Thanks Corey
I thought I'd forgotten any maths I'd learnt as kid from reading these bell curve posts. Shannow has been mistaking mean and average with these "power posts". It's good to see you posting on the WOTMB and good to see the end of the series is finally here.
Simon
Ugh, just lost half an hour of typing. I'll try again.
I've never delved into a one power discussion before, but as a stats teacher I thought I might be of some use.
To the above, and especially the bolded - yes the first statement is correct, assuming that's what RJ said, but it has nothing to do with the second statement. The second one is fallacious.
An example given above had a mean of 1 and a standard deviation of 4.1, but that was a little abstract, so why don't we use a real example? The average male height in the US is 5 foot 10 or so. That doesn't mean that the maximum possible male height is 11 foot 8, no one has ever even come close to that. All that it means is that if you took all the males in the US, added up their heights, and divided by that number of males, you'd get a mean of 5 foot 10. Shortest or tallest has no relation to that mean, in and of itself.
The second component to a bell curve is standard deviation, sort of like an 'average spread' of the curve. The standard deviation is around 3 inches (according to a quick internet search) for male height. According to the way that normally distributed data are distributed (the bell curve follows certain rules, and most things in nature are normally distributed, which makes it a heck of a lot easier to analyze stats), that just means that 68% of all males will be between 5 foot 7 and 6 foot 1 (+ or - 1 standard deviation from the mean). But even if you're 3 SD's above the mean, or even if you're the tallest man in the world, it doesn't relate to the mean at all, any more than any number or place on the normal curve does.
(note: of course, with dwarfism there would actually be a little bump in the lower part of the real distribution of height, but let's say we're talking about 'height of people not affected by a physical condition' )
In this power example, then, Lanfear can be ten times stronger than the average Aes Sedai, a hundred, whatever - ratio isn't relevant to a normal curve. Normal curve only talks in terms of probability, so if Lanfear was 3 standard deviations above the mean, it would mean that there's only a .15% chance of someone being stronger than her in the population (as 99.7% of all scores fall within +/- 3 SD of the mean, and the rest has to be split on both ends, meaning .15% below 3 SD below the mean and .15% above 3 SD above the mean). My guess is that Lanfear is even rarer, maybe 4 or 5 SDs above the mean. Regardless, that is meaningless (no pun intended) with regards to her strength relative to other channellers. She could be 1000 times as strong as the channeller that sits perfectly at the middle of the distribution, or 1.5 times as strong. She can still fit perfectly fine into a bell curve of channellers.
With regards to the problem of zero - practically, that's not so much a problem. As I've already mentioned, only .15% of the population falls below 3 SDs below the mean, and that number gets exponentially smaller with each SD you get away from the mean. Taking height as an example, then, as I said you're at 5 foot 1 when you're 3 SDs below the mean. You still have 20 more standard deviations to go before you get to zero, so by the time you get to zero, although there's practically a CHANCE that you could get someone who has zero height, the chances of that happening even assuming it was physiologically possible would be essentially one in infinity, close enough. So the fact that there are physiological limitations doesn't mean that a significant part of the population has power (or height, or whatever) slightly above zero and then hits a wall. For the most part, the zero cutoff is a non-issue in measurement, which is why it's perfectly acceptable to describe things as conforming to a bell curve, even when some of the extreme aspects of a bell curve aren't perfectly replicable in real life. I'd say RJ would be totally justified in describing power as fitting a bell curve, without having to qualify 'except for specific theoretic mathematical points that make very little difference in reality'.
I thought I'd forgotten any maths I'd learnt as kid from reading these bell curve posts. Shannow has been mistaking mean and average with these "power posts". It's good to see you posting on the WOTMB and good to see the end of the series is finally here.
Simon
A Bell Curve by definition means that the distance from the weakest to the strongest channeler is intersected at exactly the 50% mark by the mean (the average channeler). Any skewing of the distribution would mean that the term “Bell Curve” cannot be applied to the distribution. Instead, it would then be either a positively or negatively skewed distribution. But not a Bell Curve.
So the basic rule is that the average channeler has to be exactly half as strong as the strongest channeler. Or to put it differently, a channeler x standard deviations away from the mean on the weak side, must be exactly as far from the mean as a channeler x standard deviations away on the strong side.
RJ has also said that 62.5% of channelers are strong enough to become Aes Sedai. This means that Daigian – who is the weakest possible Aes Sedai – lies exactly on this margin. And it then means that 12.5% of all female channelers lie between Daigian and the average strength woman.
Since it has been strongly suggested that Lanfear is the strongest possible woman, we therefore know that 12.5% of all female channelers lie between Daigian and the channeler who has 50% of Lanfear’s strength.
So the basic rule is that the average channeler has to be exactly half as strong as the strongest channeler. Or to put it differently, a channeler x standard deviations away from the mean on the weak side, must be exactly as far from the mean as a channeler x standard deviations away on the strong side.
RJ has also said that 62.5% of channelers are strong enough to become Aes Sedai. This means that Daigian – who is the weakest possible Aes Sedai – lies exactly on this margin. And it then means that 12.5% of all female channelers lie between Daigian and the average strength woman.
Since it has been strongly suggested that Lanfear is the strongest possible woman, we therefore know that 12.5% of all female channelers lie between Daigian and the channeler who has 50% of Lanfear’s strength.
Ugh, just lost half an hour of typing. I'll try again.
I've never delved into a one power discussion before, but as a stats teacher I thought I might be of some use.
To the above, and especially the bolded - yes the first statement is correct, assuming that's what RJ said, but it has nothing to do with the second statement. The second one is fallacious.
An example given above had a mean of 1 and a standard deviation of 4.1, but that was a little abstract, so why don't we use a real example? The average male height in the US is 5 foot 10 or so. That doesn't mean that the maximum possible male height is 11 foot 8, no one has ever even come close to that. All that it means is that if you took all the males in the US, added up their heights, and divided by that number of males, you'd get a mean of 5 foot 10. Shortest or tallest has no relation to that mean, in and of itself.
The second component to a bell curve is standard deviation, sort of like an 'average spread' of the curve. The standard deviation is around 3 inches (according to a quick internet search) for male height. According to the way that normally distributed data are distributed (the bell curve follows certain rules, and most things in nature are normally distributed, which makes it a heck of a lot easier to analyze stats), that just means that 68% of all males will be between 5 foot 7 and 6 foot 1 (+ or - 1 standard deviation from the mean). But even if you're 3 SD's above the mean, or even if you're the tallest man in the world, it doesn't relate to the mean at all, any more than any number or place on the normal curve does.
(note: of course, with dwarfism there would actually be a little bump in the lower part of the real distribution of height, but let's say we're talking about 'height of people not affected by a physical condition' )
In this power example, then, Lanfear can be ten times stronger than the average Aes Sedai, a hundred, whatever - ratio isn't relevant to a normal curve. Normal curve only talks in terms of probability, so if Lanfear was 3 standard deviations above the mean, it would mean that there's only a .15% chance of someone being stronger than her in the population (as 99.7% of all scores fall within +/- 3 SD of the mean, and the rest has to be split on both ends, meaning .15% below 3 SD below the mean and .15% above 3 SD above the mean). My guess is that Lanfear is even rarer, maybe 4 or 5 SDs above the mean. Regardless, that is meaningless (no pun intended) with regards to her strength relative to other channellers. She could be 1000 times as strong as the channeller that sits perfectly at the middle of the distribution, or 1.5 times as strong. She can still fit perfectly fine into a bell curve of channellers.
With regards to the problem of zero - practically, that's not so much a problem. As I've already mentioned, only .15% of the population falls below 3 SDs below the mean, and that number gets exponentially smaller with each SD you get away from the mean. Taking height as an example, then, as I said you're at 5 foot 1 when you're 3 SDs below the mean. You still have 20 more standard deviations to go before you get to zero, so by the time you get to zero, although there's practically a CHANCE that you could get someone who has zero height, the chances of that happening even assuming it was physiologically possible would be essentially one in infinity, close enough. So the fact that there are physiological limitations doesn't mean that a significant part of the population has power (or height, or whatever) slightly above zero and then hits a wall. For the most part, the zero cutoff is a non-issue in measurement, which is why it's perfectly acceptable to describe things as conforming to a bell curve, even when some of the extreme aspects of a bell curve aren't perfectly replicable in real life. I'd say RJ would be totally justified in describing power as fitting a bell curve, without having to qualify 'except for specific theoretic mathematical points that make very little difference in reality'.
On a Bell Curve (Normal Distribution) the Mean and the Average are identical.
The Bell Curve revisited
29/10/2012 09:44:09 AM
- 1429 Views
Re: The Bell Curve revisited
29/10/2012 10:21:27 AM
- 819 Views
That's incorrect...
29/10/2012 10:26:49 AM
- 1387 Views
Re: That's incorrect...
29/10/2012 10:36:32 AM
- 834 Views
Re: That's incorrect...
29/10/2012 10:40:27 AM
- 683 Views
Re: That's incorrect...
29/10/2012 10:42:57 AM
- 679 Views
Hehe...There are a few disputing it vocally. Whether they're in their right mind, well...
29/10/2012 10:45:07 AM
- 769 Views
Re: Hehe...There are a few disputing it vocally. Whether they're in their right mind, well...
29/10/2012 10:49:49 AM
- 660 Views
Re: Hehe...There are a few disputing it vocally. Whether they're in their right mind, well...
29/10/2012 10:56:37 AM
- 748 Views
It's only as skewed as it seems when you make the assumption that the Forsaken
31/10/2012 04:34:11 AM
- 959 Views
RJ the physicist didn't know math, so that Shannow could be right...
29/10/2012 02:11:19 PM
- 718 Views
Re: RJ the physicist didn't know math, so that Shannow could be right...
29/10/2012 02:37:33 PM
- 711 Views
there are dozens of reasons for this
29/10/2012 08:18:18 PM
- 725 Views
Re: there are dozens of reasons for this
29/10/2012 09:07:35 PM
- 653 Views
Again I don't argue that genetics play no role
30/10/2012 01:57:24 AM
- 623 Views
Once again just so,we are clear on my stance with Genetics and Strength
30/10/2012 03:27:11 PM
- 674 Views
That the 1000 Novices aren't a random sample of the population?
29/10/2012 08:23:47 PM
- 608 Views
And why would it be biased towards those with lower strength?
29/10/2012 09:11:25 PM
- 603 Views
Absolutely no reason...
30/10/2012 01:35:35 AM
- 714 Views
Re: Absolutely no reason...
30/10/2012 06:43:54 AM
- 611 Views
Only if it was a random sampling. Which this is not.
30/10/2012 01:58:34 PM
- 688 Views
That's exactly the point. I want you to explain why it wasn't random.
30/10/2012 02:14:59 PM
- 617 Views
It wasn't random because it was a self-selected sample!
30/10/2012 02:43:03 PM
- 635 Views
Re: It wasn't random because it was a self-selected sample!
30/10/2012 02:47:30 PM
- 637 Views
Go read a stats text will you?
30/10/2012 02:54:16 PM
- 629 Views
Done
31/10/2012 09:34:11 AM
- 1300 Views
You seem to have perfected whining to a Talent...
10/11/2012 10:14:19 PM
- 882 Views
Re: You seem to have perfected whining to a Talent...
11/11/2012 11:37:16 AM
- 684 Views
Seriously? I went and looked at some statistics books, and you won't even reply?
01/11/2012 12:13:49 PM
- 661 Views
Yes that totally makes sense
30/10/2012 08:07:16 AM
- 754 Views
That's not what happened...
30/10/2012 02:01:52 PM
- 669 Views
I hate to get into these things
29/10/2012 05:45:50 PM
- 781 Views
I would love for you to be right, because it would solve all our problems, but 0 is the challenge...
29/10/2012 07:56:34 PM
- 724 Views
In the truest sense, you are probably right that it is skewed
29/10/2012 08:20:52 PM
- 765 Views
Overwhelm Lanfear, not match her. *NM*
29/10/2012 08:26:09 PM
- 379 Views
Truth is, Moiraine was being overly optimistic...
29/10/2012 08:39:17 PM
- 689 Views
You're pathetic...
30/10/2012 01:20:01 AM
- 619 Views
The quote isn't specific
30/10/2012 08:32:36 AM
- 739 Views
Yet neither of them are at full potential and at least equal a Forsaken
30/10/2012 03:45:24 PM
- 1227 Views
Re: In the truest sense, you are probably right that it is skewed
29/10/2012 09:10:27 PM
- 672 Views
Lots of people mean perfectly normal distribution when they say it
30/10/2012 05:25:35 PM
- 625 Views
Couldn't the Towers method of obtaining Aes Sedai be to blame?
30/10/2012 12:04:01 AM
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Re: Couldn't the Towers method of obtaining Aes Sedai be to blame?
30/10/2012 09:33:44 AM
- 740 Views
Are you sure about that?
30/10/2012 12:03:43 PM
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Re: Are you sure about that?
30/10/2012 12:19:34 PM
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That doesn't seem a coherent narrative to me
30/10/2012 04:26:25 PM
- 936 Views
Sharina did not have the Spark, nor did Nicola
30/10/2012 05:16:40 PM
- 748 Views
Re: Sharina did not have the Spark, nor did Nicola
30/10/2012 05:54:41 PM
- 641 Views
We do not know if Cadsuane or any of the Forsaken are Sparkers
30/10/2012 10:33:55 PM
- 766 Views
Re: We do not know if Cadsuane or any of the Forsaken are Sparkers
31/10/2012 12:30:52 AM
- 717 Views
A handful of examples are all we have and we have proof that an extremely strong Channeler
31/10/2012 02:58:57 AM
- 547 Views
you're confusing 2 things
30/10/2012 04:27:32 AM
- 800 Views
Re: you're confusing 2 things
30/10/2012 09:21:39 AM
- 726 Views
Not true...
30/10/2012 11:49:57 AM
- 752 Views
One thing
30/10/2012 05:23:17 PM
- 715 Views
That's the problem. The BC RJ has "built" has a minimum and a maximum value
30/10/2012 05:48:55 PM
- 729 Views