# errors in statistical hypothesis test

When we do a hypothesis test and contrast the null hypothesis against the alternative, based on the information provided by the sample, we can make two types of errors, due to the randomness of sampling:

Type I error: incorrect rejection of a true null hypothesis H0

Type II error: incorrect rejection of a true alternative hypothesis H1

Committing one or other error in a hypothesis test leads to make inappropriate decisions, as shown in the following table:

The probability of making a type I error is given by α (the significance level). This probability does not depend on sample size.

The probability of making a type II error is given by β, and depends on the true value of the parameter and the size of the sample: the lower error, the greater sample size.

If μ is the mean value, for example, and we define H0: μ=μ0, in the graph we will have distributions corresponding sample means and rejection and non-rejection regions, as well as α and β values, which are the probabilities of committing a type I or type II error, respectively.