A point estimate represents our “best guess” of a population parameter.

For example, a sample mean can be used as a point estimate of a population mean.

Similarly, a sample proportion can be used as a point estimate of a population proportion. However, there are several ways to calculate the point estimate of a population proportion, including:

MLE Point Estimate: x / n

Wilson Point Estimate: (x + z²/2) / (n + z²)

Jeffrey Point Estimate: (x + 0.5) / (n + 1)

Laplace Point Estimate: (x + 1) / (n + 2)

where x is the number of “successes” in the sample, n is the sample size or number of trials, and z is the z-score associated with the confidence level.

To find the best point estimate, simply enter in the values for the number of successes, number of trials, and confidence level in the boxes below and then click the “Calculate” button.

Number of successes (x) Number of trials (n) Confidence level (%)

Best Estimate = 0.45695

MLE Point Estimate = 0.45161

Wilson Point Estimate = 0.45695

Jeffrey Point Estimate = 0.45313

Laplace Point Estimate = 0.45455

This calculator uses the following logic to determine which point estimate is best to use:

If x / n ≤ 0.5, use the Wilson Point Estimate.

Otherwise, if x / n < 0.9, use the MLE Point Estimate.

Otherwise, if x / n < 1.0, use the smaller of the Jeffrey Point Estimate or the Laplace Point Estimate.

Otherwise, if x / n = 1.0, use the Laplace Point Estimate.