Bivariate Analysis

Analyzes relationships between two variables

Recall that there are the following Types of Variables

So there can be the following combinations:

  • Quantitative vs Quantitative
  • Quantitative vs Categorical
  • Categorical vs Categorical


typically most interesting question is:

  • "Are these variables independent"?
  • if they are dependent and correlated, then one variable can be redundant
  • and can be removed

Quantitative vs Quantitative

If two variables are numeric:

Quantitative vs Categorical

If one is numeric, and another is categorical:

Categorical vs Categorical

To compare two categorical variables

  • start from building a Contingency Table to show relative frequencies of values
    • Marginal distribution - distribution of only one of the variables in a contingency table
    • Conditional Distribution - distribution within a fixed value of a second variable
    • so it's simple to see if there's any correlation between the two variables just using this matrix
  • run some Tests of Independence: