Skip Navigation

Biometrika 1984 71(3):515-522; doi:10.1093/biomet/71.3.515
© 1984 by Biometrika Trust
This Article
Right arrow Full Text (PDF)
Right arrow Alert me when this article is cited
Right arrow Alert me if a correction is posted
Services
Right arrow Email this article to a friend
Right arrow Similar articles in this journal
Right arrow Alert me to new issues of the journal
Right arrow Add to My Personal Archive
Right arrow Download to citation manager
Right arrowRequest Permissions
Google Scholar
Right arrow Articles by LEWIS, T.
Right arrow Articles by WESTCOTT, M.
Right arrow Search for Related Content
Social Bookmarking
Add to CiteULike   Add to Connotea   Add to Del.icio.us  
What's this?

The moments of the Pearson chi-squared statistic and the minimum expected value in two-way tables

T. LEWIS, I. W. SAUNDERS and M. WESTCOTT

Faculty of Mathematics, The Open University Milton Keynes, Buckinghamshire, U.K.
CSIRO Division of Mathematics and Statistics Melbourne, Australia
CSIRO Division of Mathematics and Statistics Canberra, Australia

Explicit expressions for the first three moments of Pearson's X2 statistic for a two-way contingency table are used to investigate the accuracy of the {chi}2 approximation to its distribution. The usual ’minimum expected value' criterion is shown to give a global bound on the accuracy of the moments, but to be too conservative. This is illustrated by examples. It is shown that the adequacy of the approximation depends on the significance level that is to be used as well as the accuracy of the moments. When the {chi}22 approximation is inadequate, corrections based on the moments can be used. Numerical studies of the usefulness of these corrections are presented.

Key Words: Approximate distribution • Moment • Pearson's chi-squared statistic • Two-way table


Add to CiteULike CiteULike   Add to Connotea Connotea   Add to Del.icio.us Del.icio.us    What's this?




Disclaimer:
Please note that abstracts for content published before 1996 were created through digital scanning and may therefore not exactly replicate the text of the original print issues. All efforts have been made to ensure accuracy, but the Publisher will not be held responsible for any remaining inaccuracies. If you require any further clarification, please contact our Customer Services Department.