38
views
0
recommends
+1 Recommend
1 collections
    0
    shares
      • Record: found
      • Abstract: found
      • Article: found
      Is Open Access

      Evaluation of polynomial regression models for the Student t and Fisher F critical values, the best interpolation equations from double and triple natural logarithm transformation of degrees of freedom up to 1000, and their applications to quality control in science and engineering Translated title: Evaluación de modelos polinomiales de regresión para los valores críticos de t de Student y F de Fisher, las mejores ecuaciones de interpolación con transformación logarítmica natural de tipo doble y triple de grados de libertad hasta 1000, y su aplicación en el control de calidad en ciencias e ingenierías

      research-article

      Read this article at

      Bookmark
          There is no author summary for this article yet. Authors can add summaries to their articles on ScienceOpen to make them more accessible to a non-specialist audience.

          Abstract

          Serious gaps exist in the present critical value tables for the Student t and Fisher F or ANOVA significance tests. Statistically correct applications of these tests to the experimental data therefore become difficult. A total of 18 different regression models were evaluated for the Student t and 24 for the Fisher F critical values. These models varied from simple polynomial (quadratic to 7th order) to the combined single (ln), double (lnln), or triple (lnlnln) natural-logarithm- (ln-) transformed polynomial models. The advantage of ln-, lnln- or lnlnln-transformations of the degrees of freedom for interpolating the Student t and Fisher F critical values has been documented for the first time in the published literature. The use of critical value equations applicable in the range of 1-1000 degrees of freedom for ln-transformation, 2-1000 for lnln-transformation, or 3-1000 for lnlnln-transformation, instead of the tables, is proposed as a 21st century innovation for the computer programming of these significance tests. A number of application examples are pointed out to illustrate the usefulness of this work.

          Translated abstract

          Las tablas de valores críticos para las pruebas de significado de t de Student y F de Fisher o ANOVA, se caracterizan por serias deficiencias. Aplicaciones estadísticamente correctas de estas pruebas a los datos experimentales, por lo tanto, se hacen difíciles. Se evaluaron un total de 18 modelos de regresión para los valores críticos de t de Student y 24 modelos para los de F de Fisher. Estos modelos varían de modelos polinomiales (de tipo cuadrático hasta la 7ª. potencia) sencillos hasta los polinomiales combinados con la transformación logarítmica natural (ln) de tipo sencillo (ln), doble (lnln), o triple (lnlnln). Las ventajas de la transformaciones ln, lnln o lnlnln de los grados de libertad para la interpolación de los valores críticos de t de Student y F de Fisher se demuestran por primera vez en la literatura publicada. Para la programación computacional de dichas pruebas de significado se propone, en lugar de las tablas, como la innovación del siglo XXI, el uso de las ecuaciones de valores críticos aplicables en el intervalo de 1-1000 grados de libertad para la transformación ln, de 2-1000 para la transformación lnln, o de 3-1000 para la transformación lnlnln. Se presentan una serie de ejemplos de aplicación con el fin de ilustrar la utilidad de este trabajo.

          Related collections

          Most cited references100

          • Record: found
          • Abstract: not found
          • Article: not found

          Statistical treatment for rejection of deviant values: critical values of Dixon's "Q" parameter and related subrange ratios at the 95% confidence level

            Bookmark
            • Record: found
            • Abstract: found
            • Article: found
            Is Open Access

            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 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.
              Bookmark
              • Record: found
              • Abstract: found
              • Book: not found

              Statistics and Chemometrics for Analytical Chemistry

              This popular textbook gives a clear and lucid account of the underlying principles of statistical methods. The fourth edition has been revised and updated to reflect the growing popularity of statistics and chemometric methods and new approaches in optimization and experimental design. The authors have also addressed the quality of analytical chemistry data and experimental results, an area of increasing concern to chemists testing the safety of food and medicines.<br> <br> This book will suit undergraduate, M.Sc. and graduate courses in Analytical Chemistry and related topics, and will also be valuable for researchers and chemists working in analytical chemistry everywhere.
                Bookmark

                Author and article information

                Journal
                rmcg
                Revista mexicana de ciencias geológicas
                Rev. mex. cienc. geol
                Instituto de Geología, UNAM (México, DF, Mexico )
                1026-8774
                2007-2902
                April 2009
                : 26
                : 1
                : 79-92
                Affiliations
                [01] Temixco Mor orgnameUniversidad Nacional Autónoma de México orgdiv1Centro de Investigación en Energía Mexico spv@ 123456cie.unam.mx
                Article
                S1026-87742009000100007 S1026-8774(09)02600100007
                01f71d32-fb97-40e2-9245-589162e8b0cc

                This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.

                History
                : 04 September 2008
                : 17 June 2008
                : 04 September 2008
                Page count
                Figures: 0, Tables: 0, Equations: 0, References: 55, Pages: 14
                Product

                SciELO Mexico


                significance tests,pruebas de significado o significancia,degrees of freedom,reference material,F-ratio,critical value,ANOVA,grados de libertad,materiales de referencia,valor crítico,Relación F

                Comments

                Comment on this article