# type I error

## Type I and Type II errors in Statistics

#### Type I and Type II Errors

In hypothesis testing, there are two possible errors we can make: Type I and Type II errors.

• A Type I error occurs when you reject a true null hypothesis (remember that when the null hypothesis is true you hope to retain it).
α=P(type I error)=P(Rejecting the null hypothesis when it is true)
Type I error is more serious than type II error and therefore more important to avoid than a type II error.
• A Type II error occurs when you fail to reject a false null hypothesis (remember that when the null hypothesis is false you hope to reject it).
β=P(type II error) = P(accepting null hypothesis when alternative hypothesis is true)
• The best way to allow yourself to set a low alpha level (i.e., to have a small chance of making a Type I error) and to have a good chance of rejecting the null when it is false (i.e., to have a small chance of making a Type II error) is to increase the sample size.
• The key to hypothesis testing is to use a large sample in your research study rather than a small sample!

If you do reject your null hypothesis, then it is also essential that you determine whether the size of the relationship is practically significant.
The hypothesis test procedure is therefore adjusted so that there is a guaranteed “low” probability of rejecting the null hypothesis wrongly; this probability is never zero.

Therefore, for type I and Type II errors remember that falsely rejecting the null hypothesis results in an error called Type-I error and falsely accepting the null hypothesis results in Type-II Error.

## Significance level: why do researchers use a 0.05?

### Significance Level

The significance level is the level of probability at which it is agreed that the null hypothesis will be rejected. In academic research, usually, a 0.05 level of significance is used. The level of significance is also called a level of risk.

The level of significance of an event (such as a statistical test) is the probability that the event will occur by chance. If the level is quite low then the probability of occurring that event by chance will be quite small. One can say that the event is significant as its occurrence is very small.

#### Type I Error

It has become part of the statistical hypothesis-testing culture.

• It is a longstanding convention.
• It reflects a concern over making type I errors (i.e., wanting to avoid the situation where you reject the null when it is true, that is, wanting to avoid “false positive” errors).
• If you set the level of significance at 0.05, then you will only reject a true null hypothesis 5% of the time (i.e., you will only make a type-I error 5% of the time) in the long run.
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