Neyman-Pearson paradigm

An approach to the foundations of statistics. The Neyman-Pearson (NP) paradigm is focused on decision-making above all else, as opposed to simply quantifying evidence against the null as Fisher wanted (see Fisher’s paradigm).

NP believed that a null hypothesis $H_0$ should always be tested against an alternative hypothesis $H_1$. They want to decide when and how to reject $H_0$ in favor of $H_1$, and therefore introduce the notion of type-I error, type-II error, and power. The NP paradigm cashes out correct in terms of the frequentist principle (see frequentist statistics):

In repeated practical use of a statistical procedure, the long-run average actual error should not be greater than (and ideally should equal) the long-run average reported error.

• From Berger.

The NP procedure looks like:

• Define a test statistic $T$ based on the data.
• Reject $H_0$ if $T\ge c$, where $c$ is some pre-chosen critical value. (Being pre-chosen is crucial, see issues with p-values).
• (Perhaps more generally, compute a p-value $p$ and reject if $p\le \alpha$ where $\alpha$ is pre-chosen. Usually the p-value is computed by means of the test-statistic above).