Confidence Interval for a Proportion: Analyzing Add-to-Cart Rate
confidence interval, margin of error, binomial proportion, ecommerce, A/B testing
TL;DR: Add-to-cart is 22% (n=600); 95% CI [18.8%, 25.2%] - baseline KPI 19% is acceptable, stretch 26% isn’t; for ±2 pp precision, target ~1,472-2,401 visitors.
Answer
Method: Wald confidence interval for a proportion.
Estimate: 22% and CI 18.8%, 25.2%.
Data: E-commerce traffic, variables add_to_cart, n = 600.
Action: Baseline KPI (19%) is met; stretch goal (26%) is not.
Case
You are a data analyst for an e-commerce site. You observed a 22% add-to-cart rate over two weeks with 600 visitors. The business question: Does this performance meet the baseline KPI of 19%? Can you claim the stretch goal of 26%? To answer this, you need to compute a 95% confidence interval for the add-to-cart proportion, read the margin of error, and assess whether the KPIs are acceptable.
Dataset
Synthetic sample for a single two-week window.
| Variable | Label | Value |
|---|---|---|
successes |
Add to cart count | 132 |
n |
Sample size | 600 |
p_hat |
Observed proportion | 0.22 |
Method
We use the Wald large-sample CI for a binomial proportion (Agresti 2019):
\[ \text{MOE} = Z^* \sqrt{\frac{\hat{p}(1-\hat{p})}{n}}. \]
Calculation
Visualization
Results and Interpretation
The estimated add-to-cart proportion was 0.22 (22.0%) with a 95% confidence interval of [0.188, 0.252] (or [18.8%, 25.2%]), a margin of error of ±3.2 percentage points. The large-sample rule holds (132 successes, 468 failures) (Agresti 2019; R Core Team 2024).
KPI assessment. Baseline KPI (19%) lies within the CI; stretch KPI (26%) lies above the CI.
Business decision. The baseline KPI (19%) is acceptable given the data, suggesting acceptable performance. The stretch KPI (26%) is not supported by this sample - more visitors or performance improvements are needed to claim that goal.
Sample Size Planning
To achieve ±2 percentage points precision at 95% confidence: \[ n = \hat{p}(1-\hat{p})\left(\frac{Z^*}{\text{MOE}_{\text{target}}}\right)^2. \]
Assumptions
The Wald interval assumes:
- Independent observations: Each visitor’s cart action is independent (no clustering by session or user ID)
- Random sampling: Visitors represent a random sample from the population (not biased toward specific traffic sources or times)
- Large-sample validity: Both \(n\hat{p} \ge 10\) and \(n(1-\hat{p}) \ge 10\) (conditions met: 132 successes and 468 failures both exceed 10)
- Stable process: The true conversion rate remains constant during the observation period (no seasonal trends, promotional effects, or A/B tests running concurrently)
Use the below format to cite this page
Sharafuddin, M. A. (2024, June 10). Confidence interval for a proportion: Analyzing add-to-cart rate. Flair Marketing Intelligence (FlairMI). https://flairmi.com/blog/posts/01-margin-of-error.html
@online{sharafuddin2024-ci-proportion,
author = {Sharafuddin, Mohammed Ali},
title = {Confidence Interval for a Proportion: Analyzing Add-to-Cart Rate},
year = {2024},
date = {2024-06-10},
url = {https://flairmi.com/blog/posts/01-margin-of-error.html},
langid = {en}
}
Try it in the browser
Margins of error for proportions are built into two free browser tools: the A/B Test Calculator, which draws a confidence interval for each group, and the Net Promoter Score Tracker, which reports the margin of error for every survey wave. Both belong to the Marketing Toolkit Hub.
References
Citation
@online{ali_sharafuddin2024,
author = {Ali Sharafuddin, Mohammed},
title = {Confidence {Interval} for a {Proportion:} {Analyzing}
{Add-to-Cart} {Rate}},
date = {2024-06-10},
url = {https://flairmi.com/blog/posts/01-margin-of-error.html},
langid = {en}
}
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