Some consideration when environmental effects of observations of bio-individual characteristics are dependent upon each other : particularly concerned with variance and covariance

Abstract

When there is dependency among environmental effects, if the variance of an individual unit is E, the variance of n individuals is not to be E/n. H. F. SMITH has suggested ernpirically that it should be E/n_b (0<__-b__-<1). In this paper, the author clears up the relation between a parameter of b and the concept of a correlation directly showing dependency and indicates the appropriateness, or the limit of the appropriateness, of SMITH'S assumption. Besides, it also proves that the above-mentioned fact for the variance is fit for the covariance when two or more characteristics are observed.