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Hypothesis Tests, Multiplicity of

Elsevier Ltd
DOI: 10.1016/b0-08-043076-7/00427-7
  • Logic


Standard procedures for controlling error rates of statistical inferences assume that only a single inference is drawn from the analysis of a body of data. When an investigation yields a multiplicity of inferences, an adjustment of the error rates from standard procedures is required. Here we distinguish between two forms of multiplicity, ‘multiple determination’ and ‘multiple comparisions.’ For both, we set forth techniques for the control of a particular error rate; the rate of false discoveries (as proposed by Benjamini & Hochberg). The techniques are illustrated by applying them to state-by-state results from the National Assessment of Educational Progress. Extensions are discussed, with special attention to whether levels of the independent or classification variables should be considered ‘fixed,’ ‘variable,’ or neither.

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