Pearson's chi-squared test is used to determine if there is a relationship between two categorical variables. It has the following structure: 1) State the null and alternative hypotheses 2) Calculate the test statistic by finding residuals between observed and expected counts and summing their squares divided by expected values 3) Find the critical value based on degrees of freedom and significance level 4) Reject the null hypothesis if the test statistic exceeds the critical value, concluding the variables are dependent. Otherwise fail to reject, concluding independence. Three examples are provided to demonstrate applying the chi-squared test to determine dependence between grades and attendance, height and nose size, and weather and season.