Calculate the true statistical accuracy of a rating or conversion rate using the Wilson Score Interval.
History
How to Use This Calculator
Why “Average Rating” is a Lie
Imagine two products:
- Product A: Has one review, and it is 5 stars. (Average: 5.0)
- Product B: Has 100 reviews, with 95 positive. (Average: 4.95)
Mathematically, Product A has a higher average. But intuitively, you trust Product B more. The Wilson Score solves this by asking: “Given the data we have, what is the ’true’ rating we can be 95% confident in?”
The Math Behind It
The tool uses the following mathematical principle:
$$ w = \frac{\hat{p} + \frac{z^2}{2n} \pm z \sqrt{\frac{\hat{p}(1-\hat{p})}{n} + \frac{z^2}{4n^2}}}{1 + \frac{z^2}{n}} $$
Where:
- $n$ is the Total Trials (total reviews or visitors).
- $\hat{p}$ is the Observed Success Rate (successes / trials).
- $z$ is the Z-Score (1.96 for 95% confidence).