Analyze and Interpret A/B Test Results with Statistical Rigor

You are a senior data scientist specializing in experimentation and causal inference. I need you to perform a rigorous analysis of my A/B test results and provide clear, actionable recommendations. **Experiment Details:** - Experiment name: [EXPERIMENT_NAME, e.g., New checkout flow vs. existing checkout flow] - Hypothesis: [YOUR_HYPOTHESIS, e.g., The simplified checkout flow will increase conversion rate by at least 5%] - Primary metric: [PRIMARY_METRIC, e.g., purchase conversion rate] - Secondary metrics: [SECONDARY_METRICS, e.g., average order value, cart abandonment rate, time to purchase] - Test duration: [DURATION, e.g., 14 days] - Traffic split: [SPLIT_RATIO, e.g., 50/50] **Observed Results:** - Control group: [CONTROL_SAMPLE_SIZE] users, [CONTROL_CONVERSIONS] conversions (or [CONTROL_METRIC_VALUE]) - Treatment group: [TREATMENT_SAMPLE_SIZE] users, [TREATMENT_CONVERSIONS] conversions (or [TREATMENT_METRIC_VALUE]) - Any secondary metric observations: [SECONDARY_METRIC_RESULTS] **Please provide the following analysis:** 1. **Statistical Significance Testing**: Calculate the p-value, confidence interval (95%), and determine if the result is statistically significant. Specify whether a z-test, t-test, or chi-squared test is most appropriate and why. Show your calculations step by step. 2. **Effect Size & Practical Significance**: Compute the relative and absolute lift, Cohen's d or equivalent effect size measure, and assess whether the observed effect is practically meaningful for the business. 3. **Power Analysis**: Evaluate whether the sample size was sufficient to detect the hypothesized minimum detectable effect (MDE). If underpowered, calculate the required sample size and duration. 4. **Validity Checks**: Assess potential threats including sample ratio mismatch (SRM), novelty/primacy effects, selection bias, and Simpson's paradox. Suggest diagnostic checks for each. 5. **Segmentation Analysis**: Recommend 3-5 meaningful segments to analyze (e.g., by device type, user tenure, geography) and explain what heterogeneous treatment effects to look for. 6. **Decision Recommendation**: Based on all evidence, provide a clear ship/no-ship/extend recommendation with reasoning. Include risk considerations and suggest any follow-up experiments. 7. **Executive Summary**: Write a 3-4 sentence non-technical summary suitable for sharing with product leadership. Present all numerical results in a clean table format where applicable.