Probability of error in hypothesis testing

In hypothesis testing in statistics, two types of error are distinguished.

• Type I errors which consist of rejecting a null hypothesis that is true; this amounts to a false positive result.
• Type II errors which consist of failing to reject a null hypothesis that is false; this amounts to a false negative result.

The probability of error is similarly distinguished.

• For a Type I error, it is shown as α (alpha) and is known as the size of the test and is 1 minus the specificity of the test.
• For a Type II error, it is shown as β (beta) and is 1 minus the power or 1 minus the sensitivity of the test.

Probability of error in statistical modelling and econometrics

Many models in statistics and econometrics will usually seek to minimise the difference between observed and predicted or theoretical values. This difference is known as an error, though when observed it would be better described as a residual.

The error is taken to be a random variable and as such has a probability distribution.