Which test: Quantify the association / relationship / correlation / dependence between two variables

Which stat test

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). 
 
Examples: 
  1. To what extent are two variables related with each other?
  2. Is one variable dependent on another variable?


When the variables are BINOMIAL / BINARY / DICHOTOMOUS:

  1. Cross-tabs
  2. Chi-square test
  3. Fisher’s Exact test 
  4. Phi Coefficient
When the variables are NOMINAL:
  1. Cross-tabs
  2. Chi-square test
  3. Contingency coefficients
  4. Loglinear and Multiway Frequency Analysis for several categorical variables (an extension of the bivariate Chi-square)
 
When the variables are ORDINAL / RANK-DATA:
  1. Spearman’s rho correlation
  2. Kendall’s tau
  3. Chi-square test
 
When the variables are INTERVAL and passed the assumption of normality (parametric data):
  1. Pearson correlation
  2. Point / Biserial / Partial correlation 
  3. 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):
  1. Spearman’s rho correlation
  2. Kendall tau
  3. Tetrachoric Coefficient
  4. Contingency coefficients
_______________________________________________
/zza58