DEVELOPMENT OF A DETERGENT TEST--I evaluating the results are practically identical and it is most satisfying to find agreement on the conclusions reached. Pugh's work was carried out on a much larger scale, using naturally soiled plates, whereas the purpose of the present article--to illustrate an approach to the general problem of devising a useful laboratory service test--is best served by presentation of fewer data and of a fuller mathematical treatment. With four detergent solutions, three operators and two batches of soil, and one replication of the whole experiment, we have 4 x 3 x 2 x 2 = 48 tests. The number of plates that can conveniently be soiled and then washed within a few hours limits the number of tests per block to about four, hence the experiment was carried out with one block in the morning and one in the afternoon of each of six days. The same operator was used morning and afternoon to avoid undue interference with other work in the laboratory, and the operators worked in a random order over the six days. Two batches of soil had been prepared according to the method given above by different persons on different days. The detergent selected for the test was one of the Nansa* range (Nansa L. Liquid). One assistant not engaged in the dishwashing measured each day two quantities of 4, 8, 16 and 24 g. of the detergent into eight bottles and diluted each to about 120 mi. with water. The solutions were then numbered 1 to 8 in a random order and were used for dishwashing tests in this order. If the samples are not presented in such a "blind" manner there is a risk of introducing some bias as, for instance, an operator having washed 15 plates with 4 g/1. will expect to wash a larger number with a higher concentration and may therefore wash the first dozen or so at a faster rate than if the expected results were not known. The table below gives the results of the experiments described. The figures give the numbers of plates washed, here tabulated according to the detergent concentration and not in the order of testing: TABLE I Original Data Date 2 3 6 7 8 I 9 -- __ -- Operator Y Z X Z Y X ,. a p a p a p a p a p a p Q2 Q3 Q3 Q2 Q2 Q3 Q2 Q3 Q3 Q2 Q3 Q2 1 g/litre 7 5 6 6 7 6 5 6 6 5 6 6 2 g/litre 10 9 10 11 10 9 9 10 10 10 10 13 4 g/litre 16 14., 14 14 18 16 13 15 12 12 14 16 6 g/litre 20 16 17 18 20 17 19 18 17 17 18 17 * Nansa is a registered trade mark of Marchon Products Ltd. 99

JOURNAL OF THE SOCIETY OF COSMETIC CHEMISTS The figures of the first row give the date of the month, soil Q2 having been prepared on day 1 and Q3 on day 2, and, in line 3, (a) indicates the group of the morning and (p) that of the afternoon. STATISTICAL ANALYSIS The above data are in a form very amenable to treatment by the statistical technique of the analysis of variance. This method of analysis wa.s, in fact, anticipated when the factorial design of the test was drawn up, for efficient -analysis cannot often be done unless the experiment is properly designed. An introduction to the use of statistical methods is given in Ref. 2, where the symbols here used are defined. Before carrying out an analysis of variance, the nature of the distribution of the results must first be examined. The present data, for instance, do not represent a continuous variable, but are in reality grouped data. It is conceivable that a certain amount of detergent in a test will wash precisely 5« or 5« plates, etc., but the actual result will be recorded as 5 or as 6. The value 6 thus represents all results between 5.50 and 6.49 or possibly 5.01 to 6.00, according to the operator. Whichever interpretation is given is here irrelevant, for recording differences will simply be included in soiling tech- nique and manner of washing in a composite value (capable of further analy- sis if desired) of variation between operators, but the fact that the data are grouped does introduce a bias into the calculation of variance, for which corrections (Sheppard's adjustments) should be applied. In such as the present example, where a transformation is also called for, the adjustments would become exceedingly complicated and are, therefore, omitted with the hope that no invalid conclusions will thereby arise. Such invalidity can often be detected by omitting the results of smallest magnitude (e.g., thb•e. for 1 g/i) and examining whether the new analysis of variance points to the same conclusions but where, as in the present instance, the set of data: is only one of a series of experiments, the most harm that can be caused is a slight waste of time in seeking explanation of facts that are not real. :: ii!i Much more serious errors can result if one performs the analysis variance without first ensuring that the data are homogenous.* appropriate test for homogenity is Bartlett's test described in most bookS:'?• on statistical •et•a•d • (e.g. Ref. 4a). An alternative devised by one of writers is to ca cu e he greatest variance of the N samples (or N operatorS?? * Ref. 3 is a paper on "The Evaluation of Test Procedures," and though it deals •vithii? rather precise analyses in contrast to a somewhat empirical test here being discussed, iS•} worthy of study. However, it should be pointed out that neglect of this principle ensuring that the data are homogenous has invalidated many of the conclusions dra?•i• from the analyses of variance there carried out.