This p hat calculator takes the figures you already have and applies the relationship behind p hat calculations for you, giving p̂ from sample size and number of occurrences.
What Is the P Hat Calculator?
The p hat calculator turns a set of measurements into p̂, 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 P Hat 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 sample size set to 10, number of occurrences set to 5, the calculator returns p̂ of 0.5. Substitute your own figures and the same steps produce the same kind of answer.
Frequently Asked Questions
What do I need to work out p̂?
Enter sample size and number of occurrences. The calculator then works through the relationship and reports p̂.
What does the p hat actually calculate?
It takes sample size and number of occurrences and converts them into p̂ 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 sample size?
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.
Does anything you type get stored?
No. The whole calculation runs inside your browser, and nothing you enter is uploaded, logged or sent anywhere.