Establishing construct relationships is at the heart of social scientific research. To estimate associations between continuous (interval/ratio) variables, the Pearson’s product-moment correlation coefficient (r; developed by Karl Pearson) is often used. An r estimate indicates the direction (+/–) and the magnitude (0 to |1|) of the association between two continuous variables. However, such estimates are inappropriate for categorical-variable associations, given categorical (nominal/ordinal) variables do not follow the normal distribution nor do they have equal distances between intervals. For estimating associations between categorical variables, the Pearson chi-squared statistic (χ2; also developed by Pearson) is often used. A χ2 estimate (minimum of 0) indicates the in/dependence between two nominal variables (chi-squared statistic tends to lose power when estimating ordinal-variable associations). A significant χ2 estimate is ...
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