[Statistical evaluation of light protection factors].

The protection against erythema belongs to the cosmetic effects which lend themselves to mathematical treatment. It is demonstrated -- on the basis of the optimal definitions given by Ellinger and Schulze -- that the calculation of the mean value of the light-protection factor Q as hitherto in use, does not correspond to the real frequency-distribution. On the contrary there exists, independent of the radiation source having sunlike characteristics and of the distance from the radiator, a binary-logarithmic standard distribution. With reference to the gradation principles of the human skin a transformation of the pertinent differences of area is necessary first, i.e. a transformation responding to the Gaussian standard distribution principle. Tables are presented concerning the transformation and the practical evaluation of the light-protection factor Q. By aid of these tables a standardization of the factors Q measured by different authors has been attained as well as a standardized statistical-mathematical analysis. The investigation of the threshold dose producing erythema on the unprotected human skin has revealed a superposition of three frequency-distribution types (showing logarithmic distribution, too) having different standard deviations. The results of this entirely statistical classification permit a safe forecast: the sunburn protection inherent in the human skin is compounded of several contributing factors which are interconnected multiplicatively, not additively.