Statistics

***CaptHayfever*** · 07-19-2010, 03:17 PM

Not descriptive statistics (averages, sports records, probabilities, et cet) or probabilities, but inferential statistics. Making wide-scale assumptions (sometimes up to aleph-naught) based on small-scale tests usually with biased sample groups (sometimes as small as 30). Ignoring or attempting to "correct" outliers to fit the hypothesis rather than correcting the hypothesis to fit the results. The third type of lie Twain wrote about. And did I mention the whole using 30 as a close enough sample to approximate infinity thing!?

And remember, "I'm-a Luigi, number one!"

Panfan · 07-19-2010, 03:24 PM

99 PERCENT OF TEENAGERS HAVE MOVED ON TO DA EVIL RAP MUZIKS

IF YA PART OF THE 1 PERCENT THAT LISTENS TO GOOD STUFF PUT THIS IN YA STATUS

**Valigarmander** · 07-19-2010, 04:23 PM

97% of statistics are made up on the spot anyway.

Metal Man · 07-19-2010, 04:38 PM

32895235 hobozillion percent of people believe in statistics.

Pixelated Penguin · 07-19-2010, 10:55 PM

I don't know much about statistics, but it seems ridiculous that an extrapolation could be made from a set of 30 to a countably infinite set, especially considering that there aren't really any countably infinite collections of things in existence. Where on earth did you see that??
[edit: oh, I just realized it could be about 'all people,' including people not yet born. Well, I've certainly seen that.]

But, yeah, a lot of pop-science articles (especially psychological or sociological ones) have small sample sizes and make ridiculous assertions. It's unfortunate that the layman isn't really statistically literate; I'm certainly not. =\

***CaptHayfever*** · 07-20-2010, 12:01 AM

^Central Limit Theorem is what "allows" that rounding. The theorem itself is actually sound, but the extended reasoning that brings about the 30 cutoff basically amounts to "because we felt like it."

I've had to take 3 stat courses. Each time, I thought it would be the last time, then I later got roped into taking another. Each time*, the course made me hate statistics more & more.

And then for my masters' portfolio, I had to put together a statistical analysis of the results of an attitude survey I gave my students twice last fall.
The numbers universally went down. CLEARLY the attitude improvement efforts failed. The only way a statistical test can pass is if the numbers went up. WHY THE HECK DO I NEED TO DEVELOP AND COMPUTE A STATISTICAL TEST WHEN IT CANNOT POSSIBLY SUCCEED? IT IS A WASTE OF TIME.

*Well, the 2nd time, the course only covered probability & descriptive stats, not inferential, so it wasn't as bad as the 1st & 3rd times.

And remember, "I'm-a Luigi, number one!"

Kargath · 07-20-2010, 04:29 AM

Quote:

Originally Posted by Pixelated Penguin

aren't really any countably infinite collections of things in existence.

integers

Pixelated Penguin · 07-20-2010, 04:42 AM

In existence.

Kargath · 07-20-2010, 05:05 AM

Well I'm clearly not talking about i

Pixelated Penguin · 07-20-2010, 05:37 AM

Mmm, well, I don't know about you, but my philosophy of math is that mathematical constructs don't 'exist' in the way as material things. Real numbers are as imaginary as imaginary numbers or combinatorial games or fractals.

Oh, guys, btw: there's at least a 99% chance of any given planet being devoid of life. Therefore, it is very likely there is no life on Earth.

And if you don't believe that -- the above statement could either be true or false, so there's a 50% chance it's true.

But, since there's, say, a 1% chance of a given planet having life, if you look at 100 of them, then you have a 100% chance of finding one.

And, some may find this interesting: A random natural number has a 0% chance of being prime. It's true. Even though on any sufficiently large finite interval, it's still non-zero.

***Cosmonautical*** · 07-20-2010, 09:02 AM

Quote:

Originally Posted by Pixelated Penguin

And if you don't believe that -- the above statement could either be true or false, so there's a 50% chance it's true.

Stuff like this is what really gets me. The possible answer making up 50% of the possible values assigned to a statement, regarding truth, has no bearing on the probability of outcome.

100% of true statements are likely to be true. 100% of true statements have the possibility of being misrepresented as being false. 100% of the options available may represent an an incorrect assessment.

***CaptHayfever*** · 07-20-2010, 11:48 AM

^^Oy vey.

Quote:

Real numbers are as imaginary as imaginary numbers or combinatorial games or fractals.

Real numbers can all be used to measure physical objects. The whole numbers count things. The negative integers apply to relative positioning. Fractions are ratios of integers. Irrational numbers also represent proportions of some sort or another.

Imaginary numbers, however, exist in a wholly different plane. Literally. They're based around taking the square root of a negative number, a concept which doesn't quite make physical sense, but doesn't break the universe like dividing by 0 does. The funny thing is that imaginary numbers are still applicable to the physical universe, just not when measuring objects.

Quote:

Oh, guys, btw: there's at least a 99% chance of any given planet being devoid of life. Therefore, it is very likely there is no life on Earth.

Cogito, ergo sum. The fact of your own existence disproves your "clever" jest. That's not how probability works; you can't use it to determine whether something that has already happened...has already happened.

Quote:

And if you don't believe that -- the above statement could either be true or false, so there's a 50% chance it's true.

Probability also doesn't work like that. The number of possible outcomes has no bearing on each outcome's probability; not everything in life is a coin toss. (Technically, not even a coin toss is a coin toss...the heads side is heavier than the tails side, so tails actually has a slightly higher probability of occurrence than heads.)
If you throw a Weeble toy, it can end up on its head or on its feet, but the probability of landing on its feet is waaaaaaaaaaaayyyyyyyyy greater than landing on its head.

Quote:

But, since there's, say, a 1% chance of a given planet having life, if you look at 100 of them, then you have a 100% chance of finding one.

Probability ALSO doesn't work that way (unless you're counting Earth in that 100, cheater). The big wheel on The Price Is Right has a 5% (1/20) chance of hitting the dollar, but you could easily spin it 20+ times and never hit that dollar.

Quote:

A random natural number has a 0% chance of being prime. It's true. Even though on any sufficiently large finite interval, it's still non-zero.

This one's actually correct. That's the Central Limit Theorem (and the Law of Large Numbers) at work in its true form, not the ad-libbed form statisticians use.

And remember, "I'm-a Luigi, number one!"

Pixelated Penguin · 07-20-2010, 10:36 PM

Complex numbers can still model lots of things just as well as reals, (also: n/0, n != 0 makes sense on projective spaces, and even 0/0 makes sense on wheels) but I believe that no matter what, a mathematical concept is a concept and cannot be 'real,' is the sense of existing physically, no matter how well it models real things. Just clarifying my belief -- I don't want to sidetrack the thread any more.

Oh, and the fact that all those statements but the last one were fallacious was meant to be apparent: I've actually seen all of those before. I thought they were at least a little clever, though, even though obviously horrifying abominations of probability.

***CaptHayfever*** · 07-21-2010, 12:50 AM

I knew all of that about complexes & divisions by 0. Just curious, are you trying to out-math me? 'Cause aside from Jay and TML, nobody here out-maths me.

And remember, "I'm-a Luigi, number one!"

Kargath · 07-21-2010, 04:28 AM

Or maybe Missy or I.

Pixelated Penguin · 07-22-2010, 08:36 PM

Haha, no; I couldn't really tell whether you were just assuming I didn't know things, or didn't know them yourself.

You almost surely can out-math me; I'm not even in college, haven't taken anything more advanced than Calc II, and most of my maths knowledge comes from books/wikipedia and such. My interest in mostly casual.

07-19-2010, 03:17 PM	#1
*CaptHayfever* Smash SuperMod Join Date: Jul 2002 Location: (n) - the place where I am Gender: Posts: 27,661 Thanks: 1,991 Thanked 2,486 Times in 1,513 Posts	Statistics Not descriptive statistics (averages, sports records, probabilities, et cet) or probabilities, but inferential statistics. Making wide-scale assumptions (sometimes up to aleph-naught) based on small-scale tests usually with biased sample groups (sometimes as small as 30). Ignoring or attempting to "correct" outliers to fit the hypothesis rather than correcting the hypothesis to fit the results. The third type of lie Twain wrote about. And did I mention the whole using 30 as a close enough sample to approximate infinity thing!? And remember, "I'm-a Luigi, number one!"

07-20-2010, 12:01 AM	#6
*CaptHayfever* Smash SuperMod Join Date: Jul 2002 Location: (n) - the place where I am Gender: Posts: 27,661 Thanks: 1,991 Thanked 2,486 Times in 1,513 Posts	^Central Limit Theorem is what "allows" that rounding. The theorem itself is actually sound, but the extended reasoning that brings about the 30 cutoff basically amounts to "because we felt like it." I've had to take 3 stat courses. Each time, I thought it would be the last time, then I later got roped into taking another. Each time, the course made me hate statistics more & more. And then for my masters' portfolio, I had to put together a statistical analysis of the results of an attitude survey I gave my students twice last fall. The numbers universally went down. CLEARLY the attitude improvement efforts failed. The only way a statistical test can pass is if the numbers went up. WHY THE HECK DO I NEED TO DEVELOP AND COMPUTE A STATISTICAL TEST WHEN IT CANNOT POSSIBLY SUCCEED? IT IS A WASTE OF TIME. Well, the 2nd time, the course only covered probability & descriptive stats, not inferential, so it wasn't as bad as the 1st & 3rd times. And remember, "I'm-a Luigi, number one!" Last edited by CaptHayfever; 07-20-2010 at 12:06 AM.

07-20-2010, 10:36 PM	#13
Pixelated Penguin Junior Member Join Date: Dec 2009 Location: Philadelphia, PA Gender: Posts: 199 Thanks: 26 Thanked 9 Times in 9 Posts	Complex numbers can still model lots of things just as well as reals, (also: n/0, n != 0 makes sense on projective spaces, and even 0/0 makes sense on wheels) but I believe that no matter what, a mathematical concept is a concept and cannot be 'real,' is the sense of existing physically, no matter how well it models real things. Just clarifying my belief -- I don't want to sidetrack the thread any more. Oh, and the fact that all those statements but the last one were fallacious was meant to be apparent: I've actually seen all of those before. I thought they were at least a little clever, though, even though obviously horrifying abominations of probability. Last edited by Pixelated Penguin; 07-20-2010 at 10:42 PM.

07-19-2010, 03:24 PM	#2
Panfan AND HE PRAYS Join Date: Jun 2005 Location: Grayskull Gender: Posts: 18,806 Thanks: 1,405 Thanked 2,251 Times in 1,339 Posts Blog Entries: 15	99 PERCENT OF TEENAGERS HAVE MOVED ON TO DA EVIL RAP MUZIKS IF YA PART OF THE 1 PERCENT THAT LISTENS TO GOOD STUFF PUT THIS IN YA STATUS

07-19-2010, 04:23 PM	#3
Valigarmander The Bee's Knees Join Date: Jun 2006 Location: The land of rain and trees (Oregon) Gender: Posts: 29,755 Thanks: 1,649 Thanked 5,701 Times in 2,581 Posts Blog Entries: 20	97% of statistics are made up on the spot anyway.

07-19-2010, 04:38 PM	#4
Metal Man Fairy-Slaying Maniac Join Date: Apr 2000 Location: 1592 Miles Away From Here Gender: Posts: 18,062 Thanks: 148 Thanked 683 Times in 482 Posts	32895235 hobozillion percent of people believe in statistics.

07-19-2010, 10:55 PM	#5
Pixelated Penguin Junior Member Join Date: Dec 2009 Location: Philadelphia, PA Gender: Posts: 199 Thanks: 26 Thanked 9 Times in 9 Posts	I don't know much about statistics, but it seems ridiculous that an extrapolation could be made from a set of 30 to a countably infinite set, especially considering that there aren't really any countably infinite collections of things in existence. Where on earth did you see that?? [edit: oh, I just realized it could be about 'all people,' including people not yet born. Well, I've certainly seen that.] But, yeah, a lot of pop-science articles (especially psychological or sociological ones) have small sample sizes and make ridiculous assertions. It's unfortunate that the layman isn't really statistically literate; I'm certainly not. =\

07-20-2010, 04:42 AM	#8
Pixelated Penguin Junior Member Join Date: Dec 2009 Location: Philadelphia, PA Gender: Posts: 199 Thanks: 26 Thanked 9 Times in 9 Posts	In existence.

07-20-2010, 05:05 AM	#9
Kargath et in Arcadia ego Join Date: Jul 2001 Gender: Posts: 8,334 Thanks: 1,226 Thanked 780 Times in 488 Posts	Well I'm clearly not talking about i

07-20-2010, 05:37 AM	#10
Pixelated Penguin Junior Member Join Date: Dec 2009 Location: Philadelphia, PA Gender: Posts: 199 Thanks: 26 Thanked 9 Times in 9 Posts	Mmm, well, I don't know about you, but my philosophy of math is that mathematical constructs don't 'exist' in the way as material things. Real numbers are as imaginary as imaginary numbers or combinatorial games or fractals. Oh, guys, btw: there's at least a 99% chance of any given planet being devoid of life. Therefore, it is very likely there is no life on Earth. And if you don't believe that -- the above statement could either be true or false, so there's a 50% chance it's true. But, since there's, say, a 1% chance of a given planet having life, if you look at 100 of them, then you have a 100% chance of finding one. And, some may find this interesting: A random natural number has a 0% chance of being prime. It's true. Even though on any sufficiently large finite interval, it's still non-zero.

07-21-2010, 12:50 AM	#14
*CaptHayfever* Smash SuperMod Join Date: Jul 2002 Location: (n) - the place where I am Gender: Posts: 27,661 Thanks: 1,991 Thanked 2,486 Times in 1,513 Posts	I knew all of that about complexes & divisions by 0. Just curious, are you trying to out-math me? 'Cause aside from Jay and TML, nobody here out-maths me. And remember, "I'm-a Luigi, number one!"

07-21-2010, 04:28 AM	#15
Kargath et in Arcadia ego Join Date: Jul 2001 Gender: Posts: 8,334 Thanks: 1,226 Thanked 780 Times in 488 Posts	Or maybe Missy or I.

07-22-2010, 08:36 PM	#16
Pixelated Penguin Junior Member Join Date: Dec 2009 Location: Philadelphia, PA Gender: Posts: 199 Thanks: 26 Thanked 9 Times in 9 Posts	Haha, no; I couldn't really tell whether you were just assuming I didn't know things, or didn't know them yourself. You almost surely can out-math me; I'm not even in college, haven't taken anything more advanced than Calc II, and most of my maths knowledge comes from books/wikipedia and such. My interest in mostly casual.