42. Student's t Distribution

  1. Catherine Forbes1,
  2. Merran Evans1,
  3. Nicholas Hastings2 and
  4. Brian Peacock3

Published Online: 16 DEC 2010

DOI: 10.1002/9780470627242.ch42

Statistical Distributions, Fourth Edition

Statistical Distributions, Fourth Edition

How to Cite

Forbes, C., Evans, M., Hastings, N. and Peacock, B. (2010) Student's t Distribution, in Statistical Distributions, Fourth Edition, John Wiley & Sons, Inc., Hoboken, NJ, USA. doi: 10.1002/9780470627242.ch42

Author Information

  1. 1

    Monash University, Victoria, Australia

  2. 2

    Albany Interactive, Victoria, Australia

  3. 3

    Brian Peacock Ergonomics, SIM University, Singapore

Publication History

  1. Published Online: 16 DEC 2010
  2. Published Print: 29 NOV 2010

ISBN Information

Print ISBN: 9780470390634

Online ISBN: 9780470627242



  • probability density function;
  • student’s t distribution


The Student’s t distribution is used to test whether the difference between the means of two samples of observations is statistically significant. For example, the heights of a random sample of basketball players could be compared with the heights from a random sample of football players. The Student’s t distribution would be used to test whether the data indicated that one group was significantly taller than the other. More precisely, it would be testing the hypothesis that both samples were drawn from the same normal population. A significant value of t would cause the hypothesis to be rejected, indicating that the means were significantly different. This chapter illustrates probability density function and distribution function for Student’s t variate. It discusses variate relationships and random number generation of Student’s t variate.

Controlled Vocabulary Terms

mixture of chi square variate; probability density function