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Ubify Financial Advisory Board
FINANCIAL ANALYSTS & CPA REVIEWERS
About This Tool
This conversion rate optimization (CRO) calculator determines the minimum sample size of visitors required per variant to detect a statistically significant change in conversion rate. Concluding an A/B test too early often leads to false positives caused by natural sampling variance, while running an experiment too long wastes traffic and marketing budget.
### Statistical Model and Sizing Formulations The calculator uses standard hypothesis testing for binomial proportions assuming a two-tailed test with a $95\%$ confidence level ($\alpha = 0.05$, critical value $Z_{\alpha/2} = 1.96$) and $80\%$ statistical power ($\beta = 0.20$, critical value $Z_{\beta} = 0.84$):
- **Conversion Proportions:** - Baseline Proportion ($p_1$): $\text{Baseline Conversion (\%)} / 100$ - Expected Proportion ($p_2$): $p_1 \times (1 + \text{Relative Lift})$ - Detectable Difference ($\delta$): $|p_2 - p_1|$ - Pooled Proportion ($\bar{p}$): $(p_1 + p_2) / 2$ - **Required Visitors per Variation ($n$):** Using Evan Miller's standard two-proportion approximation: $n = \left\lceil \frac{16 \times \bar{p} \times (1 - \bar{p})}{\delta^2} \right\rceil$ - **Total Experiment Sample Size:** $\text{Total Sample} = n \times 2$ - **Estimated Experiment Duration (Days):** $\text{Runtime (Days)} = \left\lceil \frac{\text{Total Sample}}{\text{Daily Visitors}} \right\rceil$
### Worked Numeric Example Consider optimizing an e-commerce checkout flow: - Baseline Conversion Rate: $3.5\%$ - Minimum Detectable Effect (Relative Lift): $10\%$ - Daily Traffic: 2,500 visitors per day
**Step-by-Step Calculation:** 1. Proportions: $p_1 = 0.035$. With a $10\%$ lift, $p_2 = 0.035 \times 1.10 = 0.0385$. 2. Detectable Delta: $\delta = 0.0385 - 0.035 = 0.0035$. 3. Pooled Proportion: $\bar{p} = (0.035 + 0.0385) / 2 = 0.03675$. 4. Sample per Variant: $n = \lceil 16 \times 0.03675 \times (1 - 0.03675) / (0.0035)^2 \rceil = \lceil 0.56639 / 0.00001225 \rceil = 46,236\text{ visitors per variation}$. 5. Total Visitors Required: $46,236 \times 2 = 92,472\text{ visitors}$. 6. Test Duration: $\lceil 92,472 / 2,500 \rceil = 37\text{ full days}$.
### Client-Side Processing Note All statistical calculations evaluate locally in your browser memory. No website traffic data, conversion metrics, or experimental hypotheses are sent across any network.
How to Use
- 1
Enter your current baseline conversion rate as a percentage (e.g., 3.5%).
- 2
Enter your target Minimum Detectable Effect (MDE) as a relative percentage lift (e.g., 10%).
- 3
Specify the daily visitor traffic arriving at the experiment page.
- 4
Review the required sample size per variant, total required traffic, and estimated experiment duration.
Frequently Asked Questions
What is statistical power and why is 80% standard in CRO?
Statistical power (1 - beta) is the probability of correctly detecting a real lift when one exists. An 80% power level provides an industry standard balance between avoiding false negatives and requiring practical sample sizes.
Why does detecting a smaller lift require exponentially more visitors?
The formula divides by delta squared. Cutting your minimum detectable effect in half (e.g., from 10% to 5%) increases required sample size by roughly four times.
Does this calculator store experiment metrics or customer traffic numbers?
No. All calculations run strictly in your local browser session using JavaScript floating point math.