CUPED Adjusted Difference

Problem

Return the CUPED-adjusted difference in means: estimate theta = cov(covariate, outcome)/var(covariate), replace each outcome with y - theta*(x - mean_x), then return the treated mean minus the control mean of the adjusted outcomes. Return 0.0 for empty or mismatched input or an empty arm; theta is 0 when the covariate has no variance.

Hint

Center the covariate before using it to adjust the outcomes.

Test cases

case 1

in: [[1,0,1,0],[12,5,10,7],[10,4,8,6]]

expected: 0.20000000000000284

case 2

in: [[1,0],[5,5],[1,1]]

expected: 0

case 3

in: [[1,0],[10,2],[2,0]]

expected: 0

case 4

in: [[1],[3],[7]]

expected: 0

case 5

in: [[],[],[]]

expected: 0

Starter codePython

def cuped_adjusted_diff(treatment, outcome, covariate):
    # Your code here
    pass

5 test cases · run your code against them in the editor