growth-experiment-engine

name	Growth Experiment Engine
description	A/B test tracking with statistical significance — create experiments, log data, score winners with bootstrap CI + Mann-Whitney U, auto-promote to a living playbook
category	Marketing
roles	["cmo","analyst"]
platforms	["airtable"]

Growth Experiment Engine

The only skill in the system that does real statistical math. Create A/B experiments, log results, compute bootstrap confidence intervals and Mann-Whitney U significance tests, and auto-promote winners to a living playbook.

---

Step 1: Create Experiment

Define the experiment before any data is collected.

Required fields:

Field	Description	Example
Hypothesis	"Changing X will improve Y by Z%"	"Shorter subject lines will improve open rate by 15%"
Variable	What you're testing	Subject line length
Variants	2–10 variants labeled A, B, C…	A (control, 8+ words), B (4 words or fewer)
Primary Metric	What you're measuring	open_rate
Cycle	How often to check	24h / 48h / 7d
Minimum Sample	Per variant before scoring	30 (low-volume) or 100 (high-volume)

Create the experiment record:

use airtable AIRTABLE_CREATE_RECORDS '{
  "table": "experiments",
  "fields": {
    "experiment_id": "EXP-001",
    "hypothesis": "Shorter subject lines will improve open rate by 15%",
    "variable": "Subject line length",
    "variants": "A,B",
    "metric": "open_rate",
    "cycle": "48h",
    "min_sample": 100,
    "status": "running",
    "created_date": "2026-04-02"
  }
}'

Channel categories:

• Email: subject lines, send times, CTAs, body length
• Social: posting times, formats, hashtags, hooks
• Ads: headlines, creatives, audiences, bidding
• Landing pages: headlines, CTAs, layouts, social proof
• Content: titles, formats, topics, lengths

---

Step 2: Log Data Points

Log results for each variant as they come in. One record per measurement cycle.

use airtable AIRTABLE_CREATE_RECORDS '{
  "table": "experiment_results",
  "fields": {
    "experiment_id": "EXP-001",
    "variant": "A",
    "metric_value": 0.21,
    "sample_size": 120,
    "date": "2026-04-03"
  }
}'

Example data log table:

Experiment ID	Variant	Metric Value	Sample Size	Date
EXP-001	A	0.21	120	2026-04-03
EXP-001	B	0.26	118	2026-04-03
EXP-001	A	0.19	135	2026-04-05
EXP-001	B	0.28	131	2026-04-05

Rules:

• Log consistently — missing data points invalidate results
• One variable per experiment, never test multiple things at once
• Variant A is always the control group

---

Step 3: Score Experiment

This is the core value. When each variant has reached minimum sample size, run statistical analysis.

Bootstrap Confidence Interval (95%)

For each variant, compute a non-parametric confidence interval by resampling.

Algorithm (N = 1000 bootstrap iterations):

Given: observations = [x1, x2, ..., xn] for one variant

bootstrap_means = []
for i in 1..1000:
    sample = draw n values from observations with replacement
    bootstrap_means.append(mean(sample))

sort(bootstrap_means)
CI_lower = bootstrap_means[25]     # 2.5th percentile  (index 25 of 1000)
CI_upper = bootstrap_means[975]    # 97.5th percentile (index 975 of 1000)

Example calculation:

Variant A observations (open rates): [0.18, 0.21, 0.23, 0.19, 0.22, ...]

1. Draw 100 values with replacement → compute mean → repeat 1000 times
2. Sort 1000 means → [0.17, 0.18, 0.18, ..., 0.24, 0.25]
3. 95% CI = [mean at index 25, mean at index 975]

Report as: A: mean=0.205, 95% CI [0.19, 0.22]

---

Mann-Whitney U Test (non-parametric significance)

Tests whether variant B is drawn from a different distribution than variant A, without assuming normality.

Formula — step by step:

Given: group_A = [a1, a2, ..., a_nA]  (control)
       group_B = [b1, b2, ..., b_nB]  (challenger)

Step 1 — Combine and rank all observations:
  combined = group_A + group_B  (length = nA + nB)
  Assign ranks 1 to (nA + nB), lowest value = rank 1
  For ties: assign the average of the tied ranks

Step 2 — Sum ranks per group:
  R_A = sum of ranks for all observations in group_A
  R_B = sum of ranks for all observations in group_B

Step 3 — Compute U statistics:
  U_A = R_A - nA*(nA + 1)/2
  U_B = R_B - nB*(nB + 1)/2
  U   = min(U_A, U_B)

Step 4 — Z-score (valid when nA > 20 and nB > 20):
  mean_U  = nA * nB / 2
  sigma_U = sqrt( nA * nB * (nA + nB + 1) / 12 )
  z       = (U - mean_U) / sigma_U

Step 5 — Two-tailed p-value from z:
  p = 2 * (1 - Phi(|z|))
  where Phi is the standard normal CDF

  Approximation table for |z|:
    |z| = 1.65 → p ≈ 0.10
    |z| = 1.96 → p ≈ 0.05
    |z| = 2.58 → p ≈ 0.01
    |z| = 3.29 → p ≈ 0.001

Example calculation:

• Group A (n=5): [0.18, 0.19, 0.21, 0.22, 0.23]
• Group B (n=5): [0.24, 0.26, 0.27, 0.28, 0.30]

Combined ranked: A values get ranks 1–5, B values get ranks 6–10

R_A = 1+2+3+4+5 = 15, R_B = 6+7+8+9+10 = 40

U_A = 15 - 5*6/2 = 15 - 15 = 0

U_B = 40 - 5*6/2 = 40 - 15 = 25

U = min(0, 25) = 0

mean_U = 55/2 = 12.5, sigma_U = sqrt(55*11/12) = sqrt(22.9) = 4.79

z = (0 - 12.5) / 4.79 = -2.61 → |z| = 2.61 → p ≈ 0.009

---

Lift Calculation

lift = (mean_B - mean_A) / mean_A * 100    (expressed as %)

---

Winner Decision Rules

Condition	Decision
p < 0.05 AND lift ≥ 15%	KEEP — winner found, promote to playbook
p < 0.10 AND lift ≥ 10%	TRENDING — promising, collect more data
p ≥ 0.10 OR lift < 10%	INCONCLUSIVE — no winner yet
3+ cycles with no winner	DISCARD — no meaningful difference exists

---

Score Results Table

Present all results in this format:

Variant	Mean	95% CI	vs Control	Lift	p-value	Decision
A (control)	0.205	[0.19, 0.22]	—	—	—	baseline
B	0.268	[0.25, 0.29]	+0.063	+30.7%	0.009	KEEP

Update experiment status in Airtable after scoring:

use airtable AIRTABLE_UPDATE_RECORDS '{
  "table": "experiments",
  "record_id": "<record_id>",
  "fields": {
    "status": "complete",
    "winner": "B",
    "lift": 30.7,
    "p_value": 0.009,
    "decision": "KEEP",
    "scored_date": "2026-04-05"
  }
}'

---

Step 4: Living Playbook

When an experiment is marked KEEP, add the winning insight to the playbook. This is the compounding return on all experiments run.

Playbook entry format:

## [Date] — [Variable Tested]
- Winner: [Variant description] beat [Control description] by [Lift]% (p=[value])
- Insight: [What we learned in plain language]
- Apply to: [Where this insight should be used going forward]

Example entry:

## 2026-04-05 — Email Subject Line Length
- Winner: 4-word subject lines beat 8+ word subject lines by 30.7% (p=0.009)
- Insight: Brevity wins in crowded inboxes. Short subject lines increase curiosity without over-explaining.
- Apply to: All future campaign emails, automated sequences, cold outreach

Store playbook entry in Airtable:

use airtable AIRTABLE_CREATE_RECORDS '{
  "table": "playbook",
  "fields": {
    "date": "2026-04-05",
    "variable": "Email subject line length",
    "winner_description": "4-word subject lines",
    "control_description": "8+ word subject lines",
    "lift_pct": 30.7,
    "p_value": 0.009,
    "insight": "Brevity wins in crowded inboxes.",
    "apply_to": "All future campaign emails, automated sequences, cold outreach",
    "experiment_id": "EXP-001"
  }
}'

---

Step 5: Suggest Next Experiments

After each completed experiment, generate the next test to run based on results.

Decision logic:

Previous Result	Next Experiment
KEEP (strong winner)	Test variations of the winner — push further in the same direction
TRENDING (needs more data)	Continue current experiment or test a more extreme version
INCONCLUSIVE	Test a more extreme variation of the same variable
DISCARD	Move to a different variable in the same channel
No experiments in a category	Suggest the highest-leverage first experiment for that channel

Suggested first experiments by channel:

• Email: subject line length (highest open-rate impact)
• Social: posting time (AM vs PM vs evening)
• Ads: headline (value prop vs pain point vs curiosity)
• Landing page: headline (feature vs outcome vs social proof)
• Content: title format (how-to vs list vs question)

---

Step 6: Weekly Scorecard

Generate a weekly summary of all experiment activity.

Scorecard format:

## Growth Experiment Scorecard — Week of [Date]

Experiments running:         [N]
Experiments completed:       [N]
Winners found (KEEP):        [N]
Trending (need more data):   [N]
Discarded (no difference):   [N]

Total lift from winners:     [X]% (cumulative across winning metrics)

Top insight this week:
  "[Best finding from any experiment]"

Experiments to start next week:
  1. [Suggestion 1]
  2. [Suggestion 2]
  3. [Suggestion 3]

Fetch data to build scorecard:

use airtable AIRTABLE_LIST_RECORDS '{
  "table": "experiments",
  "filter": "status = 'complete' OR status = 'running'"
}'

---

Statistical Guidelines

• Minimum sample: 30 per variant before scoring (100 for high-volume channels like email blasts)
• Never declare a winner without statistical significance (p < 0.05)
• Always report confidence intervals, not just p-values — a wide CI means you need more data even if p < 0.05
• One variable per experiment — testing multiple changes at once makes it impossible to know what caused the result
• Variant A is always control — the baseline you are trying to beat
• Log data consistently — gaps or selective logging invalidate the statistical assumptions
• Bootstrap CI is preferred over parametric CI (t-distribution) because conversion rates and engagement rates are not normally distributed
• Mann-Whitney U is preferred over t-test for the same reason — it makes no distribution assumptions
• Lift threshold matters — a statistically significant lift of 2% may not be worth the operational change; require ≥ 10% lift minimum