Critical values for six Dixon tests for outliers in normal samples up to sizes 100, and applications in science and engineering

  • Surendra P. Verma Centro de Investigación en Energía, Universidad Nacional Autónoma de México, Priv. Xochicalco s/no., Col Centro, Apartado Postal 34, Temixco 62580, Mexico. Centro de Investigación en Ingeniería y Ciencias Aplicadas, Universidad Autónoma del Estado de Morelos, Av. Universidad No. 1001, Col. Chamilpa, Cuernavaca 62210, Mexico.
  • Alfredo Quiroz-Ruiz Centro de Investigación en Energía, Universidad Nacional Autónoma de México, Priv. Xochicalco s/no., Col Centro, Apartado Postal 34, Temixco 62580, Mexico.
Keywords: Outlier methods, normal sample, Monte Carlo simulations, reference materials, earth sciences.

Abstract

In this paper we report the simulation procedure along with new, precise, and accurate critical values or percentage points (with 4 decimal places; standard error of the mean ≤0.0001) for six Dixon discordance tests with significance levels α = 0.30, 0.20, 0.10, 0.05, 0.02, 0.01, 0.005 and for normal samples of sizes n up to 100. Prior to our work, critical values (with 3 decimal places) were available only for n up to 30, which limited the application of Dixon tests in many scientific and engineering fields. With these new tables of more precise and accurate critical values, the applicability of these discordance tests (N7 and N9-N13) is now extended to 100 observations of a particular variable in a statistical sample. We give examples of applications in many diverse fields of science and engineering including geosciences, which illustrate the advantage of the availability of these new critical values for a wider application of these six discordance tests. Statistically more reliable applications in science and engineering to a greater number of cases can now be achieved with our new tables than was possible earlier. Thus, we envision that these new critical values will result in wider applications of the Dixon tests in a variety of scientific and engineering fields such as agriculture, astronomy, biology, biomedicine, biotechnology, chemistry, environmental and pollution research, food science and technology, geochemistry, geochronology, isotope geology, meteorology, nuclear science, paleontology, petroleum research, quality assurance and assessment programs, soil science, structural geology, water research, and zoology.

Published
2018-04-18
Section
Articles