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Pivotal Quantities for the Substitution Values of Various Entries, Each in Place of its Best Contender, Given the Standard Analysis of Variance Model
Author(s) -
van Aarde I. M. R.
Publication year - 1994
Publication title -
biometrical journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.108
H-Index - 63
eISSN - 1521-4036
pISSN - 0323-3847
DOI - 10.1002/bimj.4710360604
Subject(s) - variance (accounting) , substitution (logic) , yield (engineering) , value (mathematics) , mathematics , statistics , mathematical economics , interval (graph theory) , econometrics , combinatorics , computer science , economics , thermodynamics , physics , programming language , accounting
Consider a yield trial involving entries such as the apple cultivars named “Cox's Pippin”, “Granny Smith”, “Rome Beauty”, etc., where interest is in mean performance, the higher the better. For any of the entries, say Granny Smith, an unknown “X” names the best of the other entries. The substitution value of Granny Smith in place of its best contender, is given in terms of expectations by E (yield of Granny Smith) — E (yield of X ). This parameter takes on any real value. A system of interval estimates of the parameter is shown to arise in the standard analysis of variance case. In fact, there arises such a system for each of the entries involved. These systems supersede procedures recently discussed in this journal by VAN DER LAAN (1992).