You're right, and that proves my point - here are the calculations and the evidence... - Edit 4
Before modification by Shannow at 18/12/2009 07:56:21 AM
Yes, true, but I think if you take a subset from a bell curve, that subset will also have the characteristics of a bell curve.
Not if the subset is not a random sampling. And the Tower is anything but a random sample. IT has several criteria of exclusion, like removing all women below a particular strength range, not having any women who do not come asking to be made AS, etc. As a result, the distribution will be skewed.
Further, if a subset has a distribution that violates the distribution of the superset, yoy have to assume an error in sampling.
See what I just said about subsets. If that is wrong, then you are right.
That is indeed wrong.
Why not? The median is just the person in the middle, not necessarily the middle of the range. For example, in the following set of numbers:
5, 20, 500, 1000, 5,000
500 is the median. True, in a bell curve, mean=median=mode, so you could have a distribution like this:
10, 20, 30, 40, 40, 60, 80
mean = median = mode = 40
Note that the middle of the range between 10 and 80 is 45.
You're assuming a discontinuous range then. That has absolutely no basis in fact. There is not one shred of proof that certain strengths between the lowest and highest strengths cannot exist, which is what you're implying by having 5 and 20 in your list, but not 10, 15, etc.
See above.
See above!
Not necessarily.
Yes necessarily. the mistake you're making is that you think the bell curve distribution is a hypothesis based on random statistical sampling of all channelers. In that case, it is indeed possible that you'll have no person occupying certain strength scales, which will shift the mean.
In this case however, RJ has declared that all his imaginary characters follow this law. And has given absolutely no indication that there are levels which no human can occupy between the minima and the maxima of the range.
I assumed Moiraine and old Siuan were equals, then Siuan was half her old strength (4K and 2K). It seemed a reasonable place to put them within the distribution, since Moiraine is one of the strongest AS. I don't know if 3K is the correct place to put an average AS, but it can make sense in a bell curve (i.e., the average channeler doesn't have to be in the middle of the range).
No it cannot. Not in this bell curve. For that, you'll have to prove that no human has strengths like 12000, 11,000, etc. Which is not true at all.
The distribution is based off the 68-95-99.7 rule (wiki it). In brief, 68% of the population of interest is within plus or minus one SD of the mean, 95% within two, and 99.7% within 3.
I'm quite aware of this, thank you. Why this is being pointed out is my (as yet unanswered) question.
Well yes, but so has RJ. OK, Morgase and a bunch of no-name novices/wilders we've never met, then.
No he has not! There are women thrown out of the Tower because they're too weak. There are women who become Accepted, but not AS. All these women are rarer than women who can become AS, but the Tower doesn't know because they don't actively hunt out all channelers.
Sorry, I skimmed most of this thread, but I saw that people were using shielding as a way to measure strengh. For example, 3 people shielding Semi vs. 2 for egwene, etc. If that is not good for measuring strength (and I don't think it is the best way, really), then forget that point.
The shield theory works okay within the same gender. But we know men can shield men more easily than men can shield women and vice versa. So I think using this to compare male and female strengths is ridiculous.
The Tower mostly excludes people who are too weak to test for the shawl. Not only do we know this for a fact, we actually know what percentage of women are excluded for this reason. 37.5% to be precise.
That means 37.5% of women are weaker than Dagian, by the way. The one indisputable fact we have in this debate.
Now, if you took a random sample, you would expect the average to be more or less equal to the average of the entire population. But this sample (the Aes Sedai)is not random, in fact, it excludes 37.5% of women who are weaker than Dagian. Thereofore, a sample consisting only of Aes Sedai would be skewed to the stronger side of the range. In other words, the average for this sample would fall above the average for the entire population.
Therefore, the average Aes Sedai is stronger than the average woman. Now from my recollection, women like Alanna and Verin are already above average for an Aes Sedai. That means, according to your theory, Alanna and Verin would each be more than 50% as strong as Rand.
But let's go back to the stats for a moment.
So we know now that the average strength woman must fall somewhere between Dagian and the average Aes Sedai. So what we are saying is that what we would consider a "weak" modern day Aes Sedai is actually comparable to the average strength woman from the general channeling population.
And according to you, such a weak Aes Sedai must be 50% as strong as Lanfear, and EFFECTIVELY, 50% as strong as Rand.
See the problem yet?
Now let's extrapolate a bit further.
So we see that out of our sample of 1000 women (the Tower), only 5 women (6 if you include Cadsuane) are of Moiraine strength or higher. I think they were given in New Spring as Moiriane, Siuan, Lelaine, Romanda and maybe Elaida. (Someone who has actually read New Spring might correct me on this).
Anyway, 5 out of 1000 gives you a percentage of 0.5, meaning that 99.5% of observations do not fall this far away from the mean. Let's double the number of people this far from the mean to 10 (to account for Cadsuane, and others who might not have been picked up, and let's also include those equi-distant from the mean on the lower end of the spectrum, like Dagian etc.), and make it a round 95%, for simplicity's sake. And what do you know. This means that Moiraine, Lelaine and Romanda's level is 2 standard deviations away from the White Tower mean (which in this case is the average Aes Sedai, not the average woman, by the way).
Let's say that again, just to hammer it down. In the 1000 woman sample from the Tower (which is already SKEWED TO THE STRONGER SIDE), someone of Moiriane's strength is 2 standard deviations above the mean. Wow.
That means you would be hard pressed to find a stronger channeler than her. That also means that Dagian is at least 2 standard deviations below the average Aes Sedai in strength.
So, since we know from Siuan that she is currently around one third of her previous strength (and only barely above Dagian in strength) we can now extrapolate the standard deviation from this.
Siuan strongly suggests that if she was two thirds he old strength, she would be of about average Aes Sedai strength.
Therefore, we can estimate that Moiraine is about half again as strong as the average woman. And since we have established that Moiraine is about 2 standard deviations from the mean, that means that the standard deviation - for Aes Sedai - equates to about a quarter of the average Aes Sedai's strength.
So, since we know that the average Aes Sedai is stronger than the average woman, it means that according to your model, we have to put the average Aes Sedai at more than 50. Let's put her at 60, just to have a round figure. It would'be be materially different if it was 55 or 56 or whatever. Anyway, if we take the average Aes Sedai to be 60, then one standard deviation above that would take you to 75, and two standard deviations above that would take you to 90. So Moiraine's level would be 90!
And since we know that Egwene is as strong as Amys and Melaine combined, (Amys is equal to Moiraine by the way), that means that Egwene would have a strenth of approximately 90 + 75 = 165.
That gives us a tiny problem, seeing as Lanfear, the strongest woman ever, is only on 100 on the female scale.
Clearly, therefore, the average Aes Sedai strength has to be FAR below 60, and therefore the average woman's strength has to be far below 50.