How does a chi-square test determine whether gender and political party are associated?

To determine whether gender and political party are associated, researchers use the chi-square test for independence, which evaluates the statistical significance of the relationship between two categorical variables.12

The process involves the following steps:

• Data Collection: Researchers count individuals from a random sample across all combinations of the two variables (e.g., female-Democrat, female-Republican, male-Democrat, and male-Republican). These counts are typically organized into a contingency table.23
• Hypothesis Testing: A null hypothesis ($H_0$) is established, assuming there is no association between gender and political party.
• Calculation: Researchers compare the observed frequencies ($O_i$) from the sample to the expected frequencies ($E_i$) that would occur if the null hypothesis were true, using the formula:
  $${\chi }^2=\sum \frac{(O_i-E_i{)}^2}{E_i}$$
• Conclusion: By comparing the calculated ${\chi }^2$ value against a critical value from a distribution table (based on a chosen $p$-value and degrees of freedom), researchers determine if the membership distribution is significantly disproportionate. If the calculated value is sufficiently high, the null hypothesis is rejected, indicating a statistically significant association.12

Unlike correlation coefficients, this test measures the significance of the association rather than its strength.2