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

ISBN-10: 0387940391

ISBN-13: 9780387940397

ISBN-10: 1461243807

ISBN-13: 9781461243809

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This work of Fisher's was a great achievement. With the inspiration only of Student's paper, to which he always gives full credit and which he often describes as revolutionary, Fisher single-handedly transformed both the theory and practice of hypothesis testing and made of it a powerful tool of nearly universal usefulness. In the wake of Fisher's work, Student's t-test has had a fundamental impact on statistics in three different ways. 1. The t-test, if one includes its extension to two samples and to regression coefficients, has probably been used more widely (although not necessarily always wisely) than any other statistical test.

Hence: X2 - X~ = -s { -/1 mtl m'2 - mtl tl m2} + S {(-/1 mtl )2 m12} -. mtl Now Xtl must, I take it, be less than X, for otherwise the general population distribution or curve would give a better fit than the distribution or curve actually fitted to the sample. But we are supposed to fit a distribution or curve to the sample so as to get the "best" values of the constants. Hence the right-hand side of the above equation must be positive. If the first term be negative then it must be less than the second, or the difference of X and Xtl is of the order, not of the first but of the second power of quantities depending on the probable errors of the sample.

New tables for testing the significance of observatIOns, Metron, 5, 105-108. The Probable Error of a Mean Student Introduction Any experiment may be regarded as forming an individual of a "population" of experiments which might be performed under the same conditions. A series of experiments is a sample drawn from this population. Now any series of experiments is only of value in so far as it enables us to form a judgment as to the statistical constants of the population to which the experiments belong.

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

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