Type I error rates, power, and sample sizes for two-stage solutions to the Behrens-Fisher problem when population distributions are non-normal

Stephen Olejnik, Wei-Ming Luh

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

Two-stage sampling procedures for comparing two population means developed by Chapman (1950) and Ghosh (1975) are compared in terms of Type I errors, power, and sample size requirements when populations are non-normal. The Ghosh procedure is shown to be less sensitive to non-normal distributions but can have actual Type I error rates greater than the nominal when sampling from distributions that are skewed and the initial sample size is small. Moderate to large sample sizes at the first sampling stage can reduce the overall total sample size needed and can minimize the inflated Type I error rate. Average sample sizes needed remain constant across distribution shapes but greater variability is found with heavy-tailed distributions. Total sample sizes needed for the Ghosh procedure were estimated for a variety of effect sizes and are compared with the Student t-test when all parametric assumptions, including equal population variances, are met. Only small differences in the sample sizes are found when the initial sample size is at least moderate.

Original languageEnglish
Pages (from-to)409-420
Number of pages12
JournalComputational Statistics and Data Analysis
Volume17
Issue number4
DOIs
Publication statusPublished - 1994 Jan 1

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Behrens-Fisher Problem
Population distribution
Type I Error Rate
Sample Size
Sampling
Students
Two-stage Sampling
Non-normal Distribution
Heavy-tailed Distribution
Effect Size
Type I error
t-test
Categorical or nominal
Minimise

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Computational Mathematics
  • Computational Theory and Mathematics
  • Applied Mathematics
  • Social Sciences(all)

Cite this

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abstract = "Two-stage sampling procedures for comparing two population means developed by Chapman (1950) and Ghosh (1975) are compared in terms of Type I errors, power, and sample size requirements when populations are non-normal. The Ghosh procedure is shown to be less sensitive to non-normal distributions but can have actual Type I error rates greater than the nominal when sampling from distributions that are skewed and the initial sample size is small. Moderate to large sample sizes at the first sampling stage can reduce the overall total sample size needed and can minimize the inflated Type I error rate. Average sample sizes needed remain constant across distribution shapes but greater variability is found with heavy-tailed distributions. Total sample sizes needed for the Ghosh procedure were estimated for a variety of effect sizes and are compared with the Student t-test when all parametric assumptions, including equal population variances, are met. Only small differences in the sample sizes are found when the initial sample size is at least moderate.",
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