A remark on statistics for detecting laboratory effects in ORDANOVA

TL;DR

This paper introduces a new statistical method for detecting laboratory effects in ordinal data analysis, providing an approximate distribution and applying it to real interlaboratory comparison data.

Contribution

It proposes a novel statistic for ORDANOVA, along with its approximate distribution and practical application to interlaboratory data.

Findings

The new statistic effectively detects laboratory effects.

Alpha-percentiles serve as reliable criteria for statistical testing.

Application to real data demonstrates practical utility.

Abstract

The present study defines a new statistic for detecting laboratory effects in the analysis of ordinal variation (ORDANOVA). The ORDANOVA is an analysis method similar to one-way analysis of variance for analysing ordinal data obtained from interlaboratory comparison studies. In this paper, we present an approximate continuous distribution for the new statistic for the case of an arbitrary number of ordinal levels, and we demonstrate that $alpha$-percentiles of the distribution are suitable criteria for conducting statistical tests. In addition, a real example involving data from an interlaboratory comparison study is analysed using the proposed statistic.