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

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 $α$-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.

💡 Research Summary

The manuscript tackles a fundamental problem in precision agriculture: how to compare the distribution of yield quality metrics (e.g., protein content, moisture, nutrient density) across several fields when the data are both non‑normal and spatially autocorrelated. Classical parametric approaches such as ANOVA or t‑tests assume independent, identically distributed observations; when spatial dependence is present, the variance is underestimated and Type I error rates can become dramatically inflated. Existing spatial solutions—geostatistical models (Kriging, spatial GLS) or permutation‑based block bootstraps—either rely on normality of residuals and a correctly specified variogram, or they are computationally intensive and sensitive to the choice of block size.

To overcome these limitations, the authors propose a rank‑based testing framework that incorporates spatial kernel smoothing directly into the construction of empirical distribution functions (EDFs). For each field (k) they define a kernel‑weighted EDF (\hat F_{k,h}(x; s_0)) at a fixed interior reference location (s_0), using a symmetric, compact‑support kernel (K_h) with bandwidth (h). The denominator of the EDF is the sum of kernel weights, which under a regular lattice design behaves like a Riemann sum and yields an effective local sample size (m_{n,k}=h^2/\Delta^2) (in two dimensions).

A pooled, weight‑averaged EDF (\hat F_h(x; s_0)=\sum_{k=1}^K (m_{n,k}/m_n)\hat F_{k,h}(x; s_0)) is constructed, where (m_n=\sum_k m_{n,k}). The contrast for field (k) is then \