Alpha levels are used in hypothesis tests. The significance level α is the probability of making the wrong decision when the null hypothesis is true.

**Contents**:

- Type I and II errors
- How do I Calculate an Alpha Level for one- and two-tailed tests?
- Why is an Alpha Level of .05 commonly used?

## 1. Alpha Levels: Type I and Type II errors

In hypothesis tests, two errors are possible, Type I errors and Type II errors.

**Type I error**: Supporting the alternate hypothesis when the null hypothesis is true.

**Type II error**: Not supporting the alternate hypothesis when the alternate hypothesis is true.

In an example of a courtroom, let’s say that the null hypothesis is that a man is innocent and the alternate hypothesis is that he is guilty. if you convict an innocent man (Type I error), you support the alternate hypothesis (that he is guilty). A type II error would be letting a guilty man go free.

An **alpha level** is the probability of a type I error, or you reject the null hypothesis when it is true. A related term, beta, is the opposite; the probability of rejecting the alternate hypothesis when it is true.

This graph shows the rejection region to the far right.

## 2. How do I Calculate an Alpha Level for one- and two-tailed tests?

Alpha levels can be controlled by you and are related to **confidence intervals**. To get the alpha level, subtract your confidence interval from 1. For example, if you want to be 95 percent confident that your analysis is correct, the alpha level would be 1 – .95 = 5 percent, assuming you had a one tailed test. For two-tailed tests, divide the alpha level by 2. In this example, the two tailed alpha would be .50/2 = 2.5 percent. See: One-tailed test or two? for the difference between a one-tailed test and a two-tailed test.

## 3. Why is an alpha level of .05 commonly used?

Seeing as the alpha level is the probability of making a Type I error, it seems to make sense that we make this area as tiny as possible. For example, if we set the alpha level at 10% then there is large chance that we might incorrectly reject the null hypothesis, while an alpha level of 1% would make the area tiny. So why not use a tiny area instead of the standard 5%?

The smaller the alpha level, the smaller the area where you would reject the null hypothesis. So if you have a tiny area, there’s more of a chance that you will NOT reject the null, when in fact you should. This is a Type II error.

In other words, the more you try and avoid a Type I error, the more likely a Type II error could creep in. Scientists have found that an alpha level of 5% is a good balance between these two issues.

Picture courtesy of the University of Texas.

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