# Type 2 Error

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## Definition: Type 2 Error

The error which occurs by failing to reject a null hypothesis when the alternative hypothesis is true is a Type II error. Type II error is also called false negative because it establishes a false negative evidence for the alternative hypothesis. The probability of occurrence of a Type II error is denoted by beta.

For example,

Suppose the null hypothesis is that: Person is not guilty; Type II error indicates that null hypothesis is accepted despite being false i.e a guilty person is set free.

A Type II error may or may not be dangerous when compared to a Type I error- it is dependent on the situation being considered. For example: suppose the null hypothesis is that: person is not healthy; a Type II error would mean that the person is decided as unhealthy – which can be subsequently proved otherwise by carrying out more tests. However, as seen in the earlier example if because of a Type II error, a guilty person is set free it could have dangerous consequences.

 Decision Null hypothesis= true Null hypothesis= false Reject null hypothesis Type 1 error Correct decision Fail to reject Correct decision Type II error

The power of a hypothesis test is given by the probability with which a Type II error will not occur and is given by:

Power = 1-β

Hence, this concludes the definition of Type 2 Error along with its overview.

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