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Related Experiment Videos

Multiplicity, directional (type III) errors, and the null hypothesis.

Juliet Popper Shaffer1

  • 1Department of Statistics, University of California, Berkeley 94720-3860, USA.

Psychological Methods
|September 24, 2002
PubMed
Summary
This summary is machine-generated.

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The standard two-sided hypothesis test can be viewed as two one-sided tests. However, in multiple testing, the directional error rate can exceed alpha/2, potentially reaching alpha.

Area of Science:

  • Statistics
  • Hypothesis Testing

Background:

  • The standard two-sided hypothesis test at level alpha can be reinterpreted as simultaneous tests of two directional inequality hypotheses, each at level alpha/2.
  • The maximum probability of a Type I error is alpha/2 if the null hypothesis is considered impossible.

Purpose of the Study:

  • To analyze the directional error rate in multiple testing scenarios.
  • To investigate the relationship between familywise error rate and directional error rate.
  • To discuss implications for confidence interval estimation and hypothesis testing practices.

Main Methods:

  • Analysis of single-step, step-down, and step-up multiple testing procedures.
  • Examination of various error rates, including the false discovery rate.

Related Experiment Videos

Main Results:

  • In multiple testing with familywise error rate controlled at alpha, the directional error rate (assuming all null hypotheses are false) is greater than alpha/2.
  • The directional error rate can approach alpha.

Conclusions:

  • The directional error rate in multiple testing is a critical consideration.
  • Practices in confidence interval estimation and hypothesis testing may need reevaluation in light of these findings.