A statistical analysis of the Biological Theory of spherical error of refraction

It is widely believed that Adolph Steiger proved in Die Entstehung der sphärischen Refraktionen des menschlichen Auges (The Origin of Spherical Refractions of the Human Eye) that the Biological Theory of spherical error of refraction statistically explains the entire distribution of such errors, hence excluding other theories such as the Use-Abuse Theory. Although Steiger's Biological Theory is a statistical argument, he never put it into formal notation. This paper puts a modernized version of the Biological Theory into formal statistical notation. It shows that the Biological Theory explains the dispersion of distributions of spherical error of refraction but not the location of their means. The Use-Abuse Theory is an explanation of mean spherical error in populations. Since a complete theory of spherical errors of refraction needs to explain both the mean and the dispersion of their distribution, the two theories are potentially complementary. No empirical evidence, however, is presented here for either theory.