A/B Test Analyzer

Overview

This skill helps design and analyze controlled online experiments (A/B and A/B/n tests) with statistical rigor and honest interpretation. It covers the full lifecycle: hypothesis framing, sample-size and duration planning, choosing the right test, computing p-values and confidence intervals, and avoiding the traps that produce false wins.

Keywords: A/B test, split test, experiment, hypothesis, sample size, power, MDE, minimum detectable effect, statistical significance, p-value, confidence interval, conversion rate, lift, two-proportion z-test, t-test, chi-square, peeking, multiple comparisons, Simpson's paradox, SRM, novelty effect.

Use this skill whenever someone wants to plan an experiment, decide if a result is real, or sanity-check an analysis someone else did.

Core Mental Model

• An A/B test estimates a causal effect by randomizing units (usually users) into control and treatment.
• You are testing a null hypothesis (no difference) against an alternative (there is a difference). A p-value is P(data this extreme or more | null is true) — NOT the probability the null is true, and NOT the probability your variant is better.
• Two error types: Type I (false positive, rate = alpha, typically 0.05) and Type II (false negative, rate = beta; power = 1 - beta, typically 0.80).
• You must fix sample size and test duration BEFORE you start. Stopping when significant ("peeking") inflates the false-positive rate dramatically.

Workflow

Follow these steps in order. Do not skip planning steps even when only asked to "analyze results" — verify the plan was sound first.

1. Frame the hypothesis. Turn the vague goal into a falsifiable statement: "Changing X will increase metric M from baseline b by at least the MDE, because [mechanism]." Identify ONE primary metric (the Overall Evaluation Criterion / OEC). Pre-register guardrail metrics. See references/methodology.md for OEC selection.
2. Pick the metric type.
   • Binary / rate (conversion, click, signup) → two-proportion test.
   • Continuous (revenue per user, time on page, order value) → Welch's t-test (means).
   • More than 2 variants → chi-square (rates) or ANOVA-style + correction.
3. Set the design parameters.
   • Baseline rate or baseline mean (b).
   • Minimum Detectable Effect (MDE): the smallest lift worth detecting. Express relative (e.g. +5%) and convert to absolute.
   • alpha (default 0.05), power (default 0.80), one- vs two-sided (almost always two-sided).
4. Compute required sample size and duration. Run scripts/abtest.py size. Divide required N per arm by daily eligible traffic per arm to get duration in days. Round duration UP to full weeks to cover weekday/weekend seasonality (min 1 week, ideally 2).
5. Run the test untouched for the full pre-planned duration. No peeking-with-action. (You may monitor guardrails for catastrophic harm only.)
6. Validate data quality BEFORE looking at the result.
   • Sample Ratio Mismatch (SRM): is the actual split close to the planned split? Run scripts/abtest.py srm. If p < 0.001, the experiment is broken — do NOT trust the result.
   • Check for logging bugs, bot traffic, and that randomization was at the right unit.
7. Run the significance test. Use scripts/abtest.py prop (rates) or scripts/abtest.py ttest (means). Report: effect size (absolute + relative lift), confidence interval, p-value, and whether it crossed alpha.
8. Interpret honestly. A non-significant result is NOT proof of no effect — report the CI to show what effects are still plausible. A significant result with a CI that includes trivially small lifts may not be worth shipping. See references/interpretation-guide.md.
9. Account for multiplicity. If you tested multiple metrics or variants, apply a correction (Bonferroni or Benjamini-Hochberg). See references/methodology.md.
10. Write it up. Use templates/experiment-report.md so decisions are reproducible and reviewable.

Choosing the Test (decision table)

Quick Worked Example

Baseline conversion 10%, want to detect a relative +5% (→ 10.5% absolute), alpha 0.05, power 0.80, two-sided:

python scripts/abtest.py size --baseline 0.10 --mde-rel 0.05 --alpha 0.05 --power 0.80

→ ~ 58,000 users per arm. At 4,000 eligible users/arm/day → ~15 days → round to 2 full weeks.

After the test, control 5,800/58,000 = 10.00%, treatment 6,150/58,000 = 10.60%:

python scripts/abtest.py prop --c-conv 5800 --c-n 58000 --t-conv 6150 --t-n 58000

→ absolute lift +0.60pp, relative +6.0%, 95% CI on absolute difference, and a p-value. Decide using the CI, not just the p-value. See examples/conversion-test.md for the full walkthrough.

Best Practices

• Pre-register: hypothesis, primary metric, MDE, sample size, duration, and the decision rule BEFORE launch.
• Randomize at the right unit (usually user, not session/pageview) and keep it consistent across the funnel.
• Run for whole weeks; account for day-of-week and novelty effects.
• Report effect size + confidence interval first; treat the p-value as secondary.
• Use one primary OEC; everything else is a guardrail or exploratory.
• Always run an SRM check before trusting any result.
• Prefer two-sided tests; one-sided needs strong justification.

Common Pitfalls

• Peeking / optional stopping: checking daily and stopping at first significance turns a 5% false-positive rate into 20-30%+. Fix sample size up front, or use a proper sequential/Bayesian method.
• p-hacking / metric shopping: testing 20 metrics and reporting the one with p<0.05. Correct for multiplicity.
• Simpson's paradox: an aggregate winner can lose in every segment if traffic mix differs. Check key segments; beware mixing pre/post populations.
• Sample Ratio Mismatch: a broken split (e.g. 52/48 instead of 50/50) signals a bug that biases everything.
• Confusing significance with importance: with huge N, trivially small lifts become "significant." Use the MDE and the CI.
• Confusing non-significance with "no effect": underpowered tests fail to detect real effects. Report the CI.
• Novelty/primacy effects: early behavior differs from steady state; don't conclude from day 1-2.
• Multiple comparisons across variants: A/B/C/D testing without correction inflates false positives.

See references/pitfalls-checklist.md for a pre-launch and pre-decision checklist to run every time.

Bundled Files

• scripts/abtest.py — runnable, stdlib-only calculator: sample size, two-proportion z-test, Welch's t-test, chi-square, SRM. Run python scripts/abtest.py --help.
• references/methodology.md — deep dive on hypotheses, OEC, power, MDE, multiplicity corrections, sequential testing, Bayesian alternative.
• references/interpretation-guide.md — how to read p-values, CIs, and what each outcome (sig/non-sig × big/small effect) actually means for a ship decision.
• references/pitfalls-checklist.md — copy-paste checklist for design and analysis review.
• templates/experiment-report.md — fill-in template for documenting an experiment.
• examples/conversion-test.md — a complete end-to-end worked example.