Breakthroughs in Statistics: Methodology and Distribution by G. A. Barnard (auth.), Samuel Kotz, Norman L. Johnson (eds.)

By G. A. Barnard (auth.), Samuel Kotz, Norman L. Johnson (eds.)

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N-3 n-5 x cosn e, which affords an easy way of drawing the curve. Also dz = dejcos 2 e. 45 The Probable Error of a Mean Hence to find the area of the curve between any limits we must find n-2n-4 _ _ . _ _ ... etc. x n-3 n-5 f n- 2 n- 4 cos n- 2 ede {n - 3 fcos = -_·--···etc. - - n-3 n-5 n-4 n-2 ede + [cosn- 3 esin e]} n-2 n - 4 . __ n - 6 ... etc. f cos n-4 e de + -_. 1 -_ n - 4 ... etc. [n-3 esm, . e] = __ cos n-5 n-7 n-3 n-5 and by continuing the process the integral may be evaluated. ~ f8 cos 6 ede 5 3 1 n 4 2 = _.

69-70. Stigler, Stephen J. (1986). The History of Statistics: The Measurement of Uncertainty, Belknap, Harvard University Press, p. 361. On the Criterion that a Given System of Deviations from the Probable in the Case of a Correlated System of Variables is Such that it Can be Reasonably Supposed to have Arisen from Random Sampling Karl Pearson University College, London The object of this paper is to investigate a criterion of the probability on any theory of an observed system of errors, and to apply it to the determination of goodness of fit in the case of frequency curves.

Da r:. and the vn 43 The Probable Error of a Mean 4 = 0'2 {n 2 - 1 - D2(3D2 - 2n + 6)}. n It is of interest to find out what these become when n is large. In order to do this we must find out what is the value of D. n - etc. 6 2 ••• (2n)2 - 2n+-+- = 2 2 2 * 2 2 16n 1 ·3 ·S ···(2n _1)2" From this we find that whether n be even or odd D2 approximates to 3 1 h . I n - 2" + 8n w en n IS arge. Substituting this value of D we get 1) 0'2 ( 0' 112 = 2n 1 - 4n ,1l3 = 3J1- 2n + 16n2 3 1 4n2 30'4 ( ' 114 = 4n2 1 1 1) + 2n - 16n2 .

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