Type I and Type II Errors

Type I and Type II Errors

Type I Error

Type I error, also known as a “false positive”: the error of rejecting a null hypothesis when it is actually true. In other words, we can say that it is the error of accepting an alternative hypothesis. So the probability of making a type I error in a test with rejection region R is P(R|H_o is true) .

• A type I error occurs if you reject the null hypothesis when it is true.

Examples:

A person is arrested by the police in a stealing case, but he has not stolen anything. In this situation type I error is made.

H_o = He is innocent

H_a = He is not innocent 

In this situation the person has not stolen. But he is arrested by the police so H_o is reject although it (H_o) is correct so therefore Type-I Error is made.

Type II Error

Type II error, also known as a "false negative": the error of not rejecting a null hypothesis when the null hypothesis is false (alternative hypothesis is the true). In other words, this is the error of failing to accept an alternative hypothesis when you don't have adequate power. So the probability of making a type II error in a test with rejection region R is P(R|H_o is false).

• A type II error occurs if you do not reject the null hypothesis when it is false.

Examples:

A person has stolen anything but he is not arrested by the police. In this situation Type-II Error is made.

H_o = He is thief

H_a = He is not thief 

In this situation the person has stolen anything, but he is not arrested  by the police so H_o is not reject (H_a is accepted) although it is not correct so therefore Type-II Error is made.

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Hypothesis Testing (Null & Alternative)