Everyday point estimate problems come down to one relationship between number of successes, number of trials and z score. This calculator turns those numbers into best point estimate, laplace estimation and jeffrey estimation, with the working shown so you can check the result rather than simply trust it.
What Is the Point Estimate Calculator?
The point estimate calculator turns a set of measurements into best point estimate, laplace estimation and jeffrey estimation, with the uncertainty made explicit rather than left implied.
Statistics is easy to quote badly. A figure without its spread tells the reader far less than they assume it does, and this calculator puts both together.
How the Point Estimate Is Calculated
The calculation uses the standard relationship for this kind of estimate, applied to the figures you supply. The intermediate steps are exposed so you can see how much of the answer comes from each one.
Sample size matters more than most people expect. Doubling the number of observations improves the precision by a factor of about one and a half, not two.
What the Result Does and Does Not Tell You
A result describes the data you gave it. It does not tell you whether the sample was representative, whether the method was appropriate, or whether there is a confound in the way the figures were collected.
Report the result together with its uncertainty. A number on its own is much easier to misread than a number with a range attached.
A Worked Example
Working through an example, with number of successes set to 10, number of trials set to 5, z score set to 2, the calculator returns mle of 2, and laplace estimation of 1.57, and jeffrey estimation of 1.75. Substitute your own figures and the same steps produce the same kind of answer.
Frequently Asked Questions
What do I need to work out best point estimate?
Enter number of successes, number of trials and z score. The calculator then works through the relationship and reports best point estimate, laplace estimation and jeffrey estimation.
What does the point estimate actually calculate?
It takes number of successes, number of trials and z score and converts them into best point estimate, laplace estimation and jeffrey estimation using the standard relationship for this problem. Each step is applied in turn, so every output is traceable back to the numbers you typed in.
How should I enter number of successes?
Use the value you actually have, in the unit shown next to the field. Enter every value in the same unit system. The calculator assumes the figures you supply are consistent, so it cannot correct a mistake that happens before the calculation starts.
Do I have to fill in every field?
Only the fields a particular result depends on. If you leave one blank, the results that need it simply show a note instead of a number, and everything else still works.
Why does a small change in one value move the answer so much?
That happens when an output depends on a ratio, because dividing by a small number magnifies any change in it. Check the units first, then check whether the value you entered is in the range the relationship was designed for.