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The objective of this research is to compare the efficiency of the three nonparametric statistical tests for 23 factorial experimental design: rank sums test, rank transform test and aligned rank transform test. The data in this research is simulated by the Monte Carlo technique and each case is replicated 1,000 times. The data is generated from the linear model of 23 factorial experimental design. In each treatment combination, it is repeated 2, 3, 4, 5 and 6 times. The criteria for comparison are Bradley’s control ability of type I error and power of a test. For the results, it is found that at the significant level 0.05, rank sums test cannot control the probability of type I error in all cases. However, rank transform test and aligned rank transform test can control the probability of type I error in almost every situation. When considering the power of a test, it is found that power of a test of aligned rank transform test is greater or equal to that of rank transform test for all situations.
Keywords: nonparametric statistic; 23 factorial experimental design; type I error; power of a test
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