AN EXAMINATION AND FURTHER DEVELOPMENT OF A FORMULA ARISING IN THE PROBLEM OF COMPARING 2 MEAN VALUES
成果类型：
Article
署名作者：
ASPIN, AA
刊物名称：
BIOMETRIKA
ISSN/ISSBN：
0006-3444
DOI：
10.1093/biomet/35.1-2.88
发表日期：
1948
页码：
8896
关键词：
摘要：
On the basis of 2 samples of size n1 and n2 drawn from 2 normal populations with true means [alpha]1and [alpha]2 and true variances [sigma]12 and [sigma]2, respectively, it is often necessary to calculate confidence intervals for ( [alpha]l- [alpha]2) from the sample means [image]1 and [image]2 and sample variances s12 and s22. This is a special case of a problem considered by Welch (Biom., 1947). Welch obtained a soln. in the form of a series expansion to terms of the order of 1/ni2; the series is extended to terms of order 1/ni4. A re-arranged expansion is given which has possibly some computational advantages. A numerical investigation for the case of 2 samples with m = n2 is attached; it appears that the rearranged expansion converges less rapidly than the original when s12 and S22 are not approx. equal.
来源URL：