Abstract:
In the statistical literature for testing differences of two or more populations
in an ordinal table, we normally use Pearson’s chi-squared test(1900),
Wilcoxon test(1945), Mantel’s test(1963) and Nair’s test(1986). In those
tests, Pearson’s chi-squared test does not have good power against ordered
alternatives and the Wilcoxon test or Mantel’s test has high powers for detecting
linear responses, but poorly behaves for detecting non-linear responses
which we are interested in this thesis. Nair’s test is, specially designed to
detect dispersion alternatives.
Jayasekara and Yanagawa(Bulletin of informatics and Cybernetics, 31(1999),
180-190) have proposed a statistical test called Qt test which has higher powers
for non-linear responses in 2 x k ordered categorical tables. The purpose
of this research work is to extend the Qt test for testing ordered categorical
data in r x k tables.
The proposed Statistic is expressed as functions of the Wilcoxon test and
a test whose score is orthonormal to the Wilcoxon score.
The asymptotic distributions of the proposed test are obtained both under
the null and alternative hypothesis.
Considering the linear and non-linear response patterns, the asymptotic
powers of the proposed test are computed.
Also using the simulation, the proposed test was compared with Mantel’s
test and Pearson’s Chi-squared test. It is shown that the test is superior to
Pearson’s chi-squared test and Mantel’s test in many cases.
