Proficiency testing with ordinal categorical data

Proficiency testing is carried out to evaluate the performance of participating laboratories by summarizing and comparing the measurement results. This paper discusses methodologies related to measurements with ordinal categorical data. It investigates in detail three methods of statistical significance test with ordinal categorical data, from the viewpoint of whether they can be applied to proficiency testing procedures. These methods are: the cumulative test proposed by Taguchi, the cumulative chi-square test proposed by Takeuchi and Hirotsu, and ORDANOVA proposed by Bashkansky, Gadrich, and Kuselman. Our results suggest that the ORDANOVA method is applicable to proficiency testing and proposes a procedure using these statistics to analyze proficiency testing with ordinal categorical data.