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<p>In this work, a Monte Carlo simulation study was conducted to evaluate the type-I-error rate and power of ANOVA F-test (F-Test), Friedman test (FR-Test) and randomization test (R-Test) for the analysis of randomized complete block design. The performance of the F-Test, FR-Test and R-Test was investigated using four effect sizes (Δ = 0.5, 0.75, 1 and 1.5), and three treatments conditions (<i>t</i> = 3, 6 and 9) that were simultaneously varied with the number of blocks (<i>b</i>  =  5, 10, 15, 20, 30, 40 and 50) under three variance ratios (<InlineEquation ID="IEq1"> <EquationSource Format="TEX">\({\sigma }^{2}\)</EquationSource> </InlineEquation> = 1, 1.5 and 3) when the error is normal or skewed (Cauchy and logistic distributions). The simulation results showed that the R-Test was robust in controlling type-I-error rates at 1% and 5% levels of significance and was more powerful than both the ANOVA F-test and Friedman test for most conditions. However, under the Cauchy distribution, the R-Test showed slight limitations at<i> t</i> = 6, with increased type-I-error and reduced power. Hence, the R-Test is highly recommended for RCBD due to its superior performance across diverse conditions.</p>

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A Monte Carlo simulation study of the type-I-error and power of ANOVA F-test, Friedman test and randomization test for randomized complete block design

  • 期刊论文

  • 发表日期：

    2025年9月15日

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  • Abimibola Victoria Oladugba,
  • Uchenna Valentine Ikebuife

摘要

In this work, a Monte Carlo simulation study was conducted to evaluate the type-I-error rate and power of ANOVA F-test (F-Test), Friedman test (FR-Test) and randomization test (R-Test) for the analysis of randomized complete block design. The performance of the F-Test, FR-Test and R-Test was investigated using four effect sizes (Δ = 0.5, 0.75, 1 and 1.5), and three treatments conditions (t = 3, 6 and 9) that were simultaneously varied with the number of blocks (b  =  5, 10, 15, 20, 30, 40 and 50) under three variance ratios ( \({\sigma }^{2}\) = 1, 1.5 and 3) when the error is normal or skewed (Cauchy and logistic distributions). The simulation results showed that the R-Test was robust in controlling type-I-error rates at 1% and 5% levels of significance and was more powerful than both the ANOVA F-test and Friedman test for most conditions. However, under the Cauchy distribution, the R-Test showed slight limitations at t = 6, with increased type-I-error and reduced power. Hence, the R-Test is highly recommended for RCBD due to its superior performance across diverse conditions.