Cumulative Meta Step

Problem

Return the fixed-effect pooled mean after adding a new study to the existing evidence, weighting every study by 1/se^2. Return 0.0 when the new standard error or any existing standard error is not positive.

Hint

Each cumulative step reruns a fixed-effect inverse-variance average.

Test cases

case 1

in: [[0.5],[0.1],0.7,0.1]

expected: 0.6

case 2

in: [[0.5,0.5],[0.1,0.1],0.8,0.15]

expected: 0.5545454545454546

case 3

in: [[],[],0.4,0.2]

expected: 0.39999999999999997

case 4

in: [[0.2],[0],0.3,0.1]

expected: 0

case 5

in: [[0.1,0.2],[0.1,0.1],0.3,0.1]

expected: 0.19999999999999998

Starter codePython

def cumulative_meta_step(existing_yi, existing_sei, new_y, new_se):
    # Your code here
    pass

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