Point Estimate Calculator

This point estimate calculator can help you quickly and easily determine the most suitable point estimate according to the size of the sample, number of successes, and required confidence level.

The calculator uses four estimation approaches to compute the most suitable point estimate: the maximum likelihood, Wilson, Laplace, and Jeffrey's methods.

How to use the calculator

  1. Input the number of successes in the sample (x) and the size of the sample (n)
  2. Choose your required confidence level from the options available in the dropdown list
  3. Click on the "Calculate" button to obtain the results.
Point Estimate Calculator

Estimation Methods

This point estimate calculator makes use of four point estimate approaches: the maximum likelihood, Wilson, Laplace, and Jeffrey's methods. The accompanying equations are as follows:

  • Maximum Likelihood Estimation (MLE): x / n
  • Wilson: (x + z 2/2) / (n + z 2)
  • Laplace: (x + 1) / (n + 2)
  • Jeffrey's: (x + 0.5) / (n + 1)
  • Where,
  • x is the number of successes in the sample,
  • n is the sample size or the number of trials,
  • z is the z-score associated with a level of confidence.

The calculator uses the following logic to compute the best point estimate:

  • If x/n ≤ 0.5, the Wilson method is applied
  • If 0.5 < x/n < 0.9, the MLE method is applied
  • If 0.9 ≤ x/n < 1.0, the Laplace or Jeffreys method is applied (the smallest of these estimates)
  • If x/n = 1.0, the Laplace method is applied.

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