Adjusting the Scott-Knott cluster analyses for unbalanced designs

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Abstract
The Scott-Knott cluster analysis is an alternative approach to mean comparisons with high power and no subset overlapping. It is well suited for the statistical challenges in agronomy associated with testing new cultivars, crop treatments, or methods. The original Scott-Knott test was developed to be used under balanced designs; therefore, the loss of a single plot can significantly increase the rate of type I error. In order to avoid type I error inflation from missing plots, we propose an adjustment that maintains power similar to the original test while adding error protection. The proposed adjustment was validated from more than 40 million simulated experiments following the Monte Carlo method. The results indicate a minimal loss of power with a satisfactory type I error control, while keeping the features of the original procedure. A user-friendly SAS macro is provided for this analysis.