Seminar Reports in Mathematics [antikvár]

ON STATISTICAL COEFFICIENTS OF LIKENESS BY PAUL G. HOEL[Received December 11, 1940]Introduction. Biologists are often concerned with the following two problems: Given p samples of n variables, do the p samples differ significantly? Given p samples of n variables, does sample c differ more from sample a than sample ? Coefficients or indices designed to answer these questions are rather common in applied literature. Among the better known coefficients, perhaps the two by Pearson and the one by Fisher [2] are the .best. It is the purpose of this paper to consider the coefficients of Pearson and Fisher and to evaluate them in the light of hypothesis testing.The first of the two problems, which requires a significance test for its solution, will be considered first. Then the possibility of solving the second problem by the methods of solution of the first problem will be considered.Pearson's method. Pearson designed an index, which he called a coefficient of racial likeness, for distinguishing between two small samples of skulls on which a large number of measurements had been taken. His assumptions and methods were as follows:Let n characters be measured for each individual from a sample of m individuals, and let p such samples be drawn. Let Xika be the measurement of character i in sample k for individual a, and let r^k be the correlation between characters i and j in sample k. Assume that the n character measurements follow a normal distribution given bywhere A'' = pij

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Cím: Seminar Reports in Mathematics [antikvár]

Kiadó: University of California Press

Kötés: Varrott papírkötés

Méret: 180 mm x 260 mm

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