Chi-Square Test

The Chi-Square test () is a non-parametric statistical test commonly used to analyze relationships between Categorical Variables. It helps determine whether the observed frequencies (counts) of outcomes in different categories differ significantly from what would be expected by chance alone.
Chi-Square Statistic (²) Measures the discrepancy between the observed and expected frequencies. A larger ² value indicates a stronger evidence against the null hypothesis.


  • Chi-Square Test doesn't reveal the direction of the relationship (positive or negative) and can be unreliable with small sample sizes or sparse data in categories.

Relate Concepts:

  • Hypothesis Testing including Alternate Hypothesis and Null Hypothesis
  • Expected Frequencies: Calculated based on the assumption of no association between the variables ().
  • Degrees of Freedom (df): Reflects the number of independent comparisons being made in the analysis. It influences the critical value used for decision-making.
  • p-Value: Probability of observing a value this extreme or more extreme, assuming the null hypothesis is true. A low p-value (typically below 0.05) suggests rejecting the null hypothesis and concluding a significant relationship.