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January 1, 1953Biometrika

A Method for Judging All Contrasts in the Analysis of Variance*

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Authors

HSHenry SchefféColumbia University

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Implication

Methodological study demonstrates exact simultaneous confidence bounds for all contrasts in analysis of variance, highlighting error control in post hoc comparisons.

Key Points

  • To establish a rigorous statistical procedure for assessing all possible linear contrasts among group means simultaneously while strictly maintaining an overall significance level.
  • Derived mathematical foundations for simultaneous confidence intervals (the S-method) spanning the space of all linear contrasts in analysis of variance.
  • Utilized the critical value of the omnibus F-distribution to construct bounded confidence intervals that hold uniformly across arbitrary combinations of group means.
  • Demonstrated that the familywise type I error rate remains bounded at the nominal alpha level across an infinite collection of post-hoc contrasts.
  • Proved that rejection of the omnibus null hypothesis via the standard F-test guarantees the existence of at least one statistically significant linear contrast.

Cite This Study

Henry Scheffé (1953) studied this question.

synapsesocial.com/papers/6a0db6b3cecdf5fb20ba937dhttps://doi.org/10.1093/biomet/40.1-2.87
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