Randomization Test - Two Binary

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 binary Y. In the example, we have sex and handedness.

Record the count in the bottom left cell. In this case, .

Assign the set of Y variables to the set of X variables randomly, and record the new value of the bottom left cell.

This is a histogram of the values found in the lower left corner of the table over many simulations of how the values might be distributed when random tables with the same marginal totals are generated. The choice to look at the lower left corner is arbitrary; any cell would do. The question to consider is whether the cell count observed in the data is typical for tables with these margins. The fraction of simulated cell counts found in the tails is given above. If you conclude that the lower left cell of the data was “rare” enough, you could choose to reject the hypothesis that the two variables are not related.

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