GART TEST OF INTERACTION IN A 2X2X2 CONTINGENCY TABLE FOR SMALL SAMPLES
成果类型：
Note
署名作者：
VENABLE, TC; BHAPKAR, VP
刊物名称：
BIOMETRIKA
ISSN/ISSBN：
0006-3444
发表日期：
1978
页码：
669672
关键词：
摘要：
For the 1-response, 2-factor design with categorical data, Gart (1972) proposed a statistic to test the hypothesis of zero 2nd-order interaction. Unconditionally the statistic approaches .infin. with probability 1 when the interaction effect is 0 and the row and column effects are not 0. Thus the null hypothesis is rejected with probability 1 and the statistic is not valid for the hypothesis, unless certain other special conditions are true. Because the sample size must be extremely large for the above conclusion to hold, merit for Gart''s test might still be found when the samples are small; the statistic was developed by approximating the exact probability. Such a conjecture is examined by a simulation in which Gart''s statistic is compared to Wald''s statistic in the 2 .times. 2 .times. 2 case, both as to respective ability to approximate the exact test and as to their power. Gart''s statistic is the better in approximating the inference of the exact test; this is because of the conservative nature of both the exact and Gart''s tests. Gart''s test is less powerful than Wald''s.