Chi-Square Test

What is Chi-Square Test? Chi-Square Test Explained.

The chi-square test is a statistical test used to determine if there is a significant association between two categorical variables. It assesses whether the observed frequencies in a contingency table differ significantly from the frequencies that would be expected if the variables were independent.

Here are the key points to understand about the chi-square test:

Contingency table: The chi-square test requires data to be organized in a contingency table, also known as a cross-tabulation table or a contingency matrix. The table displays the observed frequencies of the categories for each variable and their intersections.

Null hypothesis (H0): The null hypothesis assumes that there is no association between the variables, and any differences in the observed frequencies are due to chance. The alternative hypothesis (Ha) assumes that there is a significant association between the variables.

Test statistic: The chi-square test statistic measures the discrepancy between the observed and expected frequencies in the contingency table. It quantifies how much the observed data deviate from what would be expected under the assumption of independence.

Expected frequencies: The expected frequencies are calculated based on the assumption of independence between the variables. They represent the frequencies that would be expected if there were no associations between the variables. The expected frequencies are obtained by applying the marginal totals of the contingency table to calculate the expected cell frequencies.

Degrees of freedom: The degrees of freedom for the chi-square test depends on the dimensions of the contingency table. For a 2×2 table, the degrees of freedom are 1. For larger tables, the degrees of freedom are calculated as (number of rows – 1) multiplied by (number of columns – 1).

Critical value and p-value: The chi-square test compares the test statistic to a critical value from the chi-square distribution with the appropriate degrees of freedom. Alternatively, the p-value can be calculated to determine the probability of obtaining the observed data or more extreme data if the null hypothesis is true. If the p-value is below a predetermined significance level (e.g., 0.05), the null hypothesis is rejected in favor of the alternative hypothesis.

The chi-square test can be used in various applications, such as examining the relationship between two categorical variables, testing for independence in survey data, analyzing associations in genetics research, or assessing the goodness of fit between observed and expected frequencies.