Which test: Quantify the association / relationship / correlation / dependence between two variables
When the research objective is to understand the association / relationship / correlation / dependence between two variables, we have a choice among different statistical procedures, depending on the following variable characteristics:
Number of variables:
One dependent variable and one independent variable (technically we don’t distinguish between a dependent and independent variable in these procedures).
One dependent variable and one independent variable (technically we don’t distinguish between a dependent and independent variable in these procedures).
Examples:
- To what extent are two variables related to each other?
- Is one variable dependent on another variable?
When the variables are BINOMIAL / BINARY / DICHOTOMOUS:
- Cross-tabs
- Chi-square test
- Fisher’s Exact test
- Phi Coefficient
When the variables are NOMINAL:
- Cross-tabs
- Chi-square test
- Contingency coefficients
- Loglinear and Multiway Frequency Analysis for several categorical variables (an extension of the bivariate Chi-square)
When the variables are ORDINAL / RANK-DATA:
- Spearman’s rho correlation
- Kendall’s tau
- Chi-square test
When the variables are INTERVAL and passed the assumption of normality (parametric data):
- Pearson correlation
- Point / Biserial / Partial correlation
- Canonical Correlation Canonical R (for two sets of dependent and independent variables)
When the variables are INTERVAL but failed the assumption of normality (non-parametric data):
- Spearman’s rho correlation
- Kendall tau
- Tetrachoric Coefficient
- Contingency coefficients
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