Chi Square Test of Independence (\(\chi^{2}\))

Authors

Affiliations

Nathaniel Yomogida, B.S., SPT

Doctor of Physical Therapy

B.S. in Kinesiology

Chloë Kerstein, B.S., SPT

Doctor of Physical Therapy

B.A. in Neuroscience

To read

• Motulsky - How it works: Chi-square goodness-of-fit test p.268¹

• AKA
  • Abbreviated: (\(\chi^{2}\))
  • Pearson Chi-square test²
  • Chi-square²
• Chi-square (\(\chi^{2}\)) statistic is a non-parametric (distribution free) tool designed to analyze group differences when the dependent variable is measured at a nominal level²
• This is one of the most useful statistics for testing hypotheses when the variables are nominal².

what makes this test unique?

Similarities to other non-parametric statistics

• the Chi-square (\(\chi^{2}\)) is robust with respect to the distribution of the data (This is true for all non-parametric statistics)²
• Specifically, it does not require equality of variances among the study groups or homoscedasticity in the data².
  • It permits evaluation of both dichotomous independent variables, and of multiple group studies².

Dissimilarities from non-parametric statistics

• The calculations needed to compute the Chi-square provide considerable information about how each of the groups performed in the study.
• This richness of detail allows the researcher to understand the results and thus to derive more detailed information from this statistic than from many others.

References

1.

Motulsky H. Intuitive Biostatistics: A Nonmathematical Guide to Statistical Thinking. 4th ed. Oxford University Press; 2018.

2.

McHugh ML. The chi-square test of independence. Biochemia Medica. 2013;23(2):143-149. doi:10.11613/bm.2013.018