Torah613Torah

Morahmom- I haven’t found it, but read all the biographies.

Saysme and Snowbunny: Only to an insider. We’re actually pretty similar to an outsider.

Nechomah: Agreed.

Hello, I’m your friendly local statistician, please let me help you all out today!

Firstly, here are some online calculators make your life a lot easier. Statistical Computing for The Internet Savvy:

1. Input your data, SD (standard deviation) and at easycalculations’s calculator to obtain a z-score.

2. Plug in your Z-score at Fourmilab’s Z-score calculator to calculate the probability of your z-score, which will give you a sense of how rare your result was.

3. Or, use the normal distribution calculator by computerpsych research software, which takes your z-scores and places them on a bell curve which is conveniently drawn for you.

Another note: Chebyshev’s rule says for a standard distribution of data, 99.7% of results will fall within 3 standard deviations from the mean. So if you’re getting a z-score above 3, make sure that’s what you’re expecting.

What does this have to do with Popa’s coin flipping?

For Popa’s original scenario, a z-score of 3 or so sounds about right. 1 means typical, 2 means a little less than typical, 3 means very rare, 4 means nearly unheard of.

Popa, a Z score of 10 is about 1 in infinity. The chance of getting 1000 heads is not infinity.

We’re all familiar with IQs and SATs as probability distributions. In standardized testing, a perfect score is nearly always set to 3 SDs above the mean.

A Z score of 10 would be equivalent to an IQ of 250, which is considered a mathematically vacuous result. To put that into perspective, a Z score of 10 is the equivalent of an SAT score of 1500 PER SECTION, for a total of 3000 rather than 1600 which is the maximum SAT score. It is functionally meaningless.

I hope that was helpful. This is your friendly local statistician signing off for today!

Science still hasn’t figured out how to copy the pyramids.

“The truth is many have weighed in, but NASI did not like what they heard so shouted them down.”

Would you mind pointing me to where they weighed in? I would be interested in reading what they said. What should I google? You clearly know a lot more about NASI than I do (my knowledge comes from reading the papers, so I have no way of judging)

Hi Squeak!

“Yes, they claim many things. Its one of their greatest achievements. Making claims.”

We agree completely. What annoys me is that they claim that their claims are backed up by data, and imply that they are using well-researched statistics which “prove” that this is the problem. At least as of last week in Hamodia (letters Section D, I think). To my knowledge, not one reputable statistician has weighed in on this.

“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.”

Correct, I was not specific in my opening post. I was merely trying to make the point that it is not wise to use generalizations to compare data, since statistical differences in the data can make them invalid.

“And skoyach, popa!”

yep!

OOM: I value knowledge very much when it is useful to me in real life, and statistics is extremely useful for me. 🙂

Squeak:

“Inconclusive. He could be more or less.”

Nope – higher variance means the spread of the data is larger, covering a wider range. Assume a special bell curve. Let’s say the average Brisk IQ is 120, with a variance of 4. That’s a tall bell curve. And let’s say the average Lakewood IQ is 118, with a variance of 20. That’s a flat bell curve.

The top 50% of Brisk IQs is only 124, but the top half of Lakewood IQs would be 118-138, roughly speaking, since I am not going to make up data for my hypothetical situation. So you’d be more likely to get a smarter boy in Lakewood if there was a high variance and you’re already selecting for above average intelligence.

(Yes, I’m exaggerating to make a point about how to use statistics. They never line up so nicely in real life.) Yes, a particular boy will be what he will be, but we are discussing probabilities, and in real life we make decisions without knowing everything, through probabilities.

“Patently false. No amount of statistics yields facts.”

Really? What about a census?

“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.”

Ever saw their red, blue and gray chart? They claim it is based on statistics, exaggerated to make their point of course.

Thanks for your good wishes on my studying.

CRuzer: Good point and thanks!

WIY: I learned diligence in other ways, then applied it when necessary.

We shouldn’t depend on school to teach diligence. Not every student will learn diligence from a standardized curriculum which involves being thrown in an arbitrary social system and learning 8 different subjects for 45 minutes each a day for four years.

OOM: I take it you don’t agree?

OOM: Yes for secular subjects. For Torah subjects, you are growing as a person, so you should study even more than for the tests. For secular studies, you just need it for a parnasa, so no need to obsess about it.

PBA: Very nice of you to offer. What kind of info and what kind of significance?

Z/T are pretty basic.

OOM: I own that book. 🙂 How to Lie With and Statistics is just about my favorite secular book ever, right up there with Harry Potter, Dale Carnegie, The Phantom Tollbooth, and Larger than Life.