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

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 signifi cance 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 scientifi c and engineering fi elds. 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 fi elds 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 scientifi c and engineering fi elds 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.