A Graphical Approach for Friedman Test: Moments Approach

TL;DR

This paper introduces a graphical, moments-based approach for the Friedman test that simplifies visualization, reduces the number of comparisons, and accurately controls type I error in nonparametric block design analysis.

Contribution

It proposes a new expression for plotting Friedman test results that combines test and pairwise comparisons, along with deriving its sampling distribution using the method of moments.

Findings

Reduces the number of tests needed to identify differences.

Maintains type I error close to the nominal level.

Provides visual and intuitive understanding of treatment effects.

Abstract

Friedman test is a nonparametric method that proposed for analyzing data from a randomized complete block design as a robust alternative to parametric method and widely applied in many fields such as agriculture, biology, business, education, and medicine. After the null hypothesis of no treatment effects is rejected, the post-hoc pairwise comparisons must be applied to identify where the differences occur. As the number of groups increases, the number of required comparisons becomes large and this may increase the type I error. The aim of this study is twofold. The main aim is to suggest expression that facilitates the plotting Friedman test by gathering the test and pairwise comparisons in one simple step. The second aim is to derive the sampling distribution of the suggested expression by utilizing method of moments that helps in obtaining the decision limit. An application and simulation study are carried out to show the advantage of the suggested method and to compute the empirical type I error. The results are of great value where the proposed method makes huge reduction in the number of required tests to show where the discrepancies occur, holds the type I error close to the nominal value and provides visual, deep insight and understanding where the treatment effects occur.