Hypothesis Testing

Type 1 Error (False Positive):

This occurs when the model incorrectly rejects a true null hypothesis (H0 is true, but the model predicts H1).

Type 2 Error (False Negative):

This happens when the model fails to reject a false null hypothesis (H0 is false, but the model predicts H0).

Smoke Alarm Example

Ho : There is no fire Ha : There is fire

Type 1 Error (False Positive):

Think of it as a "False Alarm." Imagine a smoke detector in your house. A Type 1 error would be when the smoke detector goes off (alarm sounds) even though there is no actual fire. In this case, you falsely believe there is a problem when there isn't. Type 2 Error (False Negative):

Think of it as a "Missed Opportunity." Continuing with the smoke detector example, a Type 2 error would be when the smoke detector fails to sound the alarm even though there is a real fire. In this case, you miss detecting the actual problem.

These real-world scenarios can help you associate Type 1 errors with false alarms and Type 2 errors with missed opportunities. Remembering them in this context might make it easier to recall which is which.

Judge and Defendant Example

Ho: Defendant is Innocent Ha: Defendant is Guilty

Type 1 Error : Defendant is pronounced guilty, when in reality he is not guilty. In this case Ho was actually true but Judge said Ho is false.

Type 2 Error :Defendant is pronounced innocent, when in reality he was guilty. In this case Ho was actually false but Judge said Ho is true.

Pregnancy Example

Ho: Patient not pregnant Ha: Patient pregnant

Type 1 Error : Telling a man that he is pregnant Type 2 Error : Telling a pregnant woman that she is not pregnant

Simple Explanation

Type 1 error occurs when model says that Ho is false and Ha is true when in reality Ho is true and Ha is false.

Type 2 error occurs when model says that Ho is true and Ha is false when in reality Ho is false and Ha is true.

Images to understand