# Examples for Type I and Type II errors

I was checking on Type I (reject a true H$_{0}$) and Type II (fail to reject a false H$_{0}$) errors during hypothesis testing and got to to know the definitions. But I was looking for where and how do these errors occur in real time scenarios. It would be great if someone came up with an example and explained the process where these errors occur.

• See xkcd.com/882 for an illustrated example of Type I errors in a "real time scenario." Perhaps after reading that you could come up with an analogous example of Type II errors.
– whuber
Aug 3 '14 at 15:26
• It is not obvious to me what "real time scenarios" means. Do you mean "real world" perhaps? Aug 3 '14 at 19:36
• Yeah Thomas,I meant real world.I have been reading few examples as given below,but what I wanted to know is that the reason why that happens.Does it have to do something with the sample size or kind of sample we take? Aug 9 '14 at 15:22

A picture is worth a thousand words. Null hypothesis: patient is not pregnant.

Image via Paul Ellis.

• ...and a word generates a thousand images. For the benefit of all readers, of all levels of knowledge and understanding, perhaps it would be useful after the picture, to explain how and why it represents examples of type I and type II errors. Aug 3 '14 at 18:36
• @AlecosPapadopoulos And yet explaining humor carries its own problems. The OP has already indicated a familiarity with textbook explanation. Aug 3 '14 at 20:03
• So, I guess the null hypothesis in the left picture is "Pregnant" and the doctor falsely asserts it ("false positive"), while in the right picture the null hypothesis is also "Pregnant" and the doctor falsely negates it (false negative)? Aug 3 '14 at 20:43
• Not sure how you get that. The null hypothesis on the left is "not pregnant", and the error is Type I. Har har. The null hypothesis on the right is also "not pregnant" and the error is Type II. Har har. Aug 3 '14 at 21:44
• You seem to have mistakenly edited your post to mention that the null hypothesis is "pregnant", whereas it is of course "not pregnant". Aug 3 '14 at 21:55

Let's say you are testing a new drug for some disease. In a test of its effectiveness, a type I error would be to say it has an effect when it does not; a type II error would be to say it has no effect when it does.

Type I error /false positive: is same as rejecting the null when it is true.

Few Examples:

• (With the null hypothesis that the person is innocent), convicting an innocent person
• (With the null hypothesis that e-mail is non-spam), non-spam mail is sent to spam box
• (With the null hypothesis that there is no metal present in passenger's bag), metal detector beeps (detects metal) for a bag with no metal

Type II error /false negative: is similar to accepting the null when it is false.

Few Examples:

• (With the null hypothesis that the person is innocent), letting a guilty person go free.

• (With the null hypothesis that e-mail is non-spam), Spam mail is sent to Inbox

• (With the null hypothesis that there is no metal present in passenger's bag), metal detector fails to beep (does not detect metal) for a bag with metal in it

Other beautiful examples in layman's terms are give here:

Is there a way to remember the definitions of Type I and Type II Errors?

• In Type II (false negative), shouldn't it be "spam email is sent to inbox"? Dec 18 '17 at 13:01

Null hypothesis is: "Today is not my friends birthday."

1. Type I error: My friend does not have birthday today but I will wish her happy birthday.
2. Type II error: My friend has birthday today but I don't wish her happy birthday.
• These are not serious answers. Feb 14 '18 at 17:35

The boy who cried wolf.

I am not sure who is who in the fable but the basic idea is that the two types of errors (Type I and Type II) are timely ordered in the famous fable.

Type I: villagers (scientists) believe there is a wolf (effect in population), since the boy cried wolf, but in reality there is not any.

Type II: villagers (scientists) believe there is not any wolf (effect in population), although the boy cries wolf, and in reality there is a wolf.

Never been a fan of a examples that taught which one is "worse" as (in my opinion) it is dependent on a problem at hand.