Test statistic and p-value

The statistical distance of an estimate to the null hypothesis parameter value can be used as a test statistic.

Refinements

If the standard error of the estimate must itself be estimated from the sample data, the above test statistic is only approximately normally distributed. In some tests that we will describe in later sections, the test statistic has a t distribution (which has slightly longer tails than the standard normal distribution). This refinement will be described fully in the next section.

Home-based businesses owned by women

Relation to previous test

The p-value obtained in this way using a 'statistical distance' as the test statistic is identical to the p-value that was found from a normal approximation to the number of successes without a continuity correction. (The p-value is slightly different if a continuity correction is used.)

The use of 'statistical distances' does not add anything when testing a sample proportion, but it is a general method that will be used to obtain test statistics in many other situations later in this e-book.