@article{oai:rku.repo.nii.ac.jp:00005046,
 author = {鈴木, 啓祐 and スズキ, ケイスケ},
 issue = {4},
 journal = {流通經濟大學論集},
 month = {Mar},
 note = {P(論文), It is supposed that a population contains Γ red balls and Δ white balls and it is devided into N parts. And it is also supposed that the ith part of population contains τ_i balls, and γ_j red balls. If the n parts in this population are chosen, the sample ratio p which is defined by [numerical formula] is the unbiased estimator of the population ratio r which is written by [numerical formula] where t_j is the number of balls contained in the jth part of sample, c_j is the number of red balls contained in jth part of the sample, and T is the total number of balls contained in the population. When [numerical formula], the variance of p, V(p) is approximately expressed by V(p)=ωV(γ), where [numerical formula] And, when [numerical formula], V(p) is approximately expressed by V(p)=ωV(ε) which is exactly equal to the result found in Cochran's book, where [numerical formula] It is very interesting that if we represent γ_i in the graph which has coordinate axes, τ-axis and γ-axis as shown in Figure 2, the variances V(γ) and V(ε) can be expressed clearly in the graph. Both the variances V(γ) and V(ε) are regarded as the indicator of the dispersion of distribution of γ in the direction of γ-axis. When [numerical formula], the points which show the γ_i(i=1, 2, …, N) distribute along the regression line: γ=πτ and in this case, the variance V(γ) is the indicator of the dispersion of the distribution of γ in the direction of γ-axis. When [numerical formula], the points which show the τ_i's (i=1, 2, …, N) distribute along the line [numerical formula], since τ_i's are always τ^^-, and in this case, the variance V(ε) is the indicator of the dispersion of distribution of γ in the direction of γ-axis, and the variance V(ε) becomes exactly equal to the variance V(γ).},
 pages = {28--35},
 title = {標本比率の分散に関する一考察},
 volume = {15},
 year = {1981}
}