On Student's 1908 Article “The Probable Error of a Mean”

  title={On Student's 1908 Article “The Probable Error of a Mean”},
  author={Sandy L. Zabell},
  journal={Journal of the American Statistical Association},
  pages={1 - 7}
  • S. Zabell
  • Published 1 March 2008
  • Mathematics
  • Journal of the American Statistical Association
This month marks the 100th anniversary of the appearance of William Sealey Gosset's celebrated article, “The Probable Error of a Mean” (Student 1908a). Gosset's elegant result represented the first in a series of exact, “small-sample” results that were developed by Gosset, Fisher, and others to form a central component of the modern theory of statistical inference. This review celebrates the centenary of Gosset's article by discussing both its background and its impact on statistical theory and… 

In Praise (and Search) of J. V. Uspensky

. The two of us have shared a fascination with James Victor Uspensky’s 1937 textbook Introduction to Mathematical Probability ever since our graduate student days: it contains many interesting

The Significance Test Controversy Revisited

This chapter revisits the significance test controversy in the light of Jeffreys’ views about the role of statistical inference in experimental investigations. These views have been clearly expressed

Using the Student's "t"-Test with Extremely Small Sample Sizes.

Researchers occasionally have to work with an extremely small sample size, defined herein as N ≤ 5. Some methodologists have cautioned against using the t-test when the sample size is extremely

The t Distribution: A Transformation of the Employee of the Brewery

In situations where the size of the sample data set is relatively small, to assume a normal distribution. some uncertainties exist. A mistake is to use random sampling and the other the small sample

Moving to a world beyond p-value < 0.05: a guide for business researchers

  • Jae H. Kim
  • Business
    Review of Managerial Science
  • 2021
In light of the recent statements on the p-value criterion made by the American Statistical Association (ASA), it is now clear that that the current paradigm of statistical significance and its

Student's t Increments

Some moments and limiting properties of independent Student’s t increments are studied. Inde-pendent Student’s t increments are independent draws from not-truncated, truncated, and effectively

Effective Truncation of a Student's t-Distribution by Truncation of the Chi Distribution in a Chi-Normal Mixture

A Student’s t-distribution is obtained from a weighted average over the standard deviation of a normal distribution, σ, when 1/σ is distributed as chi. Left truncation at q of the chi distribution in

Using the Student ’ s t-test with extremely small sample sizes

Researchers occasionally have to work with an extremely small sample size, defined herein as N ≤ 5. Some methodologists have cautioned against using the t-test when the sample size is extremely

Replacement of Biased Estimators with Unbiased Ones in the Case of Student’s t-Distribution and Geary’s Kurtosis

Abstract The use of biased estimators can be found in some historically and up to now important tools in statistical data analysis. In this paper their replacement with unbiased estimators at least

Self-normalization: Taming a wild population in a heavy-tailed world

An overview of the salient progress of self-normalized limit theory, from Student’s t-statistic to more general Studentized nonlinear statistics is given, and some very recent advances in self- normalized moderate deviations under dependence are glimpsed.



Gosset, Fisher, and the t Distribution

Abstract Letters from W.S. Gosset to R.A. Fisher are used to describe Gosset's first contacts and growing friendship with Fisher, their collaboration over the tabulation of Student's t, and the wider

On the Transition from “Student's” z to “Student's” t

Abstract The change from the z of “Student's” 1908 paper to the t of present day statistical theory and practice is traced and documented. It is shown that the change was brought about by the

Studies in the History of Probability and Statistics. XX Some early correspondence between W. S. Gosset, R. A. Fisher and Karl Pearson, with notes and comments

Letters or extracts from letters which passed between W. S. Gosset, R. A. Fisher and Karl Pearson during the years 1912-20 are reproduced. They throw light on the start of Fisher's statistical

“Student's” Collected Papers

IT would be idle to suppose that biologists are making full use of the powerful tool given to them by modern statistics, or even that they are likely to make full use of it before statistical

The Design of Experiments

  • J. I
  • Economics
  • 1936
AbstractREADERS of “Statistical Methods for Research Workers” will welcome Prof. Fisher's new book, which is partly devoted to a development of the logical ideas underlying the earlier volume and

‘Student’ and Small Sample Theory

Abstract This year marks the Fiftieth Anniversary of the publication of “Student's” distribution. It is an appropriate time to reconsider the impact of this part of “Student's” work on the

The Theory of Probability

This book is a searching analysis of the fundamental principles of the theory of probability and of the particular judgments involved in its application to concrete problems and is in agreement with the views expressed by Dr. Wrinch and the present reviewer.


THE problem of the range of samples arises as a special case of Galton's Difference Problem, first given by Professor K. Pearson in 1902 (1). Together with the allied problem of the extrenme

The first t-test.

The data with which Student illustrated the application of his famous distribution are examined from a number of aspects and the within-patient clinical trial at Kalamazoo whose results were published by Cushny and Peebles and misquoted by Student and Fisher is discussed.

Student's t-Test under Symmetry Conditions

Abstract The size and power of Student's t-test are discussed under weaker than normal conditions. It is shown that assuming only a symmetry condition for the null hypothesis leads to effective