Logarithmic minimum test for independence in three-way contingency table of small sizes

ABSTRACT

The main aim of this paper is to propose a logarithmic minimum test for the three-way contingency table. The second aim is to compare the quality of independence tests by using their power. Each test has power of test (PoT) function of its own. The PoT functions are determined with the Monte Carlo method and then compared to each other. The third aim is to use a measure named the mean average outgoing untruthfulness level in order to ease such a PoT-to-PoT comparison. Critical values for analysed tests are determined by simulating the Monte Carlo method. Simulation study shows that the new test is more powerful than the other analysed tests, including ${\chi }^2$ test. Real data and simulation examples are presented.

KEYWORDS:

• Chi-squared statistics
• independence test
• logarithmic minimum statistic
• modular statistic
• Monte Carlo method

Subject classification codes:

• 62H15
• 62H17
• 62H20

Acknowledgments

The Author is indebted to the unknown Referees for helpful comments on a draft of this paper.

Disclosure statement

No potential conflict of interest was reported by the author.