Test statistics for contingency tables

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منو

" Test statistics for contingency tables "
M. A. Mannan R. Nassar

Document Type	:	Latin Dissertation
Language of Document	:	English
Record Number	:	1112366
Doc. No	:	TLpq304006199
Main Entry	:	M. A. Mannan
	:	R. Nassar
Title & Author	:	Test statistics for contingency tables\ M. A. MannanR. Nassar
College	:	Kansas State University
Date	:	1991
student score	:	1991
Degree	:	Ph.D.
Page No	:	111
Abstract	:	Contingency tables of dimension 2 x 2 and 2 x 2 x 2, arising from multinomial sampling, are of importance in many areas of investigations specially in survey and genetical research. To test the hypothesis of independence or no interaction between the categorical variables in a 2 x 2 contingency table, the log-odds ratio and the Pearson's chi-square (or equivalently, the square correlation coefficient r) are commonly employed. In this study two test procedures for independence in 2 x 2 and 2 x 2 x 2 contingency tables are proposed and their size and power investigated along with that of the log-odds ratio and the chi-square test procedures. The procedures are (1) the covariance test for linkage disequilibrium between two genes and (2) the natural logarithm of a cell probability divided by its marginals (multiplicative ratio test). Furthermore, the correlation coefficient r was extended to formulate a test statistic for no three-factor interaction in 2 x 2 x 2 contingency tables. Under the null hypothesis of independence, it is shown that each of the test procedures has an asymptotic normal distribution. Simulation results showed that under the null hypothesis, the proposed test procedures were as good as the Pearson's chi-square procedure. Also, the corrected Pearson's chi-square was conservative and inappropriate for 2 x 2 tables arising from multinomial sampling where the marginals can not be considered as fixed. For 2 x 2 x 2 tables, the proposed test procedures showed agreement between the observed and nomial usd\alphausd levels. By comparison, the log-odds ratio and the chi-square procedures were conservative. Power results showed that the proposed multiplicative ratio procedure had the highest power for 2 x 2 tables when the linkage disequilibrium (or correlation) between the two genes or categories was positive. For negative correlation, the covariance test gave the highest power. For 2 x 2 x 2 tables, the correlation test had the highest power, but was not substantially higher than that of the covariance test, specially for small sample size.
Subject	:	Pure sciences
	:	Statistics