Randomization Test - Binary and Quantitative

To see a relationship between variables, it can help to see those same variables with no relationship.

Take two variables, one binary variable X and one quantitative Y. In the example we have the speeds of cars driving on a hill. The speeds are associated with driving uphill or downhill.

Determine the difference of means for both values of X. In this case, .

Assign the set of Y variables to the set of X variables randomly, and repeat this difference of means calculation.

By observing many random cases, we can compare our result to a distribution of null cases.