Association between variables
Compare category shares, read scatterplots, and explain covariance, correlation and fitted lines step by step.
Study sections
Follow the order or choose a sectionTwo-variable questions and contingency tables
So far we have described one variable at a time. Now we ask whether two characteristics vary together. For example, does smartphone own…
02Row shares, column shares and association
The phrase “out of whom?” decides the denominator. The share of women who own phones and the share of owners who are women are differen…
03Scatterplots: keep the numerical pairs together
A scatterplot displays pairs of numerical values as points. Each point represents one case. Its horizontal position gives one measureme…
04Describe association: direction, shape, spread, outliers
Before calculating a coefficient, describe the scatterplot. A single number cannot capture every feature of a relationship.
05Covariance: multiply paired deviations
Covariance measures whether two numerical variables tend to move above and below their own means together. Its sign is easier to interp…
06Correlation: direction and strength without units
Correlation standardizes covariance so its magnitude can be interpreted without measurement units. Pearson’s r summarizes a straight-li…
07Fitting a line: predictions, slope and R squared
A fitted line summarizes an approximately linear pattern and lets us predict a numerical response from an explanatory value. Prediction…
08A category and a number: compare groups
When one variable is a category and the other is numerical, compare the numerical distributions within the categories. Begin with the d…