A Rank-Based Test for Comparing Multiple Fields' Yield Quality Distributions Under Spatial Dependence

TL;DR

This paper proposes a new rank-based statistical test that uses spatial kernel smoothing to compare yield quality distributions across multiple fields, effectively handling non-normality and spatial dependence.

Contribution

It introduces a novel spatially-aware rank-based testing framework with proven asymptotic properties and practical inference methods, addressing limitations of traditional parametric tests under spatial autocorrelation.

Findings

The test converges to a weighted sum of chi-squared variables.

A Satterthwaite approximation provides effective degrees of freedom.

The method is theoretically grounded for spatially dependent data.

Abstract

Comparing yield quality distributions across multiple agricultural fields is fundamental for evaluating management practices, yet it is complicated by two pervasive data characteristics: non-normality and spatial autocorrelation. Traditional parametric tests, such as ANOVA, frequently suffer from severe Type I error inflation when the independence assumption is violated by spatial dependence. This paper introduces a novel rank-based test framework that utilizes spatial kernel smoothing to construct robust empirical distribution functions (EDFs). We establish the asymptotic properties of the test statistic under $\alpha$-mixing conditions, proving its convergence to a weighted sum of chi-squared random variables. To facilitate practical inference, we employ a Satterthwaite approximation to derive effective degrees of freedom that account for the spatial 'inflation' of variance. The theoretical framework is developed in detail, providing a rigorous foundation for the proposed method. Simulation studies and applications to real yield quality data are left to future work.