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

  title={On Student's 1908 Article “The Probable Error of a Mean”},
  author={S. Zabell},
  journal={Journal of the American Statistical Association},
  pages={1 - 7}
  • S. Zabell
  • Published 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… Expand
two essays on the history of the theory of errors
These essays extract two threads from the complicated history of the theory of errors in the 19th and early 20th centuries: the Gauss-Dedekind-Luroth line produced Bayesian analysis for the normal regression model while the Fisher line developed sampling theory analysis. Expand
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 expressedExpand
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 extremelyExpand
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 sampleExpand
Student t-tests for potentially abnormal data.
  • J. Shuster
  • Mathematics, Medicine
  • Statistics in medicine
  • 2009
This paper describes statistical analysis system software to investigate both the null and power properties of various one- and two- sample t-tests and their normal approximations, as well as the Wilcoxon two-sample and sign-rank one-sample tests, allowing potential practitioners to determine, at the study design stage, whether the t-test will be robust in their specific application. Expand
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 effectivelyExpand
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 inExpand
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 extremelyExpand
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 leastExpand
Karl Pearson in Russian Contexts
The confluence of statistics and probability into mathematical statistics in the Russian Empire through the interaction, 1910-1917, of A.A. Chuprov and A.A. Markov was influenced by the writings ofExpand


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 widerExpand
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 theExpand
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 statisticalExpand
“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 statisticalExpand
The Design of Experiments
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 andExpand
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 extrenmeExpand
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. Expand
Statistical Methods for Research Workers
THIS book has done more than any other to popularize the use of modern statistical methods. Thousands of workers have been taught to use statistical machinery without the burdensome necessity ofExpand
Fisher's "Inverse Probability" of 1930
Summary In 1930 R. A. Fisher put forward the fiducial argument. This paper discusses the argument and its origins in Fisher's earlier work. It also emphasises the contribution of Mordecal Ezekiel toExpand
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 effectiveExpand