How to Calculate P-hat

By Peter Flom

In statistics notation a "hat" over a letter usually means estimate of a parameter. P means proportion. P-hat (usually written as a p with a little hat shape over it) thus means estimate of proportion. Parameters apply to populations, and statistics apply to samples. Usually, you cannot work with an entire population, so you use a sample to estimate the quantities you are interested in. For example, if you wanted to estimate the proportion of men who voted for Obama, you would ask a sample of men who they voted for.

Sample your population. For example, you might use random digit dialing to reach people, then ask any men who they voted for in the last election.

Count the number of subjects in your sample who have the property you are interested in. In the example, count the number of men who say they voted for Obama.

Divide this by the total size of your sample. This is p-hat.

About the Author

Peter Flom is a statistician and a learning-disabled adult. He has been writing for many years and has been published in many academic journals in fields such as psychology, drug addiction, epidemiology and others. He holds a Ph.D. in psychometrics from Fordham University.