Abstract
We saw in Sect. 1.3 that Student in 1908a brought a new point of view to statistical inference by determining the small-sample (exact) distribution of what he called z, now called t, under the assumption of normality. Student found the correct form of this distribution but was not able to prove it.
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- 1.
The Proceedings were not published until 1928.
- 2.
A careful analysis of Pearson’s evolving progress on this issue is given in Chap. 19, “Karl Pearson and degrees of freedom,” of Stigler (1999).
- 3.
Today such p-values are usually denoted by a lower-case rather than capital p.
- 4.
This statement is correct for some balanced designs but is not correct in general; see, for example, Scheffé (1959, p. 353).
- 5.
Published in Bennett (1990).
- 6.
William Cochran.
References
Bennett, J. H. (Ed.) (1990). Statistical Inference and Analysis: Selected Correspondence of R. A. Fisher. Clarendon Press, Oxford.
Gosset, W. S. (1970). Letters from W. S. Gosset to R. A. Fisher, 1915-1936 (with summaries by R. A. Fisher and a Foreword by L. McMullen). Printed for private circulation by Arthur Guiness, Son and Co. (Park Royal, Ltd.)
Hotelling, H. (1927). Review [untitled]. Journal of the American Statistical Association 22, 411-412.
Irwin, J. O. (1929). Review [untitled]. Journal of the Royal Statistical Society 92, 101-103.
Pearson, E. S. (1929). Statistics and biological research (review). Nature 123, 866-867; also 124, 615.
Scheffé, H. (1959). The Analysis of Variance. Wiley, New York.
Stigler, S. (1999). Statistics on the Table. Harvard University Press, Cambridge.
Student (1908a). The probable error of a mean. Biometrika 6, 1-25.
Student (1908b). Probable error of a correlation coefficient. Biometrika 6, 302-310.
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Lehmann, E.L. (2011). Fisher’s Testing Methodology. In: Fisher, Neyman, and the Creation of Classical Statistics. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-9500-1_2
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