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Updated 2026-03-07 UTC
Two‑Proportion z Test — Compare Two Conversion Rates — GetCalcMaster
Two-proportion z test formula and workflow: compare p1 and p2 using pooled proportion. Useful for A/B tests and difference in proportions.
The two‑proportion z test compares two proportions (like conversion rates). It tests whether the difference p1−p2 is larger than expected from sampling noise.
Important: Educational. For sequential testing or multiple looks at the data, adjust your testing framework.
What this calculator is
The Statistics Calculator is an interactive tool inside GetCalcMaster. It’s designed to help you explore scenarios, understand formulas, and document assumptions.
Key features
- Uses pooled proportion under H₀
- Works for large-sample binomial proportions
- Connects directly to p-values and confidence intervals
Formula
p1 = x1/n1, p2 = x2/n2
p = (x1 + x2) / (n1 + n2)
SE = sqrt(p(1-p) * (1/n1 + 1/n2))
z = (p1 - p2) / SEQuick examples
If n1 and n2 are small, the normal approximation can be poor (consider exact methods).A tiny but significant difference may still be practically unimportant—check effect size.
How to use it (quick steps)
- Compute p1 = x1/n1 and p2 = x2/n2.
- Compute pooled p = (x1 + x2) / (n1 + n2).
- Compute SE = sqrt(p(1−p)(1/n1 + 1/n2)).
- Compute z = (p1 − p2) / SE, then get p-value from the normal distribution.
- Report effect size (difference in proportions) + CI, not only p-value.
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FAQ
Is this calculator official?
No. GetCalcMaster provides educational estimates and learning tools. Always verify against official definitions, documents, or professional advice.
Do you store my inputs on the server?
No. Calculations run locally in your browser. Optional remember/restore features (if enabled) use local browser storage.
Tip: For reproducible work, save your inputs and reasoning in Notebook.