## What is a Parametric Test?

A parametric test is a statistical test which makes certain assumptions about the distribution of the unknown parameter of interest and thus the test statistic is valid under these assumptions. A significance test under a Simple Normal Model for example has the assumption that the parameter has a normal distribution, behaves like an independent variable (is the result of an independent process) is identically distributed and has a constant mean and variance. Therefore, an integral part of applying such a test is making sure it is adequate vis-a-vis the observed data. This process is called mis-specification testing.

Modern parametric statistical inference is dominated by the concept of the likelihood function: the specified statistical model fully determines the likelihood function and all estimators rely on that quality one way or another, including the notion of a uniformly most powerful test which is a cornerstone in power analysis.

Parametric tests have the benefit of being precise in their assumptions which leads to more precise inferences and the ability to run mis-specification tests.