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A theory of appropriate statistics

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Abstract

A formal theory of appropriateness for statistical operations is presented which incorporates features of Stevens' theory of appropriate statistics and Suppes' theory of empirical meaningfulness. It is proposed that a statistic be regarded as appropriate relative to statements made about it in case the truths of these statements are invariant under permissible transformations of the measurement scale. It is argued that the use of inappropriate statistics leads to the formulation of statements which are either semantically meaning-less or empirically nonsignificant.

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Author information

Authors and Affiliations

  1. University of California, Berkeley

    Ernest W. Adams

  2. University of Oregon, USA

    Robert F. Fagot

  3. University of British Columbia, USA

    Richard E. Robinson

Authors
  1. Ernest W. Adams
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  2. Robert F. Fagot
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  3. Richard E. Robinson
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Additional information

This research was supported in part by each of the following grants: National Science Foundation Grant GS-333 to the University of Oregon; National Science Foundation Grant to the Institute of Human Learning, University of California, Berkeley; and National Institute of Mental Health Grant MH-08055-01 (under the direction of Ernest W. Adams), also to the Institute of Human Learning. Work on this project was carried out in part during Robert F. Fagot's tenure as Public Health Service Special Fellow (No. MSP-15800) at the University of California, Berkeley, 1962-63; and during Richard E. Robinson's tenure as National Science Foundation Science Faculty Fellow at Stanford University, 1962–63.

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Adams, E.W., Fagot, R.F. & Robinson, R.E. A theory of appropriate statistics. Psychometrika 30, 99–127 (1965). https://doi.org/10.1007/BF02289443

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  • DOI: https://doi.org/10.1007/BF02289443

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