Standard Article

Small-Sample Statistics

  1. Joseph S. Rossi,
  2. Peter F. Merenda

Published Online: 30 JAN 2010

DOI: 10.1002/9780470479216.corpsy0883

Corsini Encyclopedia of Psychology

Corsini Encyclopedia of Psychology

How to Cite

Rossi, J. S. and Merenda, P. F. 2010. Small-Sample Statistics. Corsini Encyclopedia of Psychology. 1–2.

Author Information

  1. University of Rhode Island

Publication History

  1. Published Online: 30 JAN 2010

Abstract

The notion of small-sample or small-n statistics was first developed by Gosset, a statistician working at the Guinness Brewery in the United Kingdom. One of his duties was to analyze samples of freshly brewed stout. Due to the inherent variability in the nature of the brewing process and the length of time required to test samples, Gosset experimented with the idea of substantially reducing the number of samplings to be taken from the very large number of available barrels. He found that the sampling distribution for small samples differed markedly from the normal distribution. Further, the distribution changed depending on the size of the sample, giving rise to a whole family of distributions. The results of his experiments with small samples led to the development of the t distribution, which Gosset published in 1908 using the pseudonym Student. In addition to being the first to recognize and deal with the problem of small samples, Gosset was also the first to combine experimental design with statistical testing and probably also the first to suggest anything like the .05 level as a reasonable criterion for rejecting the null hypothesis. Although not immediately recognized as such, Gosset's work with small samples was a critical breakthrough in the history of statistics, leading to the development of a number of other procedures, including the analysis of variance.

Keywords:

  • confidence interval;
  • nonparametric statistical tests;
  • parametric statistical tests;
  • statistics in psychology