Clustered Standard Error of the Mean

Problem

Return the cluster-robust standard error of the mean: sqrt(G/(G-1) * sum_g (sum over i in g of (x_i - xbar))^2) / n. Inputs are the data and cluster ids. Return 0.0 when lengths differ, input is empty, or there are fewer than two clusters.

Hint

Cluster-level score sums carry the sampling uncertainty.

Test cases

case 1

in: [[1,2,3,4],["a","a","b","b"]]

expected: 1

case 2

in: [[1,1,2,2],["a","a","b","b"]]

expected: 0.5

case 3

in: [[1,2,3,4],["a","b","c","d"]]

expected: 0.6454972243679028

case 4

in: [[5,5],["a","b"]]

expected: 0

case 5

in: [[],[]]

expected: 0

Starter codePython

def clustered_se_mean(data, ids):
    # Your code here
    pass

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