Analyze A/B Test Results | Dataford Interview Questions

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Problem

Shopify Checkout experiments record one binary result per visitor: 1 for a completed purchase and 0 otherwise. Given control and treatment result vectors, analyze the experiment and determine whether the treatment conversion rate is significantly different at a 5% significance level.

Implement analyze_ab_test(control, treatment).

Formal Specification

Input: Two non-empty lists of integers, where each value is either 0 or 1.
Output: A dictionary containing control and treatment sample sizes, conversion rates, absolute lift, relative lift, z-score, two-sided p-value, and a boolean significant field.
Round numeric output values to four decimal places. If the control conversion rate is zero, return None for relative lift.
Use a pooled two-proportion z-test. If the pooled standard error is zero, return z_score = 0.0 and p_value = 1.0.

Constraints

1 <= len(control), len(treatment) <= 10^6
Every vector value is either 0 or 1
The vectors may have different lengths
Use a two-sided significance threshold of 0.05

Function Signature

def analyze_ab_test(control, treatment):