 391 Source of Variance Table IV Analysis ooe Variance for Data in Table II Sums of Squares Degrees of Freedom Mean Squares t•etween rows 185,415.7 m -- 1 = 7 Between columns 9,052.5 n._, -- 1 = 1 Row X column interaction 14,459.6 ( n, -- 1 ) x (•n2 -- 1 ) = 7 Residual 73,495.6 n,n,•(m -- 1) = 64 Total 282,423.4 mn=na -- 1 = 73 equals number of rows equals 8 (one for each swatch). equals number of columns equals 2 (one for each treatment). equals number of replications equals 5 (five for each swatch). 26,488. 9,052.5 2,065.7 1,148.4 swatches were used and 5 replicate runs were done on each swatch: It can be seen in Table II that the use of shampoo A resulted in a decrease of the forces required to comb 7 out of 8 swatches used. On the other hand, Table III shows that of the 8 swatches that were treated with shampoo B, 3 showed an increase and 5 a decrease in their PCLs. Analysis of Variance for Data in Table II. The statistical parameters needed to perform the analysis are shown in Table IV. The following operations are done to determine the significance of the different components of variance. Step 1. Significance of the interaction (between rows and columns) against the residual: 2,065.7/1,148.4 = 1.79. For degrees of freedom (dr) Nt = 7, N2 = 64 the above ratio is not significant at the 95 per cent confidence level. (Fisher variance ratio test.) This means that the data do not show any de- tectable statistically significant interaction between the treatment and the PCLs of the swatches. If the interaction had been significant, it would indicate that the effect of the product is a function of a characteristic of some of the swatches, in our case their initial before treatment average PCL. This seldom ,occurs if all the swatches are prepared from the same homogeneous batch of hair. If it does, it indicates inhomogeneity of the hair, m•d the best solution is to prepare more swatches and exclude from the set of swatches those that have extremely high values for their initial before treatment PCL. This should be done on the complete set of swatches participating in the experiment. The set would then be randomly divided in half into subsets to be used with each product. Step 2. Pooling of the sums of squares of the interaction and residual and their degrees of freedom: (14,459.6 q- 73,495.6)/(7 q- 64) = 1,238.8. This num- ber is now treated as a new mean square for the residual. Step 3. Significance of the variance due to differences between columns (i.e., due to shampoo A treatment). The value of the ratio of the mean square of the between columns term and that of the new residual determines the significance of the "between columns" varim•ce: 9,052.5/1,238.8 = 7.31. For degrees of freedom N• = 1 and N2 = 71 the value of the ratio indicates

392 JOURNAL OF THE SOCIETY OF COSMETIC CHEMISTS Table V Analysis of Variance for Data in Table III Source of Variance Sums of Squares Degrees of Freedom Mean Squares Letween rows 133,028.0 n• -- 1 = 7 19,004.0 Between columns 32.5 n,, -- i = 1 32.5 Row X column interaction 13,401.0 ( n•- 1 ) x (,n•-- 1 ) =7 1,914.4 Residual 59,972.0 n,n,,(m -- 1) = 64 937.1 Total 206,433.5 mn.,n• -- I = 73 nt equals number of rows equals 8 (one for each swatch). n• eqnals number of columns equals 2 (one for each treatment). n• equals number of replications equals 5 (five for each swatch). statistical significance at the 99 per cent confidence level. This means that the decrease in PCL measured experimentally (-15. per cent) can be considered statistically significant at the 99 per cent confidence level. Analysis of Variance l•or the Data in Table III. The parameters needed to perform the analysis appear in Table V. Step 1. Significance of the interaction: 1,914.4/937.1 = 2.04. For N• = 7, N•o = 64 the interaction is not significant at the 95 per cent confidence level. Step 2. Pooling of sums of squares and degrees of freedom: (13,401. + 59,972.)/(7 + 64) = 1,033.4. Step 3. Significance of the variance due to between columns differences: 32.5/1,033.4 = 0.31. For N• = 1, N2 = 71 is not significant. These results confirm that the changes noticed on combing loads (Table III) after the use of shampoo B do not indicate any effect due to this treat- ment. The analysis of variance provides us with a criteria to establish the statisti- cal significance of the observed changes in combing forces. In order to com- pare the effect of shampoo A to that of shampoo B we can proceed as follows. Step a. Calculate the difference between the average after and average be- fore treatment values for each shampoo, i.e., average difference for shampoo A = D^---116.8- 138. =-21.2 g average difference for shampoo B--D•, = 124.5- 123.2 = 1.3 g Step b. Calculate the standard error (standard deviation) of the difference in the means, i.e., Dx and D, using the formula (5) Standard error- rr x N/2: O'm ¾n

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