The Chi-square test of independence is a non-parametric statistical tool used to analyze group differences when the dependent variable is measured at a nominal level. It is robust with respect to the distribution of the data, does not require equal variances, and can handle both dichotomous independent variables and multiple group studies. The Chi-square test provides detailed information about how each group performed, making it a valuable tool for researchers. However, it has limitations, such as sample size requirements and difficulty in interpreting results with large numbers of categories. The Chi-square test assumes that the data are frequencies, the levels of variables are mutually exclusive, each subject contributes to only one cell, the study groups are independent, and the expected cell counts should be 5 or more in at least 80% of the cells. The test is calculated using the formula \(\sum \chi^2_{ij} = \frac{(O - E)^2}{E}\), where \(O\) is the observed count, \(E\) is the expected count, and \(\chi^2\) is the cell Chi-square value. In a case study, a company used the Chi-square test to evaluate the effectiveness of a vaccination program against pneumococcal pneumonia. The results showed a significant difference in the incidence of pneumonia between vaccinated and unvaccinated employees, with a p-value of 0.0011. The strength of the association was measured using Cramer’s V, which was 0.26, indicating a weak but statistically significant correlation. The Chi-square test is particularly useful when parametric assumptions are violated or when data are from convenience samples. However, it is important to ensure that the assumptions are met to maintain the reliability of the results.The Chi-square test of independence is a non-parametric statistical tool used to analyze group differences when the dependent variable is measured at a nominal level. It is robust with respect to the distribution of the data, does not require equal variances, and can handle both dichotomous independent variables and multiple group studies. The Chi-square test provides detailed information about how each group performed, making it a valuable tool for researchers. However, it has limitations, such as sample size requirements and difficulty in interpreting results with large numbers of categories. The Chi-square test assumes that the data are frequencies, the levels of variables are mutually exclusive, each subject contributes to only one cell, the study groups are independent, and the expected cell counts should be 5 or more in at least 80% of the cells. The test is calculated using the formula \(\sum \chi^2_{ij} = \frac{(O - E)^2}{E}\), where \(O\) is the observed count, \(E\) is the expected count, and \(\chi^2\) is the cell Chi-square value. In a case study, a company used the Chi-square test to evaluate the effectiveness of a vaccination program against pneumococcal pneumonia. The results showed a significant difference in the incidence of pneumonia between vaccinated and unvaccinated employees, with a p-value of 0.0011. The strength of the association was measured using Cramer’s V, which was 0.26, indicating a weak but statistically significant correlation. The Chi-square test is particularly useful when parametric assumptions are violated or when data are from convenience samples. However, it is important to ensure that the assumptions are met to maintain the reliability of the results.