Quantitative Randomization Test

Take two variables, one binary variable X and one quantitative Y. Here 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.

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

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