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Point Estimate Calculator
A point estimate is a single best guess at a population proportion. Enter the number of successes and the number of trials to get the maximum likelihood estimate and three adjusted estimates — Wilson, Jeffreys and Laplace — that behave better with small samples.
- Wilson estimate
- 0.4037
- Jeffreys estimate
- 0.401
- Laplace estimate
- 0.402
- Critical value (z*)
- 1.96
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Formula
How to use it
- Enter the number of successes observed.
- Enter the total number of trials.
- Choose a confidence level; it only affects the Wilson estimate.
- Read the estimates and pick the one suited to your sample size.
Worked examples
40 successes in 100 trials at 95% confidence
- Maximum likelihood estimate (x ÷ n)
- 0.4
- Wilson estimate
- 0.4037
- Jeffreys estimate
- 0.401
- Laplace estimate
- 0.402
- Critical value (z*)
- 1.96
3 successes in 10 trials
- Maximum likelihood estimate (x ÷ n)
- 0.3
- Wilson estimate
- 0.3555
- Jeffreys estimate
- 0.3182
- Laplace estimate
- 0.3333
No successes in 20 trials
- Maximum likelihood estimate (x ÷ n)
- 0
- Wilson estimate
- 0.0806
- Jeffreys estimate
- 0.0238
- Laplace estimate
- 0.0455
Why there is more than one estimate
The maximum likelihood estimate is the plain sample proportion and is the right choice for large samples. With little data it can be extreme: 0 successes in 20 trials gives an estimate of exactly 0, even though the event is clearly not impossible.
The other three pull the estimate toward 50% by adding imaginary observations. Laplace adds one success and one failure. Jeffreys adds half of each. Wilson adds z² ÷ 2 successes and z² trials — about 2 and 4 at 95% confidence. For 0 in 20 they give 0.045, 0.024 and 0.081.
Large samples agree
As the number of trials grows, the adjustments stop mattering. For 485 successes in 1,000 trials all four estimates round to 0.485. A point estimate also says nothing about its own uncertainty; pair it with a margin of error or confidence interval.
Questions people ask
What is the point estimate for 40 successes in 100 trials?
0.40 by maximum likelihood. The Wilson estimate at 95% confidence is 0.4037.
What is a point estimate?
A single number used to estimate an unknown population value, such as a sample proportion standing in for the true proportion. An interval estimate gives a range instead.
Which point estimate should I use?
For large samples, the maximum likelihood estimate x ÷ n. For small samples, or when you saw no successes or no failures, one of the adjusted estimates is more reasonable.