The tutor explores the questions, from statistics, “What is a type I error? What is a type II error?”, with a couple of examples.

In statistics, hypothesis testing is done when you think you know a value but want confirmation.

Let’s imagine a bakery manager believes the bakery’s standard loaf of bread is 454g. However, every once in a while, that’s checked. With new bakers and aging implements, the actual mean mass of a loaf could wander.

The null hypothesis would, in such a case, be H₀=454g. The alternative: H_a≠454g. The test statistic would be identified – likely a normal or t variable – and a rejection region defined. I’ll go into those specifics in coming posts.

When the test is run, and the result is compared to the rejection region, the null hypothesis is either retained or rejected.

A type I error happens when the null hypothesis is rejected, yet it’s true. In this baking example, coming to believe the mean loaf mass is no longer 454g, when in fact it still is, constitutes a type I error.

A type II error happens when the null hypothesis is retained, but in fact is false. In this baking example, a type II error would be continuing to believe the mean loaf mass is 454g when in fact it’s 470g.

Generally, type I errors might be seen as more serious than type II.

Source:

Harnett, Donald L. and James L. Murphy. Statistical Analysis for Business and Economics. Don Mills: Addison-Wesley, 1986.

Jack of Oracle Tutoring by Jack and Diane, Campbell River, BC.