An apparent inconsistency arising from tests of significance based on fiducial distributions of unknown parameters

A - Papers appearing in refereed journals

Yates, F. 1939. An apparent inconsistency arising from tests of significance based on fiducial distributions of unknown parameters. Mathematical Proceedings Of The Cambridge Philosophical Society. 35 (4), pp. 579-591. https://doi.org/10.1017/S0305004100021356

AuthorsYates, F.
Abstract

It has been observed that the Behrens and Fisher test of the difference of the means of two samples gives a smaller percentage of significant results than might be expected on the analogy of the ordinary t test with a pooled estimate of variance. The cause of this apparent anomaly is explained, and it is shown that the criticisms of the test to which the anomaly has given rise have their origin in (a) neglect of the relevant information provided by the estimated values of the variances, and (b) an insufficient appreciation of the fiducial basis of all tests of significance (including the ordinary t test) on small samples.

Year of Publication1939
JournalMathematical Proceedings Of The Cambridge Philosophical Society
Journal citation35 (4), pp. 579-591
Digital Object Identifier (DOI)https://doi.org/10.1017/S0305004100021356
Open accessPublished as non-open access
PublisherCambridge University Press
Cambridge University Press (CUP)
ISSN0305-0041

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