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Limites unilaterais e bilaterais na análise estatística

1946; INSTITUTO AGRONÔMICO DE CAMPINAS; Volume: 6; Issue: 10 Linguagem: Inglês

10.1590/s0006-87051946001000001

1678-4499

F. G. Brieger,

Genetics and Plant Breeding

SUMMARY 1) The present paper represents a continuation and complement to a previous publication (Brieger 4) in which I explained the mathematical relations between the four most important types of chance distributions. While carrying out a large number of statistical analysis, of genetical and agricultural experiments, I came to the conclusion that the existing tables for the limits of chance distributions (Fisher and Yates, 7, Snedecor, 8, Brieger 2) are not satisfactory in three repects. a) The tables of Fisher and Yates and of Snedecor give the limits of the t-test and of the z or F-test with different systems of ordinates ; b) there are only tables for bilateral limits of t (Student) and for unilateral limits of z (Fisher), F (Snedecor) or theta (Brieger) ; c) the tables contain only values for a limited number of degrees of freedom without an auxiliary table for interpolation. The tables, included here, are calculated in such a way as to avoid these objections. 2) The basic value for all of the new tables is the relative deviate ,which may be either simple or compound : A simple relative deviate is the quotient of a difference between a variate and its ideal value which generally is the mean divided by the respective standard error. When comparing several deviates simultaneously, we unite them in one balanced mean estimate which is the square root of the mean square deviate (the sum of the squares of deviates divided by their degree of freedom). This value divided by the best estimate of the respective standard error is the compound relative deviate. The four main types of chance distributions may be defined mathematically in such a form that the relative deviates form the abscissa and their frequencies the ordinates, as shown in the preceding publications (Brieger 4). Simple relative deviates follow Students' distribution when the degree of freedom of the divisor is small (t-test) and the Gaussean distribution (delta-test) when the degree of freedom is infinitely large, accepting as a reasonable aproximation to infinity a value bigger than 100. Relative compound deviates, on the other side, follow either Fisher's or Pearson's distribution, when the degree of freedom of the dividend is bigger than one and that of the divisor is either a limited or unlimited value (theta-test). 3) I explained (4) in