> For the complete documentation index, see [llms.txt](https://gautamnaik1994.gitbook.io/snippets/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://gautamnaik1994.gitbook.io/snippets/data-science/statistics/hypothesis-testing.md). # 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 {% embed url="" %} ### Precision vs Recall Mindset A system with high precision might leave some good items out, but what it returns is of high quality A system with high recall might give you a lot of duds, but it also returns most of the good items Precision: Book recommended out of all good books will be best book Recall: Burgular robing a house will take everything including useless things