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In another topic, OOM states that “Generalizations are almost as bad as statistics”. I think her statement is worthy of deeper examination.
OOM, by way of introduction, it may interest you as a Humanities person that a very early description of statistics – “by a small sample, we may judge of the whole piece”, comes from Don Quixote.
Statistics are not exactly the same thing as a generalizations, but they are more similar then they look. A generalization uses statistics in exactly the same way that a three year old boy uses calculus when learning how to aim a ball. He has no idea of the principles involved, but he can do it anyway. He can’t build an Iron Dome without calculus, though.
The world, and most of our life, especially our shidduch system, runs on generalizations. Girls from seminary x are type x. Boys from x chabura are good boys. This works, or doesn’t work, depending on who you ask, but it is useful.
Generalizations may help in making choices, but they can’t be validated or compared. Most boys from Brisk are smart, but how smart? Are they less smart then boys from Gush? If Lakewood boys have a lower average intelligence, but with higher variance, than boys from Brisk, then if you date an above average boy from Lakewood, he is probably more intelligent than an average Brisk boy. A generalization would not help you in deciding a question like which boy to date, but statistics would.
Statistics allows you to say TRUE or FALSE by turning generalizations into quantified facts. “Seminary is really important for spiritual growth” vs. “Seminary attendance increases average prayer time by 2 hours per student per day in the three-year post-seminary period”. Either the students pray for 2 hours more a day, or they don’t. The former statement can be argued with. The latter speaks for itself.
However, statistics are no substitute for judgment (paraphrased). NASI (National Abusers of Statistical Information), is an example of an organization that abuses statistics. They use statistics as a drunken man uses lamp-posts- for support rather than illumination. (paraphrased) However, the drunken man could not see the lamp-posts, were it not for illumination. So they have the right idea, even if they are not going about it properly.
Both statistics and generalizations can be used to argue for or against anything you wish. Real Truth is only found in the Torah.
Your thoughts?
Popa knows statistics. He can run a Z score, and a T score, and all the clever things he can do to convince you of things that aren’t true.
Knowing statistics can make you sound very smart, when in fact you are really dumb. I use this to great effect.
Relying on statistics is way worse than relying on generalizations.
Read How to Lie with Statistics by Darrell Huff (favorite book of LIFE).
I don’t mean citing a study; I mean knowing how examine info for statistical significance.
I don’t think I ever did it on this site, but on a different one, I did. You won’t find it.
But if the occasion arises, I’ll do it for you.
yayz Phantom Tollbooth
I wrote a college admissions essay on that book. ^_^
There is something funny about a book that purports to use numbers to show how numbers are manipulated, and everyone reading the book believes it.
Perhaps the book is self proving.
It doesn’t use numbers. Did you read the book?
I took “use” to imply that they are the basis for his ideas. They aren’t.
And I have to ask, how is that book of any use to someone who is ideologically opposed to knowledge?
” If Lakewood boys have a lower average intelligence, but with higher variance, than boys from Brisk, then if you date an above average boy from Lakewood, he is probably more intelligent than an average Brisk boy.”
Inconclusive. He could be more or less.
” Statistics allows you to say TRUE or FALSE by turning generalizations into quantified facts.”
Patently false. No amount of statistics yields facts.
” NASI (National Abusers of Statistical Information), is an example of an organization that abuses statistics.”
No, their entire problem is that they completely lack statistics and instead use emotional anecdotery. Would that they abused statistics, for then they could be made to see reason.
You asked for our thoughts so here they are. Study harder for your test.
Squeak is as usual correct. Statistics allow you to predict how accurate your outcome is by determining how likely it is that a sample would have the outcome you have if the underlying population did not have the criteria you hypothesize. But it will always be a likelihood.
If you flip a quarter 10 times and get 10 heads, statistics will tell you that the quarter is weighted and we will say that it is statistically significant at the 99% level. But we still don’t know it is true, because it will still happen with a normal quarter 1% of the time.
(z score=3.16 p hat is 1, and p is .5. Square root of .5*.5 is .5. Divided by square root of 10 is .158. Which means we are 3.16 stdevs off the mean.)
Stated differently, if you took 100 quarters and flipped each one of them 10 times, you could expect that one of the times you would have either 10 heads or 10 tails. If you do it with one quarter though, it is so unlikely that it will happen, that you can still conclude that it is weighted with reasonable certainty.
Torah613: Maybe what I just did is pretty basic, but I’m pretty proud of myself for knowing how to do it anyway and very few of my friends can do that.)
I don’t think anything bothers me more than intelligent people who drink the Kool-Aid…
“Ever saw their red, blue and gray chart? They claim……..”
Yes, they claim many things. Its one of their greatest achievements. Making claims.
” higher variance means the spread of the data is larger, covering a wider range.”
But that doesnt tell you enough. If one mean is hgher than the other, there will be some above average points in set 1 that are still below the other mean. Sure, you can make up an example that proves your point, but you didnt give enough information at first to state your conclusion.
And skoyach, popa!
Studies have shown that 83.6% of statistics are made up on the spot.
Popa- your example with the quarter is also incorrect, sorry. Shame on me because I just skipped over it expecting you to be right. But the chance of a quarter landing on the same side 10 times in a row is less than one in a tbousand. I dont know t and z, but I can multiply 50% by itself as many times as need be.
“Stated differently, if you took 100 quarters and flipped each one of them 10 times, you could expect that one of the times you would have either 10 heads or 10 tails. If you do it with one quarter though, it is so unlikely that it will happen, that you can still conclude that it is weighted with reasonable certainty.”
I don’t think that is correct. If the percentage of weighted quarters in circulation is less than 1% (and I would guess it is whole lot less than that) and you picked up the coin at random, then it more likely that you just got lucky with your flipping than that the coin is weighted.
This is like the urban legend of the young man that shot himself after testing positive for AIDs. Only .04% of the tests produced false positives, but that number was still much larger than the percentage of people with AIDs in society. In other words there were more false positives with this test than true positives.
” To my knowledge, not one reputable statistician has weighed in on this.”
The truth is many have weighed in, but NASI did not like what they heard so shouted them down.
When have statisticians weighed in on NASI’s theories?
Squeak: I rounded some of the numbers. Some because my calculator only goes to 10 decimals. And including the final 3.16 since the z table I used only went to the second decimal.
Squeak: I think the real answer to your question is that the distribution of sample means approximates a normal distribution, but it does not do so precisely, and it gets more precise as the sample size grows bigger.
I used a sample size of 10 (I spun 10 times to divine what would happen if I spun it infinite times), which is not so large. I think if I ran it with a sample size of 100, it would be much closer to the mathematical answer.
The z score for that is an even 10, but I can’t find a z table that goes that low, so…
This is starting to go over my head, but I think you missed what I said. You claimed that 1% of the time you would get a quarter to land on ten heads in a row and I pointed out that it is only a tenth as likely. Everything you said after that was to try and confuse me.
Torah- there are several other blogs that discussed nasi and posters known to be experts (ie not anonymous to the forum) made their points. But most of my due diligence was by asking real people what they think, not online, so I have no links for that. But if you are interested reach out and ask someone who has the analytical ability to help you figure it out for yourself. Nasi offers the easy blameless answer, so it takes some willpower to allow yourself to disbelieve it.
Squeak: I understand what you are asking now. I have no idea what the answer is. I double checked my math, and it is correct, and I double checked the z score and it is correct. There is .4992% to the left of the score, which means there is slightly less than a 1% chance of falling this far off the mean. Which means that it will happen about 1% of the time even with a quarter that is evenly weighted.
I frankly have no idea what the mistake I am making is.
Torah613: Squeak points out that the chances are in fact 1 in a thousand, while a z score of 3.16 gives us about a 1 in a hundred chance. Which makes absolutely no sense.
I don’t get it; I’ll ponder more tomorrow.
But, just to show you that I’m still more correct than you, I will note that the mathematical chances are 1/500–not 1/1000.
This is because I am calculating the chances of being this far off the mean in either direction, which would happen if there are either 10 heads or 10 tails. Therefore, the formula is 1*.5*.5*.5*.5*.5*.5*.5*.5*.5. Because the first time it doesn’t matter which one it lands on.
This is true even though I said the case was 10 heads. Because I am calculating the chances that a sample of 10 would be that far off the mean of all spins which is .5, and it would be that far off the mean whether it was 10 heads or 10 tails.
Snort at you.
Hopefully we won’t end up with a debate between the Bayesians and the Frequentists. Otherwise, things here will get REALLY ugly.
If you guys are struggling with 10 flips, maybe you can reduce it to 2 flips for simplicity. The chance of getting two heads in a row is one in four. Same chance of getting two tails in a row. With three flips, the chance is one in eight, count em. Just add two possibilites to each of the four from the two flip case. Keep adding a flip at a time and youll get to ten. All your fancy z scores dont mean a thing if they give you the wrong answer.
I never would have imagined that I would one day be explaining something to a statistician. Too bad we lost dr. Pepper.
The opening post shows some good insights for a 14-year old, or some egregious gaps in the education of a 21-year old.
Statistics is a branch of mathematics that enables us to draw reliable conclusions about a phenomenon based on a sample of information that about that phenomenon. Generalizations are non-statistical conclusions about a phenomenon that are untested and unproven, e.g., all Jews love money, all frum Jews are crazy. all goyim are stupid. Generalizations are an important tool for yentas. Statistics are an important tool for scientists.
Statistics are an important tool for scientists.
As the progeny of two scientists who have engrained in me a deep disdain of statistics, to that I say HA.
Forget the 100 flips.
Back to squeak’s question. If the odds of getting 10 in a row of heads or tails can be computed by multiplying .5 to the 9th power and gives us 1 in 500, then how can the z score for the same thing be 1 in 100?
Squeak: You don’t get a reliable z score on 2 flips because the sample size is not big enough, so it won’t approximate a normal distribution.
nfgo3,
Generalizations are not necessarily “untested and unproven.” E.g. if I have statistical evidence that the average Jewish IQ is nearly 2 standard deviations above the national average, I can then make the generalization “Jews are smart.”
“If the odds of getting 10 in a row of heads or tails can be computed by multiplying .5 to the 9th power and gives us 1 in 500, then how can the z score for the same thing be 1 in 100?”
Since torah613 decided to patronize me, let me provide the answer. Not 42. I refer to popas first post in the thread. “Popa knows statistics. He can run a Z score, and a T score, and all the clever things he can do to convince you of things that aren’t true.”
QED
lol
I’ll ask someone who knows stuff.
Torah:
Again, we are discussing that you flipped one quarter 10 times and got 10 heads.
The calculation is this:
p-hat minus p
divided by
square root of (p*1-p) / square root of sample size
Where, p hat is the sample mean and p is the population mean.
So,
p-hat is 1, and p is .5
square root of (.5*.5)=.5
divided by square root of 10 = 0.15811388300841896659994467722164
Now, I subtract p from p-hat and get .5
.5/0.15811388300841896659994467722164 = 3.1622776601683793319988935444326
Then I google a handy dandy z table and find that the value for z score of 3.16 is .4992, which means that half a percent of results on a normal distribution lie to the left of z score 3.16, which means that there is a 1/100 chance of getting a result this far off the mean if you pick results at random from the distribution.
So where do you disagree?
Oh, I get it. I’m reading the z table wrong. It’s formatted differently than I’m used to–it is showing the percentage between z score and mean instead of percentage left of the z score.
.4992 means there is 49.92% between the z score and the mean, which means that there is only .08 outside, which means a total of .16% on both sides, which is much closer to 1/500 than to 1/100
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