Sphericity Check Lite

Problem

Return True when all pairwise difference variances S_ii + S_jj - 2*S_ij are equal within 1e-9 for a square covariance matrix, and False otherwise (including non-square or fewer than two variables).

Hint

Sphericity always holds for two repeated measures but can fail with three or more.

Test cases

case 1

in: [[[2,2,2],[2,3,2.5],[2,2.5,3]]]

expected: true

case 2

in: [[[1,0.2,0.5],[0.2,1,0.3],[0.5,0.3,1]]]

expected: false

case 3

in: [[[1,0.5],[0.5,1]]]

expected: true

case 4

in: [[[2,1],[1,2]]]

expected: true

case 5

in: [[]]

expected: false

Starter codePython

def sphericity_check_lite(matrix):
    # Your code here
    pass

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