STATISTICAL APPROACH TO COMMON VARIABLES 441 TABLE 3--PREDOMINANTLY O/W EMULSIONS Methyl- Mineral Cottonseed Oleic phenyl Emulsifier Oil Oil Acid Silicone G-263 #3 o/w IPADBS o/w o/w G-2159 X Brij 35 //3 o/w Tween 60 //6 o/w Tween 80 //6 //6 o/w Renex 678 X o/w Myrj 45 //6 //6 //6 Tween 81 //6 o/w Span 20 Span 60 #4 Span 80 Span 85 o/w -- all o/w emulsions X -- o/w or nonmeasurable numbers are the preparative meth- ods forming one w/o emulsion per set of 12 procedures in the experimental design (Table 1). In these cases, the character of the emulsifier and oil in combination deter- mine that the oil is to be the discontinuous phase of the emulsion. For the emulsifier-oil pairs indicated in Table 3, within the limits of these ex- periments, it is evident that the preparative variables have little or no influence on the emulsion type formed. Where blanks occur in Table 3, two or more w/o emulsions were formed for each emulsifier-oil combination. The combinations indicated by blanks are capable, at least to some extent, of being made to form either o/w or w/o emulsions by the influence of one or more preparative variables. It is with these combinations that the results of the experimental design have yielded information on the impor- tance or lack thereof of the six preparative variables on emulsion type formed. To evaluate the importance of the different preparation factors, an arbi- trary scale was applied to the emulsion type results: an o/w emulsion was assigned a value of -3-1, a w/o emulsion, a value of - 1 and a nonmeasurable type a value of zero. (Stability of emulsions was not considered in connec- tion with the emulsion type evaluations.) The indicated numerical values were algebraically summed for each factor for the four experiments with 90 per cent of water and for the four experiments with 30 per cent of water, the 'difference between these two groups determined and divided by four to obtain average values. The magnitude of this difference is a measure of the relative importance of each level of the factor studied. The calculation is illustrated by the results for each factor for mineral oil emulsified with Tween 60. In this case, the quantity of water is seen to be more important than the other factors. There were 30 emulsifier-oil combinations forming two or more w/o emulsions when the 90-30 groups of experiments were compared similarly, nine combinations fitting this criterion were found with the

442 JOURNAL OF THE SOCIETY OF COSMETIC CHEMISTS 90-50 groups. The distributions of average differ- ences are shown in Tables 4 and $ for each factor. Inspection of the frequency of differences reveals the overwhelming importance of quantity of water compared to the other factors. This is evident in both the 90-30 and the 90-50 comparisons. In the cases of surfactant concentration, surfactant location, temperature and methods of agitation the values of the differences are small (0.to 1.00) in relation to the differences found in the case of proportion of water (1.00 to 2.00). It is concluded that these preparative variables are of little importance in determining emulsion type. In the case of addition order, a partial concentration of differences at a value of 1.00 is suggestive tha•t this fact6r has some importance in determining emulsion type. The con- clusion that larger quantities of water and adding oil to water leads to o/w emulsions while the reverse leads to w/o emulsions is consistent with emulsion technology practices. A confirmation of this conclusion is obtained by noting the common factors in the methods which yielded only one w/o emulsion from the set of experi- ments with several emulsifier-oil combinations (Table 3). To form an emulsion of the opposite type from that which is predominately determined by the nature of the emulsifier and oil indicates considerable impor- tance for one or more factors in the singular prepara- tion methods. Method 6 appears in this category seven times, method 3 appears twice and method 4 once. The only common factor in these three methods (Table 1) favoring w/o emulsions is the use of 30 per cent water. No other factors are common to all three of these preparation methods. In methods 6 and 4, water is added to oil. Emulsion Stability In the analysis of the stability results, a procedure similar to that employed to evaluate the influence of the six preparative variables on emulsion type was used. Thus the stability values for a given emulsifier-oil pair for the 90, 50 and 30 per cent experiments were summed, and averaged differences were calculated for the 90-30 and 90-50 groups. Combination of stability results for '1 q- I+