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June 1, 1949Biometrics

Comparing Individual Means in the Analysis of Variance

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Authors

JTJohn W. TukeyAT&T (United States)

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Implication

Methodological analysis demonstrates a procedure to partition treatment means in analysis of variance, highlighting reliable grouping beyond omnibus test statistics.

Key Points

  • Establish a standardized statistical procedure to divide individual treatment means into distinct, meaningful groups following an analysis of variance.
  • Examined theoretical distributions of relevant test statistics to evaluate differences among treatment means.
  • Formulated a step-by-step decision framework to partition heterogeneous means into distinct clusters.
  • Demonstrated the application of the partitioning framework across sample ANOVA datasets.
  • Constructed a definitive classification procedure that segments treatment means into distinguishable subsets rather than relying solely on overall significance tests.
  • Derived rules to identify latent heterogeneity within clustered treatment subsets even when data cannot establish specific pairwise rankings.

Cite This Study

John W. Tukey (1949) studied this question.

synapsesocial.com/papers/69d7e40ef39344339dd18c45https://doi.org/10.2307/3001913
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