# Type - I Error & Type - II Error: Pregnancy test analogy - is it legit? I found this picture in my stats book but I'm now confused to what 'positive' and 'negative' is referring to.

As seen in the table below, Type 1 error is the error that its H0 is actually true but FALSEly claims that it's false. Type 2 error, on the other hand, is the error that its H0 is actually false but FALSEly claims that it's true.

So my question is, how do the pregnancy analogy and whole 'false positive' & 'false negative' thing make sense?

For the first picture to be a type 1 error, H0 (null hypothesis) should be "The person is NOT pregnant" so that "You're pregnant" statement becomes false.

However, the second picture has the complete opposite H0, where H0 should be "The person is pregnant" so that "You're not pregnant" statement becomes false.

I thought it was really confusing because I thought false POSITIVE and false NEGATIVE corresponded to "You're pregnant"(positive) / "You're NOT pregnant"(negative)

But based on the Chart given below, that doesn't seem to make any sense.

So the question is, is there anything that I'm missing here or is it just that textbook's analogy sucks? Presumably here

• the null hypothesis is $$H_0:$$ You are not pregnant
• the alternative hypothesis is $$H_1:$$ You are pregnant

so being pregnant would be the positive result.

You take a pregnancy test

• if the pregnancy test gives a positive result when you are not pregnant then this is a false positive, a Type I error when the null hypothesis $$H_0$$ is in fact true but has been rejected by the test

• if the pregnancy test gives a negative result when you are pregnant then this is a false negative, a Type II error when the null hypothesis $$H_0$$ is in fact untrue but has not been rejected by the test

So in a statement of being a true/false positive/negative test, the true/false part is about the accuracy of the test while the positive/negative part is about the result of the test rather than being the real situation

• This is very clear. Thank you, Henry. I must have been confused at some point. One more question if it's okay though: is it normal to set H0 as ~ is NOT true rather than ~ is true? Say, if I wanna know whether an economic theory is right, is it normal to set H0 as "Theory A is NOT true" rather than "~ is true"? – user8491363 Apr 8 '19 at 0:39
• @user8491363 The null hypothesis is often formed as a no-change statement, such as "using this experimental drug does not affect survival rates" or "knowing variable X does not change the ability to predict variable Y" or in this example "the patient continues not to be pregnant". The alternative hypothesis then points towards what sort of evidence might be deemed significant enough to reject the null hypothesis. – Henry Apr 8 '19 at 7:20
• Thank you again. It is much clear noe. – user8491363 Apr 8 '19 at 7:24

I'm sorry, this is probably better a comment than an answer, but I don't have sufficient points:

In the diagram you've included, Type I and Type II errors are more properly conditional probabilities.

$$\alpha$$ = Prob( Reject $$H_0$$ | $$H_0$$ ) (= probability of saying not not-pregnant, conditional on actually not-pregnant))

$$\beta$$ = Prob( Fail to reject $$H_0$$ | $$H_1$$ ) (= probability of not saying not not-pregnant, conditional on actually not not-pregnant)

If H0 is considered as H0: PATIENT IS NOT PERGANENT AGAINST Ha:PATIENT IS PERGANENT,then all information in the pictures and table are logic. But normally ,when patient refers to check its pregnancy ,the patient is woman and her expectancy for H0 is :Patient is Perganent,,,,and this cause missunderstanding of above pictures