Notes:Hypothesis testing

Warning:This page is for my notes on work I haven't done for 5 years, don't rely on it - this is mainly for my own benefit, but if it helps someone else, that's fine by me.

Introduction

A test has two "hypotheses":

• $H_0$ - the null hypothesis - for now we assign no meaning to it
• $H_1$ - the alternative hypothesis - a distinct claim from the null

Test outcomes and events

There are 2 outcomes:

1. Reject $\mathbf{H_1}$ or "stay with $H_0$"
2. Accept $\mathbf{H_1}$ or "discard $H_0$"

Despite the recommendation of avoiding terminology like "accept/reject $H_0$" it is often used just for symmetry of treatment - remember though that symmetry isn't there!

There are 4 events:

1. Correctly reject $H_1$ / accept $H_0$
2. Wrongly reject $H_1$ / accept $H_0$ - this is sometimes called a type-II error or a type-B error - we denote the probability of such error as $\epsilon_b$
3. Correctly accept $H_1$ / reject $H_0$
4. Wrongly accept $H_1$ / reject $H_0$ - this is sometimes called a type-I error or a type-A error - we denote the probability of such an error as $\epsilon_a$