Analyze A/B Test Results with Statistical Rigor and Business Recommendations

You are an expert data analyst and statistician specializing in experimentation and A/B testing. Analyze the following A/B test results and provide a comprehensive, statistically rigorous evaluation with actionable business recommendations. **Experiment Details:** - Experiment name: [EXPERIMENT_NAME, e.g., 'Checkout Button Color Change'] - Hypothesis: [HYPOTHESIS, e.g., 'Changing the checkout button from blue to green will increase conversion rate by at least 5%'] - Primary metric (KPI): [PRIMARY_METRIC, e.g., conversion rate, click-through rate, revenue per user] - Secondary metrics: [SECONDARY_METRICS, e.g., bounce rate, average order value, time on page] - Test duration: [DURATION, e.g., 14 days] - Traffic split: [SPLIT, e.g., 50/50] **Results Data:** - Control group (A): [CONTROL_SAMPLE_SIZE] users, [CONTROL_CONVERSIONS] conversions - Treatment group (B): [TREATMENT_SAMPLE_SIZE] users, [TREATMENT_CONVERSIONS] conversions - Any additional metric data: [ADDITIONAL_DATA] **Please perform the following analysis:** 1. **Descriptive Statistics**: Calculate conversion rates for both groups, the absolute and relative lift, and confidence intervals for each group's conversion rate. 2. **Statistical Significance Testing**: Conduct a two-proportion z-test (or appropriate test). Report the z-score, p-value, and whether the result is significant at [SIGNIFICANCE_LEVEL, e.g., 95%] confidence level. Explain what these numbers mean in plain language. 3. **Power Analysis**: Assess whether the sample size was adequate to detect the hypothesized minimum detectable effect (MDE). If underpowered, calculate how many more samples would be needed. 4. **Practical Significance**: Beyond statistical significance, evaluate whether the observed effect size is practically meaningful for the business. Estimate the projected annual impact in terms of [BUSINESS_METRIC, e.g., additional revenue, extra conversions]. 5. **Segmentation Analysis**: Suggest 3-4 key segments (e.g., device type, new vs. returning users, geography) to cut the data by, and explain what differential effects to look for. 6. **Validity Threats**: Identify potential threats to the experiment's validity including novelty effects, sample ratio mismatch, seasonality, or selection bias. 7. **Final Recommendation**: Provide a clear GO / NO-GO / ITERATE recommendation with justification and suggested next steps. Format the output with clear sections, include the mathematical formulas used, and present a summary dashboard in a table format.