Some properties of students z: Correlation, regression and scedasticity of z with the mean and standard deviation of the sample.
成果类型：
Article
署名作者：
Pearson, K
刊物名称：
BIOMETRIKA
ISSN/ISSBN：
0006-3444
发表日期：
1931
页码：
19
关键词：
摘要：
The correlation of x, the mean of a sample, with z= (x [long dash]m)/[sigma], where m is the mean of the sampled population and [sigma] is the standard deviation of the sample, is high and approaches 1 as n, the number in the sample, increases. The regression is linear, but arrays of z are not homoscedastic. For n< 5, [beta]2''s of arrays of z are infinite. rz[sigma]-=0, but arrays of z for a given [sigma] are not homoscedastic. The z test is not so efficient even for small samples as some have held. It may indeed suffice to show an improbability, but if it show nothing improbable, we must then bear in mind that it is not a very stringent test, and that other tests may indicate improbability where the z test indicates none..