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 cont
Keywords: F-ratio, ANOVA, critical value, degrees of freedom, reference material, signiﬁcance tests
AbstractSerious gaps exist in the present critical value tables for the Student t and Fisher F or ANOVA signiﬁ cance tests. Statistically correct applications of these tests to the experimental data therefore become difﬁ cult. 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 ﬁ rst 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 signiﬁ cance tests. A number of application examples are pointed out to illustrate the usefulness of this work.
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