explain xkcd - User contributions [en]

Talk:1347: t Distribution

2014-03-26T13:17:17Z

Wwt:

http://en.m.wikipedia.org/wiki/Student%27s_t-test

[[Special:Contributions/173.245.50.73|173.245.50.73]] 05:20, 26 March 2014 (UTC)Adam

I think this is a comment of the quality of education today - it is difficult to grade students on a distribution curve and even more so when you take into account the distribution curve of the teachers ability. {{unsigned ip|108.162.249.205}}

I noticed the teacher's curve is symmetrical, and after further inspection it could be interpreted as an edge detection: high values show where an edge occurs. The two highest peaks would nicely align with the edges of the paper, the next highest peaks fit the edges of the table, and the rest could be approximation artefacts, as they're equidistant and rather insignificant compared to those four. I'm not statistics pro, but maybe that rings someone's bells? [[Special:Contributions/108.162.210.239|108.162.210.239]] 07:56, 26 March 2014 (UTC)

:Interesting observation. It may play into an age-long legend told and re-told among the students that some teachers grade papers by tossing the whole pile in the air; those sheets that land on the teacher's desk get a pass, those falling to the floor get a fail. Sometimes the story gets modified in such a way that papers falling on the teacher's book (or other object) laying on the desk will get a higher marking than those simply hitting the desk. The latter version would explain the higher sheet-size-apart peaks. [[Special:Contributions/108.162.210.111|108.162.210.111]] 08:57, 26 March 2014 (UTC)

To be more explicit, I think the sheet of paper represents some data. Cueball is not happy with the results of applying Student's t test, so ze is trying more complex tools in the hope of getting significance. -- TimMc / [[Special:Contributions/173.245.52.27|173.245.52.27]] 11:51, 26 March 2014 (UTC)

Man, normally these explanations clear the comic right up for me, but I've read this one thrice now and I still can't figure out what a t-distribution is, much less a joke based on one. The only definition being a Wikipedia quote written in legalese doesn't help. So a t-distribution estimates...the probability of a population's average when there's unknown information?[[Special:Contributions/108.162.216.48|108.162.216.48]] 12:17, 26 March 2014 (UTC)
:The unknown information is the sample size (class size, for example) and standard distribution (by how much, on average, is something going to vary from the mean). The unknown information is not "in the data".[[User:Jarod997|Jarod997]] ([[User talk:Jarod997|talk]]) 12:28, 26 March 2014 (UTC)
:Basically, if you have an underlying process that would produce samples with a Gaussian distribution with mean of 0, and stddev of 1, and then you pull a finite number of samples out of it, and do the usual "average" operation on those samples (i.e. sum them and divide by the number of samples) you would expect that that computed average would be close to zero. But it might not be! By chance the samples you pulled might mostly have been from the far right or left side of distribution and the average you got would be way off. Student's T distribution (for a certain number of samples, n) is basically "given that the underlying process a Gaussian with mean zero and stddev of 1, if I repeatedly take n samples from that distribution and compute the average of those samples to get an "estimated mean", this is how I expect that estimated mean to be distributed". Naturally, this is important in questions like "I took 100 samples and got an average of 0.02 -- does this mean that it is sensible to think that the mean of the underlying distribution is actually zero?"
: Of course, most of the joke is that the distribution is named "Student's", which is not strongly dependent on the nature of the statistics. [[User:Vyzen|Vyzen]] ([[User talk:Vyzen|talk]]) 12:42, 26 March 2014 (UTC)
The teacher's t-distribution looks like multiple spikier curves with different centres added together
and it doesn't fit the table. [[User:Wwt|Wwt]] ([[User talk:Wwt|talk]]) 13:17, 26 March 2014 (UTC)

1347: t Distribution

2014-03-26T12:35:35Z

Wwt: /* Transcript */

{{comic
| number = 1347
| date = March 26, 2014
| title = t Distribution
| image = t_distribution.png
| titletext = If data fails the Teacher's t test, you can just force it to take the test again until it passes.
}}

==Explanation==
{{incomplete|Why does Cueball disapprove of the Student's t-distribution?}}
According to {{w|Student's t-distribution|Wikipedia}}, "In probability and statistics, Student's t-distribution (or simply the t-distribution) is a family of continuous probability distributions that arise when estimating the mean of a normally distributed population in situations where the sample size is small and population standard deviation is unknown." The distribution is named for the pseudonym of William Gosset, an employee of Guinness Brewery who did not want to reveal his real name when publishing his work. A Student's t distribution is similar to a standard Gaussian (symmetric bell curve) distribution, but has "fatter tails"; thus, the one shown in the comic is roughly the right shape.

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.

The title text plays on the word "test". The first part of the sentence refers to a potential "Teacher t-test" which would be used in a statistical context to test for the significance of some observation, as opposed to the real "Student's t-test" which is used to determine if two sets of data differ by a statistically significant amount. On the other hand, the second part of the sentence refers to the possibility for students to take tests (or exams) until they pass. The resulting sentence may refer to statistical fallacy, or the (conscious or unconscious) action of manipulating observations or misconducting experiments to give statistical significance to a false fact.

==Transcript==
:[Cueball is wobbling a bell-curved cutout labelled 'Student's T Distribution' on a piece of paper on a table]
:Cueball: Hmm

:[Cueball examines the paper]
:Cueball: ...Nope.

:[Cueball takes away the student's distribution cutout]

:[Cueball attempts to place a wider and far more complicated multi-modal cutout labelled 'Teacher's T Distribution' on the table]

{{comic discussion}}

User talk:Wwt

2014-03-26T12:34:31Z

Wwt: Created page with "1347: t Distribution"

[[1347: t Distribution]]

User:Wwt

2014-03-26T12:34:16Z

Wwt: Created page with "1347: t Distribution"

[[1347: t Distribution]]