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Chi-Square Test

  1. Joseph S. Rossi

Published Online: 30 JAN 2010

DOI: 10.1002/9780470479216.corpsy0174

Corsini Encyclopedia of Psychology

Corsini Encyclopedia of Psychology

How to Cite

Rossi, J. S. 2010. Chi-Square Test. Corsini Encyclopedia of Psychology. 1.

Author Information

  1. University of Rhode Island

Publication History

  1. Published Online: 30 JAN 2010


The chi-square (χ2) test was developed by Karl Pearson in 1900; this is often regarded as a seminal event in the history of statistics. The test and the statistical distribution on which it is based have wide application not only in psychology and the behavioral sciences but also in numerous related disciplines. Its two principal uses are to test the independence of two variables and to assess how well a theoretical model or set of a priori probabilities fits a set of data (goodness of fit). In both cases the test is typically thought of as a nonparametric procedure involving observed (O) and expected (E) frequencies. The expected frequencies may be determined either theoretically or empirically. The basic formula for calculating χ2 is

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  • nonparametric statistics;
  • research design;
  • statistical analysis;
  • multivariate analysis