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The objective of this research was to multi-compare the control efficiency of probability of type I error and power of a test between parametric and nonparametric tests of a randomized incomplete block designs. The 6 statistics were Duncan’s new multiple range, Waller-Duncan and Fisher’s least significant difference, Conover, Durbin and Skillings-Mack. In all cases, we used randomized data with a normal distribution, gamma distribution and beta distribution for calculating the probability of type I error and the power of a test. Creating a randomized incomplete block designs will determine the number of treatments (that equal to 3, 4, 5, 6 and 7 treatments), and the number of blocks (that equal to 3, 4, 5, 6 and 7 blocks). Two significance levels were used 0.05 and 0.10. The results for probability of type I error revealed that, for controlling probability of type I error, the Waller-Duncan and Fisher’s least significant difference were the best in controlling it. For the power of a test, the Waller-Duncan showed the highest power of a test.
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