1347: "t Distribution"

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CorruptUser
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1347: "t Distribution"

Postby CorruptUser » Wed Mar 26, 2014 4:04 am UTC

Image

Title text: If data fail's the Teacher's t test you can just force it to take the test again until it passes.



Also, BRILLIANT!
Ok, that joke might be too obscure.
Spoiler:
The reason it's called "Student's t" and not "Gosset's t" is because William Gosset was working for Guinness Brewers, and they had a policy of no publications. Trade secrets and all. So he published under the pseudonym "Student".

Also Gosset was in contact with Fisher, basically helping create modern Statistics. Yes, the Fisher who was friends with John Maynard Keynes and the Darwin family.

"BRILLIANT" was a series of ads for Guinness a few years back.
Last edited by CorruptUser on Wed Mar 26, 2014 4:12 am UTC, edited 1 time in total.

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Re: 1347: "Student's t"

Postby krickit » Wed Mar 26, 2014 4:12 am UTC

God dammit xkcd, stop bringing up concepts the day after I learn them.

The comic has gotten slowly funnier since middle school.

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Re: 1347: "t Distribution"

Postby cyanyoshi » Wed Mar 26, 2014 5:17 am UTC

I wonder if its inverse Fourier transform looks like a cat.

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Re: 1347: "t Distribution"

Postby magemax » Wed Mar 26, 2014 8:18 am UTC

"Yes, a xkcd comic about probabilities, my field of practice"

10 seconds later

"Why didn't I get this joke ?"

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Re: 1347: "t Distribution"

Postby Envelope Generator » Wed Mar 26, 2014 8:29 am UTC

Oh yeah, I need to check the poisson distribution in my aquarium.
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Re: 1347: "t Distribution"

Postby Pfhorrest » Wed Mar 26, 2014 8:47 am UTC

Ok I think I need a bit more explanation. I get that "Student's t Distribution" is a kind of statistical distribution, and the joke involves punning on the pseudonym "Student" by taking it to mean the t distribution of schoolkids, and that their t distribution is being replaced by the teacher's instead. But, visually, what the heck are the things being moved around? I get that they are shaped like distribution curves but... are they displays in a science fair or something? Is that a piece of paper on the desk next to them? Is that of some significance? I'm lost, visually.
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Re: 1347: "t Distribution"

Postby PsiSquared » Wed Mar 26, 2014 9:11 am UTC

I didn't get it either.

I mean, I know what a t-distribution is, but I still don't understand the joke.

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Re: 1347: "t Distribution"

Postby lebigz » Wed Mar 26, 2014 9:25 am UTC

Doesn't that joke imply a wrong idea about the application of distribution curves in testing? The "new" distribution has multiple maximas, and the hovertext implies that this would lead to a test where you could just retake it and get a positive result. But testing relies in most cases not on the number of maxima but on the integral below the distribution curve, better: a certain percentile, the percentage of a distribution on one side of a certain "critical value". One often tests for a distribution parameter like mean, variance or sometimes percentiles like the median, but almost never on the amplitude of a distribution, at least not in the distribution of the test parameter. Also, if i interpret the moving of the curve in panel 1 as "adjusting for effect size", it implies that he is using the central student's t for the alternative hypothesis distribution, but here the non-central -t which looks a little more skewd would be the one to use, since this distribution also accounts for unknown distance to it's base distribution (the null hypothesis distribution in a testing scenario).

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Re: 1347: "t Distribution"

Postby orthogon » Wed Mar 26, 2014 9:25 am UTC

magemax wrote:"Yes, a xkcd comic about probabilities, my field of practice"

10 seconds later

"Why didn't I get this joke ?"

Yeah, for me there was an extra step in which I realised that once again my phone wasn't showing me the fourth panel. "Ah, ok when I see the whole thing I'll probably get it ... hmm maybe not".
The Teacher's distribution has something of Batman about it. The Fourier transform of the cat didn't have that type of symmetry (which come to think of it suggests the cat was complex...)

Edit: Is the paper a test that the student has done? The good people at explainxkcd.com seem to be unsure too.
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Re: 1347: "t Distribution"

Postby eidako » Wed Mar 26, 2014 10:04 am UTC

Image

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Re: 1347: "t Distribution"

Postby jadrevenge » Wed Mar 26, 2014 11:09 am UTC

Is it just me, or do others get the urge to shout "Because I'm Batman!" ? ;-P

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Re: 1347: "t Distribution"

Postby Klear » Wed Mar 26, 2014 11:27 am UTC

explainxkcd wrote:The comic is a play on the name "Student" (the pseudonym of the creator) vs. "Teacher". The idea is that a "teacher's" distribution would be more complex, and that it would be used for fitting data when the student's distribution wasn't sophisticated enough. Of course, in actuality, such a complex distribution as the one shown in the comic would have many parameters, and in practice would probably lead to overfitting and/or bias. Thus, the comic (and the title text) can be seen as making fun of the conflation of complexity and sophistication, or perhaps of the idea that a statistician's job is to use more and more sophisticated tools to force the data to yield a "publishable" result, rather than to use the simplest appropriate tool and let the chips fall where they may.


That's a bit of a letdown. I was hoping there's more to it.

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Re: 1347: "t Distribution"

Postby cellocgw » Wed Mar 26, 2014 11:45 am UTC

CorruptUser wrote:
Also, BRILLIANT!
Ok, that joke might be too obscure.
Spoiler:
The reason it's called "Student's t" and not "Gosset's t" is because William Gosset was working for Guinness Brewers, and they had a policy of no publications. Trade secrets and all. So he published under the pseudonym "Student".

Also Gosset was in contact with Fisher, basically helping create modern Statistics. Yes, the Fisher who was friends with John Maynard Keynes and the Darwin family.

"BRILLIANT" was a series of ads for Guinness a few years back.


Well, to be even more obscure, FTFY: "Brillant" :mrgreen:
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Re: 1347: "t Distribution"

Postby RFife » Wed Mar 26, 2014 12:06 pm UTC

While I have a feeling it isn't, my first thought was there was a level of commentary on the Common Core debate in education right now, and how it is expecting teachers in all situations to be able to use the same education plan to meet high standardized expectations. Teachers are now getting "scores" that they have to measure up to based on student performance, and so retesting and teaching to tests is what they are all worrying about so they don't get canned.

Again, don't think that was what Randall was actually going for, but it is what I took from it.

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Re: 1347: "t Distribution"

Postby geologami » Wed Mar 26, 2014 12:20 pm UTC

For shame...! "Data" are not an "it"!

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Re: 1347: "t Distribution"

Postby ChrisJohns » Wed Mar 26, 2014 12:55 pm UTC

Is this commentary on how teachers aren't subject to the standards they place on students? Like, for continuing education for teachers, they are able to retake tests until they pass and aren't graded the same way they grade their students?

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Re: 1347: "t Distribution"

Postby thevicente » Wed Mar 26, 2014 1:28 pm UTC

I don't get even what the stick figure is doing and what is that with that piece of paper.

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Re: 1347: "t Distribution"

Postby rmsgrey » Wed Mar 26, 2014 1:41 pm UTC

I find more amusement in the title text than the main comic, though here in the UK, things are finally moving away from the "resit until you get a pass" that's been increasingly popular over the last couple of decades...

Still, on the one hand you have the common-practice-with-dubious-validity of resitting exams until you get an acceptable grade; on the other, you have the common-practice-with-dubious-validity of re-examining data until you get the "right" result (Simpson's Paradox may be of use here), making for an apt comparison.

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Re: 1347: "t Distribution"

Postby forward4 » Wed Mar 26, 2014 1:49 pm UTC

I'm gonna be honest and say I don't get this comic. But I've never liked T-tests. I'll do some research and come back, see if I get it. It seems like the alt-text and comic are two different jokes, really.
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Re: 1347: "t Distribution"

Postby CorruptUser » Wed Mar 26, 2014 1:52 pm UTC

Part of the joke is that in statistics, your distributions will never match a normal or a t distribution perfectly. Especially when the distributions are drawn as continuous while your measurements are discrete. So you will end up with 3 readings at 26 when you only expected .7 readings, etc. This is to be expected, as the measure of the events only becomes a normal distribution as it approaches infinity, though after 30 you do get enough to make reasonable conclusions.

Of course, this relies on every event to have the same underlying distribution, and that the second moment is finite. This may not be the case with stocks, and while stocks are easily predicted in the bulk of the events, when all your risk is in the very tip of the tails...


Oh and Simpson's paradox is simply that the sign of the betas in regression analysis can flip if additional variables are added. Don't think that applies. For example, having a low birth weight increases the risk of infant mortality. But low birth weight and a mother that smokes reduces infant mortality. This is because smoking causes low birth weights, and is less deadly than other causes of low birth weight.

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Re: 1347: "t Distribution"

Postby rmsgrey » Wed Mar 26, 2014 2:10 pm UTC

CorruptUser wrote:Oh and Simpson's paradox is simply that the sign of the betas in regression analysis can flip if additional variables are added. Don't think that applies. For example, having a low birth weight increases the risk of infant mortality. But low birth weight and a mother that smokes reduces infant mortality. This is because smoking causes low birth weights, and is fewer deadly than other causes of low birth weight.


Depending on which side you're on, you can argue that the statistics show that smoking mothers increase infant mortality (more children of smokers die than non-smokers'), or that the statistics show that smoking mothers reduce infant mortality (both low weight infants and normal weight infants have a higher survival rate when their mother smokes).

When it comes to interpreting statistics to support a particular conclusion, finding data which illustrates Simpson's paradox is like Christmas...

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Re: 1347: "t Distribution"

Postby orthogon » Wed Mar 26, 2014 2:17 pm UTC

rmsgrey wrote:(... normal weight infants have a higher survival rate when their mother smokes).

I was following the rest of it (and thanks for introducing me to another interesting quirk of statistics), but can you explain this part? Are you saying that normal weight infants whose mothers spoke have a higher survival rate than normal weight infants whose mothers don't smoke?
xtifr wrote:... and orthogon merely sounds undecided.

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Re: 1347: "t Distribution"

Postby ctdonath » Wed Mar 26, 2014 2:18 pm UTC

Insofar as the teacher can grade the test subjectively to some degree, he will be biased toward (or away from) grade boundaries. A score of 73 is kinda mushy; 70 or 75 is more emphatic (assuming either no letter grading or C is 70-79). Score is 68 but student really does work hard and "went beyond" with something not formally scored? oh look, there's a couple extra points so now he gets a 70. Student really hasn't learned anything, but obviously abuses "teamwork" to achieve a technically passing D-? oops, overlooked a mistake here and there...yup, F.

Aside from completely objective quantified grading, the score distributions are _not_ a smooth bell curve when graded by a human.

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Re: 1347: "t Distribution"

Postby mathmannix » Wed Mar 26, 2014 2:45 pm UTC

Pfhorrest wrote:Ok I think I need a bit more explanation. I get that "Student's t Distribution" is a kind of statistical distribution, and the joke involves punning on the pseudonym "Student" by taking it to mean the t distribution of schoolkids, and that their t distribution is being replaced by the teacher's instead. But, visually, what the heck are the things being moved around? I get that they are shaped like distribution curves but... are they displays in a science fair or something? Is that a piece of paper on the desk next to them? Is that of some significance? I'm lost, visually.


thevicente wrote:I don't get even what the stick figure is doing and what is that with that piece of paper.


The figure is testing to see if the Student's T-distribution fits his data. Except that, instead of using calculations to do so, this is presented as literally trying to fit a distribution (represented as a four-foot-wide cardboard cutout) to his data (represented by a sheet of paper.) The cardboard cutout is symbolic and not really part of the joke. The joke is that if there is a Student's T-distribution, then there must be an even better Teacher's T-distribution, by analogy to a teacher's edition of a math textbook which includes annotations and more complete solutions than the students' edition.
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Re: 1347: "t Distribution"

Postby brochastic » Wed Mar 26, 2014 2:54 pm UTC

While we're making statistics puns, I'm just about to go to the departmental tea & pastries. I intend to take pastries one at a time, with a probability based exponentially on the time since I last has one. It could be said that I'm sampling from a Croissant distribution.

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Re: 1347: "t Distribution"

Postby hercynium » Wed Mar 26, 2014 3:45 pm UTC

First thing that came to mind...

t_distribution.jpg
t_distribution.jpg (7.73 KiB) Viewed 14697 times

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Re: 1347: "t Distribution"

Postby Trickster » Wed Mar 26, 2014 4:06 pm UTC

OH FOR LUNA'S SAKE PEOPLE

The piece of paper is a TEST. The distribution is "taking a test". It gets the answers wrong so Cueball grabs another (albeit fictional) distribution to try to complete the test correctly.

It's a test. The paper is a test. A literal exam being taken by the distributions.

also I agree with Cow Tools re: Teacher's shape, would have posted it myself were I here earlier

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Re: 1347: "t Distribution"

Postby Sir Real » Wed Mar 26, 2014 4:17 pm UTC

hercynium wrote:First thing that came to mind...

t_distribution.jpg

Thank you; me too.

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Re: 1347: "t Distribution"

Postby Mikeski » Wed Mar 26, 2014 4:30 pm UTC

The Monday comic was playing with two definitions of "dream".

Today's is playing with two definitions each for both "Student" and "test".

There's a pattern developing here; I should see if it fits to any known curve.

There might be a 3rd joke with the shape of the teacher's curve (the result of trying to curve-fit too few points, since there are more students than teachers at most schools), but I think it's just that a Batman-esque cutout looked cool.

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Re: 1347: "t Distribution"

Postby dash » Wed Mar 26, 2014 4:43 pm UTC

Worst...XKCD...ever....

The emperor has no clothes. This comic SUCKS. Not funny, clever, or anything. Even the explanations suck.
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Re: 1347: "t Distribution"

Postby Jebobek » Wed Mar 26, 2014 5:18 pm UTC

As a teacher I got it pretty fast and laughed. Here is my interpretation:

He's looking at Grades, and sees the Student's distribution. "Hmm, not quite fitting it.. maybe if I slightly adjust the normal distribution.. NOPE. Not gonna work!" Then he places his own distribution down which students tend to get on his exam.

Below is an image of two ACTUAL practical grade distributions in my own classes via sloppily-made histograms. Thursday looks a bit normal but Tuesday has some crazy outliers. I can fix my bin sizes but you get the point. It's not really the normal curve that teachers would like to see.

Histograms of scores.png
Image

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Re: 1347: "t Distribution"

Postby SchighSchagh » Wed Mar 26, 2014 6:15 pm UTC

Trickster wrote:OH FOR LUNA'S SAKE PEOPLE

The piece of paper is a TEST. The distribution is "taking a test". It gets the answers wrong so Cueball grabs another (albeit fictional) distribution to try to complete the test correctly.

It's a test. The paper is a test. A literal exam being taken by the distributions.

also I agree with Cow Tools re: Teacher's shape, would have posted it myself were I here earlier


Wow, the visuals here really went overy everyone's heads, didn't it?

As for the alt text, I think it clearly refers to the fact that in statistics, if you keep throwing data at a statistical test, you will eventually get a false conclusion by chance. See http://xkcd.com/882/.

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Re: 1347: "t Distribution"

Postby senor_cardgage » Wed Mar 26, 2014 6:18 pm UTC

CorruptUser wrote:Title text: If data fail's the Teacher's t test you can just force it to take the test again until it passes.


I'm trying to make sense of this. Fail obviously possesses something (the Teacher's t test belongs to fail, I guess), but I can't get the rest of the sentense to make sense using fail's as a possessive noun.

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Re: 1347: "t Distribution"

Postby brenok » Wed Mar 26, 2014 6:28 pm UTC

senor_cardgage wrote:
CorruptUser wrote:Title text: If data fail's the Teacher's t test you can just force it to take the test again until it passes.


I'm trying to make sense of this. Fail obviously possesses something (the Teacher's t test belongs to fail, I guess), but I can't get the rest of the sentense to make sense using fail's as a possessive noun.

Assuming you're not being sarcastic, I'm pretty sure the apostrophe is a typo.

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Re: 1347: "t Distribution"

Postby Jebobek » Wed Mar 26, 2014 6:34 pm UTC

senor_cardgage wrote:
CorruptUser wrote:Title text: If data fail's the Teacher's t test you can just force it to take the test again until it passes.


I'm trying to make sense of this. Fail obviously possesses something (the Teacher's t test belongs to fail, I guess), but I can't get the rest of the sentense to make sense using fail's as a possessive noun.


So as a teacher, for my class where my Tuesday's group (see previous post) got a 16 the joke is that I'd make them take it again until they get a 22, thus fitting my normal curve. It is a lighthearted jab at the educational system.


Either I'm underthinking this or everyone is really overthinking this.
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Re: 1347: "t Distribution"

Postby Envelope Generator » Wed Mar 26, 2014 6:36 pm UTC

Is there a hidden jokelet in the curious shape of teacher's distribution graph?
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Re: 1347: "t Distribution"

Postby pavja2 » Wed Mar 26, 2014 7:25 pm UTC

As someone with no backing at all in stats I read the joke as something along the lines of how student grades are 'curved' to meet some kind of ideal distribution but the grade of one test across multiple teachers will be very much a chaotic if not random distribution of scores. But perhaps I'm just bitter about how much picking the right prof impacts my GPA....

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Re: 1347: "t Distribution"

Postby jpers36 » Wed Mar 26, 2014 8:35 pm UTC

cellocgw wrote:Well, to be even more obscure, FTFY: "Brillant" :mrgreen:


Paula?

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Re: 1347: "t Distribution"

Postby cellocgw » Wed Mar 26, 2014 8:37 pm UTC

jpers36 wrote:
cellocgw wrote:Well, to be even more obscure, FTFY: "Brillant" :mrgreen:


Paula?


Yep, you got it :-)
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Re: 1347: "t Distribution"

Postby jonat » Wed Mar 26, 2014 8:55 pm UTC

When I saw the comic, I was reminded of this story: http://deedy.quora.com/Hacking-into-the ... ion-System


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