The chi-square (χ²) statistic is a statistical test used to determine if there is a significant association between two categorical variables. It is useful when assessing relationships between nominal or ordinal variables. The test compares observed and expected frequencies in a contingency table. The formula for calculating the chi-square statistic is χ² = Σ [(O – E)² / E]. O represents observed frequency, and E represents expected frequency. The chi-square test involves formulating null and alternative hypotheses, collecting data and creating a contingency table, calculating expected frequencies, calculating the chi-square statistic, determining degrees of freedom, looking up critical values or finding p-values, and comparing the calculated statistic to the critical value or p-value. If the calculated statistic is greater than the critical value or if the p-value is less than the chosen significance level, the null hypothesis is rejected. The chi-square test is widely used in biology, social sciences, and market research to analyze categorical data and assess independence or association between variables.