Chi-Square Test for Independence

By Anthony M. Wanjohi:

Chi-square is useful for analyzing whether a frequency distribution for a categorical variable, say sex is consistent with expectations (a goodness of fit test), or whether two categorical variables are significantly associated with each other (a test for independence). This article provides an overview of chi square tests for independence. The first part of the article presents assumptions before using an example to illustrate the tests.

Chi square assumptions

The general assumptions about Chi Square are that: a) Chi-square statistic does not give any information about the strength of the relationship, b) Chi-square statistic only conveys the existence or nonexistence of the relationships or association between the variables investigated, c) Chi-square statistic compares counts (frequencies) and not means.

Typically, chi square test assumes the following:

  1. Use of frequency data,
  2. The two variables under study must be categorical,
  3. Expected frequency counts for each cell must be NOT less than 5,
  4. The sample size should be representative.


In order to gain a better understanding of chi-square test for independence, an hypothesis is stated from the null. A statistical application, namely SPSS is used to run the test.

H0:  There is no statistically significant association between gender and preferred mode of learning.

Chi-Square test for independence

Value df Asymp. Sig. (2-sided)
Pearson Chi-Square 2.255(a) 5 .813
Likelihood Ratio 2.636 5 .756
Linear-by-Linear Association 1.019 1 .313
N of Valid Cases 149
a  0  cells (0%) have expected count less than 5. The minimum expected count is .45

Since the obtained level of significance for the association between Gender and Preferred Mode of Learning is greater than 0.05, χ² (5, N = 149) = 2.255, p = .813, the null hypothesis is not rejected. The study therefore concludes that there is no significant association between Gender and Preferred Mode of Learning. This implies that the preferred mode of learning is independent of gender; that is males and females equally prefer online learning and regular classroom learning.

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