The Chi-Square (χ²) test is a statistical tool that helps researchers and analysts understand the association or independence between two categorical variables. Categorical variables are those that represent categories or groups and are not numerical in nature.
Here’s a more detailed explanation of the Chi-Square test:
1. Contingency Table:
– The Chi-Square test is often applied to data organized in a contingency table. This table displays the frequency distribution of the joint occurrences of two categorical variables.
2. Null Hypothesis (H₀) and Alternative Hypothesis (H₁):
– The test involves setting up two hypotheses: the null hypothesis (H₀) assumes that there is no association between the variables, and any observed differences are due to random chance. The alternative hypothesis (H₁) suggests that there is a significant association.
3. Expected Frequencies:
– Under the assumption of independence, the Chi-Square test calculates the expected frequencies for each cell in the contingency table. These expected frequencies represent what would be anticipated if the variables were independent.
4. Degrees of Freedom:
– The degrees of freedom for the Chi-Square test are determined by the dimensions of the contingency table. For a 2×2 table, the degrees of freedom would be 1, for a 2×3 table it would be 2, and so on.
5. Critical Value or P-value:
– The calculated Chi-Square value is compared to a critical value from the Chi-Square distribution table or, more commonly, to a p-value. A small p-value (< 0.05) suggests that the observed data significantly deviates from what would be expected under the assumption of independence, leading to the rejection of the null hypothesis.
6. Interpretation:
– If the p-value is less than the chosen significance level (commonly 0.05), it is concluded that there is a significant association between the variables. If the p-value is greater than 0.05, there is insufficient evidence to reject the null hypothesis, indicating independence.
The Chi-Square test is versatile and can be applied to various scenarios, such as analyzing survey responses, examining the distribution of traits in different populations, or assessing the effectiveness of categorical variables in predicting outcomes.