Type I and Type II Errors Simplified


Notice that a black doctor and a woman doctor are the ones making the errors.

Equality has arrived to MR.

He could be an Indian doctor. Or a Middle Eastern doctor

Tiresome comments, on the other hand, have been here for awhile. Thanks a lot for insisting on pooping on even the most light-hearted post.

What are you talking about. What is the probability of black doctor and a woman doctor in the same post, and the probability of both being the ones who make the error.

So, this is not a false positive?

Damn, I wouldn't have thought Bill was a black female.

Stock photos usually try to display diversity. It's not atypical for a large amount of stock photos of doctors to be of visible minorities or females. Notice how both the patients in either photo are also of visible minority or women? The idea is that a looott of stock photography deviates from the white male stereotype because of people like you who claim outrage by reading subtext into photos that don't have any.

Chances are OP just googled "doctor male patient" and "doctor pregnant patient".
In fact here's some evidence: http://is.gd/VTPkW1

Enjoyed it, but it actually proves my point.

Of the 18 pictures, two are black doctors, so 1/9 probability of selection. I couldn't find the way to find "female patient pregnant" but if you do, please post.

Now, a 1/9 probability times whatever you find for the "doctor pregnant patient" number and report back.

Same with white males. It's all in your head, Bill.

TMC, what do you mean?

Congratulations! You derailed the comment thread right from the start!

It was there for all to see and wasn't hard.

Except as Joseph said above, stock photos are disproportionately minority and female. That doesn't fit the oppression studies worldview, however.

Sorry, Thomas, but if you look at his selection, and my response, you will see there is a 1/9 chance of a black doctor in the picture files. Now, look for a female doctor with a pregnant patient and report back as to that percentage and multiply by 1/9 for the probability of a black doc and a white female doc with a pregnant patient.

good luck.

Report your finding below.

Jesus Christ your type are tiresome, you know that ?

I feel the same way about the portrayal of black and women doctors.

Shorter Bill: Blacks and women aren't qualified as doctors.

Way to be a bigot, Billy Boy!

Vernuft, The photo message is: only blacks and women doctors make obvious mistakes.

Bill - get your head out of your ass and stop obsessing over trivial bullshit.

If it is trivial you wouldn't notice it or care, would you?

Bill, the message of this particular thread of comments is:

Only Bill thinks that Professor Tabarrok trying to give a simple, easily remembered, and light-hearted mnemonic for Type 1 and Type 2 errors is fraught with socio-political undertones.

Ken, The persons who comment on this site aren't necessarily the persons who would see it as it would probably conform to their beliefs as witnessed by some of the comments.

And, if you look at some of the comments on black doctors making more errors, that the black doctor should have Obamas face, and comments about a woman doctor you can see for yourself.

I've taught graduate marketing, and still teach exec ed. There is no way...none whatsoever, that you would ever get a pictorial message like this in any advertisement with any persons brand name in it. If you think a black doctor and a woman doctor being selected as being stupid, along with their patient in the case of the black patient, is random, think again. It was probably some person who selected these images who thought it was cute to play stereotypes.

Whoever did the original post--it wasn't Alex because it was a link--made an error that they would not make in the advertising world if they wanted to keep their job.

Finally, I could care less what the number of people think. Its that YOU should think for yourself, and that others should think before they post making fun of others in minority categories.

Oh, and Ken, I DARE you to take these pictures to a newspaper of general circulation, a magazine of general circulation, or an advertiser of any scale, and without mentioning my comments, ask them "Would you see any problem with these pictures" and type 1 and 2 errors appearing in their magazine, newspaper, or advertisement. You can even go to a journalism prof or marketing prof if you want.

I doubt they would be clueless.

Although I was being polemical for effect, my apologees Bill I misread your point.

List of people who made errors:
A Black person
A White person
A Man
A Woman

How the hell did you find prejudice in that?!

Bill, you do realize some on just took someone else's PC tripe and added their qouyes?

To paraphrase Chris Rock, we have arrived when they are allowed to be bad doctors.

Bill's comment gets the spell check it deserves. New service by android.

Andrew': What is the probability that two groups...blacks and women, jointly--are pictured to make obvious mistakes. When you say that they have arrived when they can be depicted as being incompetent is really saying they haven't left the discriminated against category if they are jointly portrayed...not randomly,...as incompetent.

Someone made a choice.

Notice that the black male doctor is with a black male; the white female doctor is with a white female.

Segregation has arrived to MR.

So, this isn't a false negative?

What I don't understand is the "type I" and "type II" terminology. "False positive" and "false negative" at least can be worked out. (I guess they sometimes confuse people, but if you stop to think about them, you can figure out what they are.) There's no logic at all in calling them "type I" or "type II", and you just then have to learn what "false positive" and "false negative" is anyway. So, people should drop the Type I and Type II terminology.

That is a brilliant insight.

@Matt, the Type N nomenclature subtly suggests "the types of error is not bounded." See http://en.wikipedia.org/wiki/Type_I_and_type_II_errors#Various_proposals_for_further_extension

Claims that someone has committed Marasculio and Levin Type IV error appears frequently in this blog.

In 1970, L. A. Marascuilo and J. R. Levin proposed a "fourth kind of error" – a "type IV error" – which they defined in a Mosteller-like manner as being the mistake of "the incorrect interpretation of a correctly rejected hypothesis"; which, they suggested, was the equivalent of "a physician's correct diagnosis of an ailment followed by the prescription of a wrong medicine" (1970, p. 398).

The Type N nomenclature also subtly suggests that there is some underlying objective taxonomy of all types of human errors, which is not really true. So I'm with Matt. "False positive" and "false negative" make a lot more sense, in my view.

I'm not familiar with the types of errors, but the first is a category on it's own. A man cannot become pregnant, so any discussion of whether he is pregnant or not is ridiculous. Someone who even starts going down that path becomes the pathology in the situation.

I'm training a couple of people in my trade, which includes troubleshooting problems and coming up with solutions. One fellow would phone and ask questions that betrayed a complete lack of understanding of what he was even looking at. His diagnoses were mistaken not due to a misinterpretation of the data inputs, but a fundamental misunderstanding of the systems. That is far different from someone with more experience running into a confusing set of data that could point either way, and needs more investigation.

If your crew is making lots of the first type of error, you have a serious problem. The second type may be as nasty if misdiagnosed, but more investigation can clear it up. The first you bring them home and set them cleaning the stables.

derek -- I agree with yoru 3rd paragraph. Your first paragraph nicely illustrates both the problem of the "Type N" nomenclature for errors as well as the limits of the simplified example of the OP. If a doctor misdiagnosed a young, fertile, married woman as pregnant, even when she wasn't, it would still be a false positive.

Yeah, I'm gonna call that a "not good enough" reason.

Yup. I've often wondered what sort of dunderhead would ascribe names of no mnemonic value whatsoever. Can anyone name the culprit?

We totally agree that the "type I" and "type II' labels are lame and should be discarded … even the labels "false positive" and "false negative" are a bit cumbersome … why not use "False Alarms" and "Misses" instead, like these guys do: http://library.mpib-berlin.mpg.de/ft/dg/DG_Beauty_2011.pdf

For another example of the use of the "false alarms" and "misses" terminology, check this out too: http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1978017

"Miss" is very vague and has colloquial meanings that aren't necessarily related to the meaning of Type II error. "False alarm" is equivalent to "false positive", and if you're not replacing "false negative", you lose the dichotomy by saying "false alarm".

How about "false alarm" and "false complacency"?

from the link given above (Flowing Data), those dunderheads are

"Type I" and "Type II" errors, names first given by Jerzy Neyman and Egon Pearson to describe rejecting a null hypothesis when it's true and accepting one when it's not,"

Hardly dunderheads, despite this failure to mnemonicize.

As someone who's had to teach this stuff and still gets confused (and is also named Matt), I wholeheartedly agree.

There is a joke:

Type I error: false positive

Type II error: false negative

Type III error: not knowing the difference between a Type I and Type II error.

Actual answer given last semester:

Me: "What's a type II error?"

Good student: "That's when you make two type I errors."

It's my own fault: that was a joke choice on the multiple choice quiz for that week.

I immediately thought the same, but upon reflection it is correct. The implication here is that there is some sort of test that the doctor conducted, e.g. a urine test.

A Type I error is rejecting the null hypothesis when it is true. The null hypothesis would be "not pregnant." You reject this when the calculated value of the test statistic is extreme compared to the expected result if Ho is true. The level of significance is the probability that the test would render a false positive result of pregnancy.

A Type II error is failing to reject the null hypothesis when it is false. You can achieve this result by not testing at all.

The reason for your confusion is that we observe a second set of data - the gender of the patient on the left and the bulbous belly of the patient on the right. This data is collected independently of the pregnancy test. But in this picture, that "data" represents the unobservable parameter of pregnancy. In the trivial case, we could edit out the patients and put in some label that says, "Actually not pregnant" and "Actually pregnant."

We could, of course, send a man's urine to a lab for pregnancy testing, and they might indicate he is pregnant without knowing his gender. The woman could have a very large abdominal tumor.

I'm afraid that this "simplification" only makes the concept of Type I and Type II errors more difficult to understand. The crux of statistics is that you have UNOBSERVED reality, and this example muddies that important point.

Right for the wrong reason.
Wrong for the wrong reason.

This was a reply to A Wiseguy comment

Also note that the black doctor is so stupid he thinks a) a man can become pregnant and b) to check pregnancy you have to use a stethoscope

This is pre-Obamacare

The only thing missing is to put Obama's face on the black doctor and Palin's face on the female doctor. Might I also suggest the black patient gets Tim Scott's face and the female patient gets Nancy Pelosi's face!

Very sad in the case of the male doctor that the implication is left-handed, vision-impaired people make errors.

Let me explain the iconography to the slow of understanding. First, someone thought it would be witty to have a man being diagnosed as pregnant, and a pregnant woman as not. Then he thought that he'd better have the woman's doctor as female too, so that there's no suggestion of privileging the male as always being in the wrong, and for the same reason he'd better make both of the same race. Then he thought that if one pair of models was white the other had better be black. See? Easy-peasy!

N.B. I've used "he" throughout because the joke, being essentially unfunny, was probably devised by a woman.

Statistics is an integral part of my work and I have taught statistics in the past. I never use the terminology "type I" and "type II" and always have to look it up when I see it. It is incredibly bad terminology.

David, it's silly terminology. "Incredibly bad" is an "incredible exaggeration."

But if you have to look it up when you see it, you ought to have studied harder when you were in school.

If you don't use the terminology Type I and Type II errors and the analogous alpha (level of significance) and beta (1 minus the power), then you aren't doing statistics. It isn't merely necessary, it is crucial terminology because hypothesis tests are meaningless without them.

My biggest peeve about statistics is that people routinely choose a level of significance arbitrarily without understanding that alpha and beta are negatively correlated. The correct choice of alpha should be based on an a priori cost-benefit analysis of Type I and Type II errors. If a Type II error is extremely costly, a level of significance of 20% or more is reasonable.

Someone needs to cite Andrew Gelman, on why he's never made a type 1 or type 2 error.

Plus a more relevant classification: type S and type M errors.


Experts agree, if we can just get more poor and disadvantaged people to eat mozzarella cheese, we can drive more people out of poverty and improve american infrastructure!

Black doctors actually do make more errors on average. Due to Affirmative Action, the average black doctor will be less competent than the average non-black doctor.

The male patient peed on a home pregnancy test kit and his doctor is telling him, in a light-hearted manner, that, despite the positive, he does not have testicular cancer but (Ha! Ha! Ha!) he's pregnant.

The woman has an extreme case of pseudocyesis with an abdominal tumor.

Best and easiest teaching tool I've seen on type "I" and "II" errors.

Why can't we just call them false negatives and false positives?

'you're not pregnant you just have a basketball under your shirt'. Wrong - it's a soccer ball. False negative.

I agree with the comments above re disregarding the type 1 and type 2 error jargon. False positive/negative is a much better form of language. Using this form also means teachers don't have to write unnecessary quiz questions for students to see if they understand a definitiion, rather than a concept. The concept surely being the important part.

I think this way of explaining Type I / Type II errors is problematic, A woman could potentially be pregnant, but a man can *inherently* not be pregnant. The left picture might suggest that Type-I errors are about treating something *inherently* impossible as actually happening. But the definition of Type I error does not have this limitation in its meaning.

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