Testing hypotheses about the common mean of normal distributions

Arthur Cohen, H. B. Sackrowitz

Research output: Contribution to journalArticlepeer-review

25 Scopus citations


An overview of hypothesis testing for the common mean of independent normal distributions is given. The case of two populations is studied in detail. A number of different types of tests are studied. Among them are a test based on the maximum of the two available t-tests, Fisher's combined test, a test based on Graybill-Deal's estimator, an approximation to the likelihood ratio test, and some tests derived using some Bayesian considerations for improper priors along with intuitive considerations. Based on some theoretical findings and mostly based on a Monte Carlo study the conclusions are that for the most part the Bayes-intuitive type tests are superior and can be recommended. When the variances of the populations are close the approximate likelihood ratio test does best.

Original languageEnglish (US)
Pages (from-to)207-227
Number of pages21
JournalJournal of Statistical Planning and Inference
Issue number2
StatePublished - Mar 1984

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty
  • Applied Mathematics


  • Admissibility
  • Asymptotically Bahadur optimal
  • Common mean
  • Convex acceptance sections
  • Hypothesis testing
  • t-test


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