• Thomas W. MacFarland
  • Jan M. Yates


The Chi-square test is perhaps the most frequently used (or overused) nonparamteric statistical test. The Chi-square test, named for the Greek letter χ (i.e., Chi or the Greek letter for x), is typically used to test for differences in proportions between two or more groups. The Chi-square test is also called a goodness of fit test. That is to say, the Chi-square test is used to see if grouped data actually fit into declared groups, or if the data instead do not fit into the group. For this lesson, Chi-square will be demonstrated using data in two formats: (1) Chi-square using R will first be demonstrated where the data are presented as an external file imported into R, with data organized at the level of individual subjects, (i.e., each row represents the data for an individual subject) and (2) Chi-square using R will also be demonstrated where data are not at the level of individual subjects but data are instead presented in summary format, as a collapsed contingency table.


Bar plot (stacked, side-by-side) Boolean Central tendency Chi-square Code book Comma-separated values (.csv) Contingency table Crosstabs Distribution-free Dotplot Frequency distribution Goodness of fit Histogram Mosaic plot Nominal Nonparametric Normal distribution Null hypothesis Parametric Probability (p-value) Proportion Representation Statistical significance Yates correction 

Supplementary material

385146_1_En_3_MOESM1_ESM.csv (0 kb)
GenderTrait (CSV 1 kb)

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Thomas W. MacFarland
    • 1
  • Jan M. Yates
    • 2
  1. 1.Office of Institutional EffectivenessNova Southeastern UniversityFort LauderdaleUSA
  2. 2.Abraham S. Fischler College of EducationNova Southeastern UniversityFort LauderdaleUSA

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