Efficiency Comparison of Statistical Tests of Independence under the Differences of Data Distributions and Relationships

The purpose of this research is to compare the efficiency of statistical tests of independence under the differences of data distributions and relationships. These tests are considered type I error and power of a test of five statistical tests which are Pearson’s chi-squared test, Yates's test, the log likelihood ratio test, the modified log likelihood ratio test and the Neyman’s test. The simulation is used Monte Carlo technique 10,000 times. Under the condition of 2x2 contingency tables from uniform, moderately skewed and highly skewed distribution with weak, medium and strong relationships. The sample sizes are 20, 30, 40, 50, 100, 150, 200 and 300. The significance levels are 0.01 and 0.05. The results show that with the differences of data distribution and relationships for all sample sizes and significance levels, the Neyman’s test and the log likelihood ratio test are more efficient than the modified log likelihood ratio test, Pearson’s chi-squared test and Yates's test, respectively. For all data distributions, power of a test of five statistical tests vary with relationships, sample sizes and significance levels and are more as relationships, sample sizes and significance levels increase. Keywords : type I error, power of a test, statistical test of independence, Contingency table