Math
Two-proportion z statistic
Compare two independent observed proportions using a pooled normal-approximation statistic.
Calculators / Math / Observed event-rate ratio
Observed event-rate ratio calculator
Compare event proportions between two observed groups, such as defects in two production batches.
On this page
First event rate20%
Second event rate10%
First-to-second rate ratio2
Calculator controls
How to calculate
Compare event proportions between two observed groups, such as defects in two production batches.
First event rate =
x1/n1*100 %Second event rate =
x2/n2*100 %First-to-second rate ratio =
(x1/n1)/(x2/n2)Worked example
- First event count: 20
- First exposure count: 100
- Second event count: 10
- Second exposure count: 100
- First event rate: 20 %
- Second event rate: 10 %
- First-to-second rate ratio: 2
Assumptions and limits
Events cannot exceed exposure counts; the reference event count must be positive. This reports observed association without confidence intervals or causal claims.
Results are rounded for display; calculations use unrounded values. Read our calculation methodology.
Understanding the result
Compare event proportions between two observed groups, such as defects in two production batches. A ratio of two means the first observed proportion is twice the second; it does not identify why the batches differ.
When this tool is useful
A ratio of two means the first observed proportion is twice the second; it does not identify why the batches differ.
Understanding your inputs
| Input | Example |
|---|---|
First event count x1 | 20 |
First exposure count n1 | 100 |
Second event count x2 | 10 |
Second exposure count n2 | 100 |
Frequently asked questions
Which assumptions matter for this result?
Events cannot exceed exposure counts; the reference event count must be positive. This reports observed association without confidence intervals or causal claims.
How can I check the worked example?
Use the displayed example inputs in the stated formula. Keep each quantity in its labelled unit and compare the unrounded result before applying display rounding.