Population proportions and probabilities

We now consider how to estimate the proportion in one category of a categorical population that we will call "success". The population proportion of successes is denoted by π and is also the probability of a single sampled value being a success.

Parameter estimate and error

The proportion of successes, p, in a random sample is used to estimate the population proportion, π.

Since p is found from a random sample, it is itself random. There will therefore be an estimation error that has a distribution,

error   =   p − π

Rice survey

This example presents an estimate of a population proportion and asks how close it is likely to be.

Error distribution

We use a simulation to show that the estimation error has a distribution.

The error distribution describes the likely size of errors from this type of estimate.

Note that this is not a practical way to obtain the error distribution since we can rarely take multiple samples from the population. However it does illustrate the concept of an error distribution.