Statistical Methods for Evaluating Results from Soil Micronutrient Analyses in Interlaboratory Programs

Abstract

Interlaboratory comparison programs have been found to be useful to investigate potential error sources and therefore to remove or minimize their effects. A proficiency test was performed for five soil micronutrients [boron (B), iron (Fe), manganese (Mn), copper (Cu), and zinc (Zn)] by forty-nine independent Brazilian laboratories on four duplicated soil samples. Extraction of B was performed by hot water, whereas Fe, Mn, Cu, and Zn were extracted by diethylenetriaminepentaacetic acid (DTPA). The objectives were to compare the performance of different statistical methods for assessing between-laboratory variability (reproducibility) and to quantify the variability within single laboratories (repeatability). The statistical methods employed to compare interlaboratory analytical results were (1) Agronomic Institute method (mean, standard deviation, coefficient of variation), (2) Z1 score (mean and standard deviation, including outliers), (3) Z2 score (mean and standard deviation, excluding outliers), (4) robust Z score (median and standardized interquartile amplitude) denoted as Z3, (5) Cochran test, and (6) Cochran + Grubbs tests. In addition, the robust Z-score method, denoted as Z4, was used to assess intralaboratory variability. The performance of any laboratory for the analysis of soil micronutrients varied depending on the statistical method applied. The percentage of laboratories providing satisfactory results was 79 percent (Agronomic Institute), 95 percent (Z1), 92 percent (Z2), 89 percent (robust Z3 score), 97 percent (Cochran), and 95 percent (Cochran + Grubbs). The Z-score tests become stronger and more rigorous when outliers were excluded (Z2) or when the standardized interquartile amplitude was used (Z3). Cochran and Grubbs tests, which are based on the removal of extreme values, were weaker than the other tests evaluated. In conclusion, the method employed by the proficiency test of the Agronomic Institute for removing outliers has been found to be the strongest and strictest one, yielding a reliable comparison of the results from soil micronutrient analyses.Color versions of one or more of the figures in the article can be found online at www.tandfonline.com/lcss.