Understanding the Chi-Square Test for Independence

Chi-square test

A test for independence between two categorical variables.

Chi-square test assessment

Whether there is a difference in proportions between two sets of categorical data.

Contingency table

A table used in the chi-square test.

Variables in chi-square test

Two nominal variables or one nominal and one ordinal variable.

Null hypothesis (H₀)

That the two variables are independent (no association).

Alternative hypothesis (H₁ or Hₐ)

That the two variables are NOT independent (there is an association).

Observed value

The count actually observed in a cell of the contingency table.

Expected value

The count expected in a cell if the null hypothesis is true (no association).

Test statistic in chi-square test

Compares the observed counts to the expected counts.

Example of chi-square test

Whether high blood pressure (HBP) distribution varies by obesity status.

Key values in HBP and obesity example

87% of obese participants had HBP vs. 63% of non-obese participants.

Observed difference in HBP prevalence

24% higher in the obese group.

P-value in HBP and obesity example

0.007.

Conclusion with p-value < 0.05

The result is statistically significant, and there is evidence against the null hypothesis.

P-value of 0.007

Indicates strong evidence of an association between obesity and high blood pressure.

Result of chi-square test in example

Suggests that obesity status is associated with different prevalence rates of high blood pressure.

Statistical significance requirement

p-value < 0.05 (commonly used significance level).

Significant chi-square test meaning

There is likely an association between the variables being tested.

Contingency table purpose

To organize categorical data and show the frequency distribution of variables.

Importance of expected counts

They represent what counts would look like under the null hypothesis.