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Research Methods in the Behavioral Sciences

Research Methods in the Behavioral Sciences 246 Reviews 01 Statistical and Economic Books [part II, vagueness and with interpersonal differences in decision situations". The discussion is largely centred on the minimax rule and the "group minimax rule". These two rules are respectively attempts to achieve the two aims of statistics proper, just mentioned. The definitions of the two rules are necessarily technical and will be given here very succinctly. Let E be an experimental result, where any observations of random numbers used in the design of the experiment, or otherwise, are regarded as part of the experiment itself. Let/(.), a randomized decision function, be a function of E taking values that are decisions to perform certain acts. (To announce that a hypothesis is true is one example of an act.) Let Hi (i = I, 2, ... ) be all possible simple statistical hypotheses (so that peE I Hi) is tautologically known) and let j index the members of a group of people (such as a jury). Let VU(.), i, j) be the expected utility of 1(.), given Hi, according to i, before E is observed. Let the "expected regret" be defined by RU(.), i,j) = max V(f'(.), i,j) - V(f(.), i,j). /,(.) The rule http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of the Royal Statistical Society Series A (Statistics in Society) Oxford University Press

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Copyright
© 1955 The Authors
ISSN
0964-1998
eISSN
1467-985X
DOI
10.2307/2343134
Publisher site
See Article on Publisher Site

Abstract

246 Reviews 01 Statistical and Economic Books [part II, vagueness and with interpersonal differences in decision situations". The discussion is largely centred on the minimax rule and the "group minimax rule". These two rules are respectively attempts to achieve the two aims of statistics proper, just mentioned. The definitions of the two rules are necessarily technical and will be given here very succinctly. Let E be an experimental result, where any observations of random numbers used in the design of the experiment, or otherwise, are regarded as part of the experiment itself. Let/(.), a randomized decision function, be a function of E taking values that are decisions to perform certain acts. (To announce that a hypothesis is true is one example of an act.) Let Hi (i = I, 2, ... ) be all possible simple statistical hypotheses (so that peE I Hi) is tautologically known) and let j index the members of a group of people (such as a jury). Let VU(.), i, j) be the expected utility of 1(.), given Hi, according to i, before E is observed. Let the "expected regret" be defined by RU(.), i,j) = max V(f'(.), i,j) - V(f(.), i,j). /,(.) The rule

Journal

Journal of the Royal Statistical Society Series A (Statistics in Society)Oxford University Press

Published: Dec 5, 2018

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