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This research purposed to study and compare the efficiencies of multiple comparisons tests with and without parameter of completely randomized design consisting of 6 tests, i.e., Student-Newman-Keul’s test (SNK test), Duncan’s new multiple range test, Waller-Duncan test, Conover test, van der Waerden test and Nemenyi test. The study was conducted in data randomly obtained from normal distribution, gamma distribution and log-normal distribution. For the probability calculation of type I error and power of a test using identical and different sample sizes, divided into small size, medium size and large size, i.e., (10,10,10), (30,30,30), (50,50,50), (5,10,15), (25,30,35) and (45,50,55), and there were 2 levels of significance: 0.01 and 0.05. The results of the study, according to objective 1, indicated that for every situation, the best probability control capability of type I error was found in Student-Newman-Keul’s test, Duncan’s new multiple range test, Waller-Duncan test, Conover test and van der Waerden test. As Weller-Duncan test provided the best power of a test for every situation and the results of the study, according to objective 2, Waller-Duncan test is most suitable for testing data with normal distribution, gamma distribution and log-normal distribution.
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