Summary
The distinction between statistical significance and material significance in hypotheses testing is discussed. Modifications of the customary tests, in order to test for the absence of material significance, are derived for several parametric problems, for the chi-square test of goodness of fit, and for Student’s hypothesis. The latter permits one to test the hypothesis that the means of two normal populations of equal variance, do not differ by more than a stated amount.
This paper was prepared with the partial support of the Office of Naval Research, U.S.A.
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Hodges, J.L., Lehmann, E.L. (2012). Testing the Approximate Validity of Statistical Hypotheses. In: Rojo, J. (eds) Selected Works of E. L. Lehmann. Selected Works in Probability and Statistics. Springer, Boston, MA. https://doi.org/10.1007/978-1-4614-1412-4_15
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