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TYPE I ERRORS AND THEIR DECISION BASIS
Author(s) -
Rodger R. S.
Publication year - 1967
Publication title -
british journal of mathematical and statistical psychology
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.157
H-Index - 51
eISSN - 2044-8317
pISSN - 0007-1102
DOI - 10.1111/j.2044-8317.1967.tb00377.x
Subject(s) - statistical hypothesis testing , type i and type ii errors , variance (accounting) , mathematics , statistics , basis (linear algebra) , econometrics , set (abstract data type) , context (archaeology) , word error rate , computer science , artificial intelligence , paleontology , geometry , accounting , business , biology , programming language
It is proposed that an error‐rate 1 should be set for each statistical decision to be made. Methods for testing statistical hypotheses in the context of analysis of variance are reviewed and evaluated from the decision‐based error‐rate viewpoint. If decisions are the proper bases for the choice of an error‐rate, the available methods for testing any or all linear contrasts or linear functions of the means are unacceptable. Two new methods (R and D) are proposed for testing all contrasts or linear functions. One implication of the arguments given here is that, for most purposes, research workers have been using the wrong tables of F to test their statistical hypotheses.