Abstract
Recent years have seen an almost universal acceptance among statisticians of the basic philosophy which underlies sampling theory: that whenever a statistic is employed to estimate some characteristic of a parent population, an estimate should be made of the sampling variation to which this statistic is subject. The estimate of ‘reliability’ or ‘significance’ may take a wide variety of forms — from the simple probable error, to the chi-square test, the t test, the z test and the more general Neyman-Pearson tests of hypotheses.
[Journal of the American Statistical Association 40, 80–84 (1945)].
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Notes
For simplicity, an agricultural illustration is used throughout this paper. The argument is certainly not limited to that particular field of application. As a matter of fact, the author originally developed this approach in connection with a study of optimum case loads for social workers in a public welfare agency.
George W. Snedecor, Statistical Methods (Ames, Iowa: The Collegiate Press, 1937), p. 60.
Cf. Dr. M. J. Van Uven, Mathematical Treatment of the Results of Agricultural and other Experiments (Gronigen-Batavia: P. Noordhoff, 1935), pp. 49–51.
J. Neyman and E. S. Pearson, ‘On the Problem of the Most Efficient Tests of Statistical Hypotheses’, Phil. Trans. Roy. Soc., Series A, 702, 231, 289–337 (1933).
There is the risk that a hypothesis will be rejected when it is true (error of the first kind), and the risk that the hypothesis will be accepted when it is false (error of the second kind). In the symmetric tests to be proposed in this paper, the two types of errors become identical.
J. Neyman, ‘Basic Ideas and Some Results of the Theory of Testing Statistical Hypotheses’, Journal of the Royal Statistical Society 105, 304 (1942).
It should perhaps be pointed out that the difference in cost between the two treatments should include all costs, not excepting interest and depreciation on investment to be made. This raises the troublesome question whether, in setting the depreciation rates, the risk should be included that after the investment has been made the treatment now thought preferable may be found the less desirable of the two on the basis of additional data, and may therefore be discontinued. Reflection convinces the writer that no allowance should be made for this risk, since in evaluating the desirability of changing a decision already made, these investments would be treated as sunk costs and would not count in the comparison.
Herbert A. Simon, ‘Symmetric Tests of the Hypothesis that the Mean of One Normal Population Exceeds That of Another’, Annals of Mathematical Statistics 14, 149–154 (1943). (Reprinted as Chapter 1.1 of this volume.)
Herbert A. Simon, ‘Symmetric Tests of the Hypothesis that the Mean of One Normal Population Exceeds That of Another’, Annals of Mathematical Statistics 14, (1943), pp. 152–153.
See, for instance, J. Neyman, Lectures and Conferences on Mathematical Statistic (Washington, D.C., Graduate School of the U.S. Department of Agriculture, 1938), passim.
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© 1977 D. Reidel Publishing Company, Dordrecht, Holland
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Simon, H.A. (1977). Statistical Tests as a Basis for ‘Yes—No’ Choices. In: Models of Discovery. Boston Studies in the Philosophy of Science, vol 54. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-9521-1_2
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