Types of Errors

There are two types of errors one can make in their decision -  to reject or fail to reject the null hypothesis (Ho ).

If you reject the null hypothesis when it is true, you make a Type I error. 

If you fail to reject the null hypothesis when it is false, you make a Type II error.

Consider a researcher interested in comparing the effectiveness of two drugs. The null and alternative hypotheses are:

Null hypothesis  (Ho ): d1 = d2

Alternative hypothesis (H1 ): d1 is not = d2

If someone commits a Type I error, they reject the null hypothesis by concluding that the two drugs are different when they are not. 

If the drugs are the same in effectiveness, they may not consider this error as too serious because patients are receiving the same level of effectiveness.

If someone commits a Type II error, they fail to reject the null hypothesis when you should have rejected it. 

That is, when someone concludes that the drugs are the same when, in fact, they are different.  

The probability of making a Type I error is a, which is the level of significance you set for your hypothesis test. An a of 0.05 indicates that you are willing to accept a 5 percent chance that you are wrong when you reject the null hypothesis. 

The probability of making a Type II error is b, which is a value that you typically cannot know. However, you can lessen your risk of committing a Type II error by making sure your test has enough power. You can do this by making sure you sample size is large enough to detect a difference when one truly exists.