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Central Limit Theorem

  1. Carolyn J. Anderson

Published Online: 30 JAN 2010

DOI: 10.1002/9780470479216.corpsy0160

Corsini Encyclopedia of Psychology

Corsini Encyclopedia of Psychology

How to Cite

Anderson, C. J. 2010. Central Limit Theorem. Corsini Encyclopedia of Psychology. 1–2.

Author Information

  1. University of Illinois, Urbana-Champaign

Publication History

  1. Published Online: 30 JAN 2010

Abstract

Many statistical inferential procedures such as hypothesis testing and the estimation of confidence intervals are based on the assumption that the distribution of a sample statistic is normal. The Central Limit Theorem (CLT) often justifies the assumption that the distribution of a sample statistic (e.g., mean, sum score, and test statistic) is normal. The Central Limit Theorem states that, for a large sample of n observations from a population with a finite mean and variance, the sampling distribution of the sum or mean of samples of size n is approximately normal.

Keywords:

  • mean;
  • sum;
  • population;
  • sampling distribution;
  • normal distribution