Encyclopedia of Clinical Neuropsychology

2018 Edition
| Editors: Jeffrey S. Kreutzer, John DeLuca, Bruce Caplan


  • Matthew J. L. PageEmail author
Reference work entry
DOI: https://doi.org/10.1007/978-3-319-57111-9_1179


The chi-square (χ2) test is a nonparametric statistical method primarily used to evaluate frequency data for categorical variables, by examining the differences between observed and expected frequencies for each category. A one-way chi-square test is used to determine whether differences in frequencies across levels of a nominal variable are due to chance (the null hypothesis) or represent a true difference (the alternative hypothesis). The chi-square is calculated by dividing the squared difference between the observed and expected frequency by the expected frequency in each category and summing the results (χ2 = Σ((OE)2/E)). When two variables are involved, a contingency table is constructed, depicting the observed frequency and the expected frequency in each cell. The chi-square is calculated again by, within each cell, squaring the difference between the observed and expected frequency and dividing by the expected frequency, and then summing each result.


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Further Readings

  1. Campbell, I. (2007). Chi-squared and Fisher-Irwin tests of two-by-two tables with small sample recommendations. Statistics in Medicine, 26, 3661–3675.PubMedCrossRefPubMedCentralGoogle Scholar
  2. Cochran, W. G. (1952). The χ2 test of goodness of fit. Annals of Mathematical Statistics, 25, 315–345.CrossRefGoogle Scholar
  3. McHugh, M. L. (2013). The chi-square test of independence. Biochemical Medicine, 23, 143–149.CrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Allegheny General HospitalPittsburghUSA
  2. 2.PsychologyAllegheny Health NetworkPittsburghUSA