Stratified Sampling and Distribution-Free Confidence Intervals for a Median
作者:
PhilipJ. McCarthy,
期刊:
Journal of the American Statistical Association
(Taylor Available online 1965)
卷期:
Volume 60,
issue 311
页码: 772-783
ISSN:0162-1459
年代: 1965
DOI:10.1080/01621459.1965.10480826
出版商: Taylor & Francis Group
数据来源: Taylor
摘要:
This paper presents the results of a limited investigation which brings into focus the difficulties encountered in developing exact distribution-free methods for stratified simple random sampling. It is shown that exact distribution-free confidence intervals for a population median can be obtained from a stratified sample under very special circumstances. The principal result concerns the order statistics of the combined separate strata samples, where proportional allocation is employed. It is proved that a pair of symmetric order statistics provides a confidence interval for the population median whose confidence coefficient is not less than the confidence coefficient obtained from the corresponding order statistics of a random sample of the same total size drawn from the entire population. Furthermore, it is shown by means of a numerical example that this result necessarily holds only when proportional allocation is employed.
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