The Pearson correlation coefficient is ideal for studying the linear relationship between two continuous variables that are normally distributed and measured at the interval or ratio level. It assumes homoscedasticity and the absence of highly significant outliers. The Spearman rho is a nonparametric test used when the data are ordinal or when Pearson's assumptions, such as normality, are altered. It assesses the monotonic relationship between two variables by ranking the data. The chi-square test is ideal for testing associations between categorical variables, especially for frequencies in a contingency table. It does not assume normality, but requires a sufficiently large sample size and expected frequencies. Understanding these assumptions ensures valid results and avoids misinterpretations. Selecting the correct test based on the type and distribution of the data is crucial for accurately identifying and interpreting relationships.