Type I and Type II Errors When Sampling a Population

Type I and Type II Errors When Sampling a Population

In hypothesis testing, we set a null and alternative hypothesis. We are seeking evidence that the alternative hypothesis is true given the sample data. By using a sample from a population and not measuring every item in the population, we need to consider a couple of unwanted outcomes. Statisticians have named these unwanted results Type I and Type II Errors.

A Two-Way Decision Process

Unknown to us, hence wanting to conduct a hypothesis test to learn something, the null hypothesis for the population under study may actually be true. On the other hand, the null hypothesis may not be true.

The view of the population we have is via the sample taken. We will make a decision based on the sample and determine if we accept or reject the null hypothesis.

This set of four possible outcomes is often presented as a two-way decision process as so:

When the actual null hypothesis is true and our sample indicates that is the case, that is a reflection of what is correct…