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Type 1 Error & Type 2 Error's pregnancy test analogy: is it legit?

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2

$begingroup$

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 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 table 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?

statistics

share|improve this question

asked 11 hours ago

user8491363user8491363

132

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2

$begingroup$

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 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 table 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?

statistics

share|improve this question

asked 11 hours ago

user8491363user8491363

132

New contributor

user8491363 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

$endgroup$

add a comment | 

$begingroup$

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 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 table 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?

statistics

share|improve this question

asked 11 hours ago

user8491363user8491363

132

New contributor

user8491363 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

$endgroup$

share|improve this question

asked 11 hours ago

user8491363user8491363

132

New contributor

user8491363 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

share|improve this question

asked 11 hours ago

user8491363user8491363

132

New contributor

user8491363 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

asked 11 hours ago

user8491363user8491363

132

New contributor

user8491363 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

asked 11 hours ago

user8491363user8491363

132

1 Answer
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votes

3

$begingroup$

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

share|improve this answer

answered 10 hours ago

HenryHenry

3,826316

$endgroup$

add a comment | 

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3

$begingroup$

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

share|improve this answer

answered 10 hours ago

HenryHenry

3,826316

$endgroup$

add a comment | 

3

$begingroup$

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

share|improve this answer

answered 10 hours ago

HenryHenry

3,826316

$endgroup$

add a comment | 

$begingroup$

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

share|improve this answer

answered 10 hours ago

HenryHenry

3,826316

$endgroup$

share|improve this answer

answered 10 hours ago

HenryHenry

3,826316

answered 10 hours ago

HenryHenry

3,826316

answered 10 hours ago

HenryHenry

3,826316