Difference in Proportions CI Calculator

Measure gaps between two observed proportions confidently. Analyze campaigns, surveys, and quality outcomes with precision. See interval bounds, error terms, and clear interpretation instantly.

Calculator Input

Example Data Table

Sample observations you can test immediately inside the calculator.

Scenario Group A Successes Group A Size Group B Successes Group B Size Observed Difference
Email conversion test120500954800.0421
Defect reduction review1830031310-0.0400
Survey response campaign2109001768700.0313
App signup comparison84250622450.0829

Formula Used

This calculator uses the unpooled Wald confidence interval for two independent sample proportions.

p₁ = x₁ / n₁, p₂ = x₂ / n₂
Difference = p₁ − p₂
SE = √[(p₁(1−p₁)/n₁) + (p₂(1−p₂)/n₂)]
Margin of Error = z × SE
CI = (p₁ − p₂) ± z × SE

For context, the page also reports a pooled z test, relative lift, risk ratio, and odds ratio.

How to Use This Calculator

  1. Enter labels for the two groups you want to compare.
  2. Provide the number of successes and total sample size for each group.
  3. Select a confidence level that matches your reporting standard.
  4. Choose decimal precision for cleaner presentation or deeper review.
  5. Click Calculate Interval to show results above the form.
  6. Review the difference, interval bounds, p-value, and supporting comparison metrics.
  7. Export the result table or example data as CSV or PDF when needed.

Why This Calculator Helps

A difference in proportions interval helps you judge whether two observed rates differ meaningfully. This is useful for A/B testing, defect tracking, clinical response comparisons, survey analysis, and campaign evaluation when outcomes are coded as success or failure.

If the interval excludes zero, the observed difference is less likely to be explained by sampling noise alone. Wider intervals suggest more uncertainty, usually caused by smaller samples or rates near the middle.

FAQs

1. What does this interval measure?

It measures the plausible range for the true difference between two population proportions, based on observed sample outcomes and your selected confidence level.

2. When should I use this calculator?

Use it when comparing binary outcomes between two independent groups, such as conversions, defects, approvals, completions, recoveries, or response rates.

3. What does it mean if zero is inside the interval?

If zero lies inside the interval, the observed gap may be compatible with no real population difference at the chosen confidence level.

4. Why does sample size matter so much?

Larger samples reduce standard error, which narrows the interval. Smaller samples create wider intervals and make conclusions less stable.

5. Is this the same as a significance test?

Not exactly. The confidence interval estimates a range, while the z test evaluates a null hypothesis. They complement each other.

6. Can I compare more than two groups here?

No. This page is designed for two-group comparisons only. For multiple groups, use methods built for multi-arm categorical analysis.

7. What assumptions should I keep in mind?

Assume independent groups, binary outcomes, accurate counts, and samples large enough for normal approximation to behave reasonably.