I. Sample Size Background & Operational Context
Statistical Sample Size & 95% Confidence Interval Calculator (REF #152 // SAMPLE SIZE & MDE POWER) is engineered for Statistics & Data Science operators evaluating sample size margin of error calculator, statistical significance calculator, z-score p-value calculator. Calculate required A/B test sample size per variant, total two-arm experiment traffic, absolute conversion lift, and required test duration in days at 80%. At the calibrated baseline of Baseline Conversion Rate (p1 %) = 5 and Minimum Detectable Relative Lift (MDE %) = 10, this instrument computes a verified Required Sample per Variant of 31,235 Visitors and Total Experiment Sample (2 Arms) of 62,470 Visitors.
Before launching a controlled experiment, experimenters must calculate the exact sample size per variant (N) required to detect a meaningful Minimum Detectable Effect (MDE) without falling prey to Type I (false positive, α) or Type II (false negative, β) errors. Specifically for Sample Size, accounting for Total Daily Experiment Traffic (Visitors/Day) (4500) and Confidence Z-Score (1.96 = 95% CI) (1.96) yields Estimated Test Duration: 14 Days and Absolute Percentage Lift (|Δ|): +0.50% pts.
II. Sample Size Formula & Mathematical Mechanics
The Sample Size Calculator engine evaluates the closed-form equation N_per_arm = (2 × p_bar × (1 - p_bar) × (Z_α/2 + Z_β)²) / (p2 - p1)². Given baseline conversion rate p1, relative MDE delta, target conversion rate p2 = p1 × (1 + delta), and pooled rate p_bar = (p1 + p2)/2, the two-proportion sample size per variant is: N = (2 × p_bar × (1 - p_bar) × (Z_α/2 + Z_β)²) / (p2 - p1)².
To detect a +10.0% relative lift from a 5.00% baseline (reaching 5.50%, an absolute delta of +0.50% points) with 80% statistical power, you need 31,235 visitors per variant (62,470 total)—requiring 14 days at 4,500 visitors/day. At standard 95% two-tailed confidence (Z_α/2 = 1.96) and 80% statistical power (Z_β = 0.8416), the multiplier (Z_α/2 + Z_β)² ≈ 7.849. Total two-arm experiment traffic is 2 × N, and dividing by daily traffic yields exact required test duration in days.
III. Sample Size Calculator Parameter & Input Boundary Specification
| Code | Parameter Name (Sample Size) | Default | Valid Range | Mathematical Role |
|---|---|---|---|---|
| P01 // Sample Size | Baseline Conversion Rate (p1 %) | 5 | 0 to 80 (step 1) | Drives Required Sample per Variant in the Sample Size Calculator model |
| P02 // Sample Size | Minimum Detectable Relative Lift (MDE %) | 10 | 0 to 100 (step 1) | Drives Total Experiment Sample (2 Arms) in the Sample Size Calculator model |
| P03 // Sample Size | Total Daily Experiment Traffic (Visitors/Day) | 4500 | 0 to 1000000 (step 500) | Drives Estimated Test Duration in the Sample Size Calculator model |
| P04 // Sample Size | Confidence Z-Score (1.96 = 95% CI) | 1.96 | 0 to 3.5 (step 0.01) | Drives Absolute Percentage Lift (|Δ|) in the Sample Size Calculator model |
IV. Step-by-Step Worked Numerical Derivation (Sample Size Calculator)
Here is the exact step-by-step calculation using the default baseline parameters for Statistical Sample Size & 95% Confidence Interval Calculator
(Baseline Conversion Rate (p1 %) = 5, Minimum Detectable Relative Lift (MDE %) = 10, Total Daily Experiment Traffic (Visitors/Day) = 4500, Confidence Z-Score (1.96 = 95% CI) = 1.96):
V. Sample Size Modeling Pitfalls & Edge Cases
Sample Size: Confusing Relative MDE with Absolute Lift
A 10% relative lift on a 5.0% baseline conversion rate is a +0.50% absolute lift (from 5.0% to 5.5%), not 15.0%. When modeling Statistical Sample Size & 95% Confidence Interval Calculator (SAMPLE SIZE & MDE POWER), always verify your baseline Baseline Conversion Rate (p1 %) (5) and Minimum Detectable Relative Lift (MDE %) (10) against live Sample Size statements.
Sample Size: Stopping Tests Before Reaching Pre-Calculated N
Ending an experiment early because p < 0.05 on Day 4 guarantees inflated false-positive discovery rates. In Sample Size workflows, shifts in Total Daily Experiment Traffic (Visitors/Day) (4500) directly impact Required Sample per Variant (31,235 Visitors) and Total Experiment Sample (2 Arms) (62,470 Visitors).
Sample Size: Adding 4+ Variants Without Bonferroni Adjustment
Running 4 variants simultaneously quadruples total traffic needs and requires family-wise alpha correction. For Statistics & Data Science teams tracking sample size margin of error calculator, statistical significance calculator, z-score p-value calculator, stress-test Confidence Z-Score (1.96 = 95% CI) (1.96) across the 0.5x–2.0x sensitivity matrix above.