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Numerical comparison of improved methods of testing in contingency tables with small frequencies

Technical Report:

Abstract

The significance levels of various tests for a general c x k contingency table are usually given by large sample theory. But they are not accurate for the one having small frequencies. In this paper, a numerical evaluation was made to determine how good the approximation of significance level is for various improved tests that have been developed by Nass, Yoshimura, Gart, etc. for c x k contingency table with small frequencies in some of cells. For this purpose we compared the significance levels of the various approximate methods (i) with those of one-sided tail defined in terms of exact probabilities for given marginals in 2 x 2 table; (ii) with those of exact probabilities accumulated in the order of magnitude of Chi/sup 2/ statistic or likelihood ratio (=LR) statistic in 2 x 3 table mentioned by Yates. In 2 x 2 table it is well known that Yates' correction gives satisfactory result for small cell frequencies and the other methods that we have not referred here, can be considered if we devote our attention only to 2 x 2 or 2 x k table. But we are mainly interested in comparing the methods that are applicable to a general  More>>
Publication Date:
Nov 14, 1968
Product Type:
Technical Report
Report Number:
ABCC-TR-22-68
Reference Number:
EDB-84-059877
Subject:
99 GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE; STATISTICAL MODELS; BIOLOGY; CALCULATION METHODS; MEDICINE; STATISTICS; MATHEMATICAL MODELS; MATHEMATICS; 990200* - Mathematics & Computers
OSTI ID:
5166944
Research Organizations:
Atomic Bomb Casualty Commission, Hiroshima (Japan)
Country of Origin:
Japan
Language:
Japanese and English
Contract Number:
AC01-76EV03081
Other Identifying Numbers:
Other: ON: DE84008145
Availability:
NTIS, PC A02/MF A01.
Submitting Site:
HEDB
Size:
Pages: 17
Announcement Date:

Technical Report:

Citation Formats

Sugiura, Nariaki, and Otake, Masanori. Numerical comparison of improved methods of testing in contingency tables with small frequencies. Japan: N. p., 1968. Web.
Sugiura, Nariaki, & Otake, Masanori. Numerical comparison of improved methods of testing in contingency tables with small frequencies. Japan.
Sugiura, Nariaki, and Otake, Masanori. 1968. "Numerical comparison of improved methods of testing in contingency tables with small frequencies." Japan.
@misc{etde_5166944,
title = {Numerical comparison of improved methods of testing in contingency tables with small frequencies}
author = {Sugiura, Nariaki, and Otake, Masanori}
abstractNote = {The significance levels of various tests for a general c x k contingency table are usually given by large sample theory. But they are not accurate for the one having small frequencies. In this paper, a numerical evaluation was made to determine how good the approximation of significance level is for various improved tests that have been developed by Nass, Yoshimura, Gart, etc. for c x k contingency table with small frequencies in some of cells. For this purpose we compared the significance levels of the various approximate methods (i) with those of one-sided tail defined in terms of exact probabilities for given marginals in 2 x 2 table; (ii) with those of exact probabilities accumulated in the order of magnitude of Chi/sup 2/ statistic or likelihood ratio (=LR) statistic in 2 x 3 table mentioned by Yates. In 2 x 2 table it is well known that Yates' correction gives satisfactory result for small cell frequencies and the other methods that we have not referred here, can be considered if we devote our attention only to 2 x 2 or 2 x k table. But we are mainly interested in comparing the methods that are applicable to a general c x k table. It appears that such a comparison for the various improved methods in the same example has not been made explicitly, even though these tests are frequently used in biological and medical research. 9 references, 6 figures, 6 tables.}
place = {Japan}
year = {1968}
month = {Nov}
}