Randomization Test - Binary and Quantitative

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

This graph is a side by side dotplot of the selected variables.

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.

This is a histogram of the differences in the means of the two groups when the observed values are assigned to the groups at random. The difference actually observed in the data is indicated. If the observed difference is “rare” as compared to the distribution we’d expect for randomly distributed values, we may conclude that it was not random and reject the hypothesis of no difference in the groups.

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