Chi-square Test of Independence

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The Chi-square test of independence (chi-square test for association) determines if there is an association between two nominal variables. It does not give any information on strength or magnitude of any association (Cramer’s V can be used to estimate of the strength of the association between the two variables).

The test works by comparing the observed frequencies in each of the cells to the frequencies you would expect if there was no association between the two nominal variables.

The Mathematical Formula for Chi Square:
Chi-square test for independence

Assumptions/Requirements for the Chi-square Test of Independence:

  • The two variables are nominal
  • The observations should be independent
  • All data cells should have counts greater than or equal to five

Calculating the Chi-square Test of Independence in SPSS:

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