عنوان

Test statistics for contingency tables

Number

TLpq304006199

.Language of Text, Soundtrack etc

انگلیسی

Title Proper

Test statistics for contingency tables

General Material Designation

[Thesis]

First Statement of Responsibility

M. A. Mannan

Subsequent Statement of Responsibility

R. Nassar

Name of Publisher, Distributor, etc.

Kansas State University

Date of Publication, Distribution, etc.

1991

Specific Material Designation and Extent of Item

111

Dissertation or thesis details and type of degree

Ph.D.

Body granting the degree

Kansas State University

Text preceding or following the note

1991

Text of Note

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.

Pure sciences

Statistics

M. A. Mannan

R. Nassar

Electronic name

p

[Thesis]

276903

a

Y