The One Power Bell Curve: Proof that it is not centered on 50% of the strongest channeler's strength - Edit 2
Before modification by Shannow at 18/12/2009 09:15:07 AM
I've started a new thread specifically to focus on an analysis of the One Power Bell Curve. The thread below deals with comparing Cadsuane, Nynaeve, Egwene and others, and it took a swing towards the One Power Bell Curve topic, which interests some more than others.
I happen to be one of those who find it interesting. In any case a massive debate has arisen as to whether the Bell Curve implies that the strongest channeler is only twice as strong as the average channeler. Here I have simple proof that this is not the case:
Firstly, the only reasonably sized channeler sample that we have some in depth knowledge of is the White Tower. This sample consists of 1000 channelers.
Normally you would think that a random sample - if it is large enough - accurately reflects the general population it is drawn from. But in the case of the White Tower, RJ has specifically refuted this, by saying that 37.5% of female channelers are too weak to be tested for the shawl.
That means that the Tower sample exludes the weakest 37.5% of the channeling population. Therefore, the White Tower sample is clearly biased to the stronger side of the general channeling populations's strength range.
In other words, the average Aes Sedai is stronger than the average woman. This makes sense, since the average population's mean strength would be dragged down by the 37.5% of women who are too weak to be included in the Tower. The Tower does not have a similar exclusion on the upper side of the strength scale, which means that it is more heavily weighted in favour of stronger women at the expense of the 37.5% of weaker women.
So the one fact we can take from this is that the average Aes Sedai is stronger than the average Randland woman.
Right.
Now, if the Bell Curve was perfectly proportioned and centered on a strength of 50 (with Lanfear on 100 and the weakest woman on 0), then you would expect the average woman to sit on a strength of 50.
And that would mean that the average woman is exactly half as strong as the strongest possible woman (Lanfear in this case.)
However, if the average woman is placed at 50, then it means that the average Aes Sedai must be higher than 50, based on the the fact that the Tower sample is skewed in favour of stronger women.
And if an average Aes Sedai is higher than 50 (let's for the moment leave out the magnitude of the difference) then a strong Aes Sedai like Moiraine must be even further above 50.
And if that's the case then how strong must Egwene be - who according to Aviendha is stronger than Amys and Melaine combined?
Amys is stated as being equal to Moiriane in strength, and Melaine is stated to be as strong as a strong Aes Sedai.
Both are significantly stronger than the average Aes Sedai, who in turn is stronger than the average woman - who in a symmetrical Bell Curve is supposed to be half as strong as Lanfear.
If that's the case, then Egwene must be significantly stronger than Lanfear, the strongest woman! Clearly, this disproves the notion that the Bell Curve is centered at 50% of the strongest woman's strength.
I have deliberately left estimated strengths for the likes of Egwene, Moiraine and the average Aes Sedai out of this post, as I wanted to prove the concept first. But we have very good evidence for assigning comparative strengths to these various levels as well, should the debate go into that direction.
All I wanted to achieve with this first post is to prove once and for all that the Bell Curve that RJ referred to cannot be a normal distribution centered on the halfway mark between the weakest and strongest woman's strengths. At least, not in absolute terms.
It is far more likely that it is a relative distribution, where the distance from the mean depicts a proportional increase or decrease in strength, rather than an absolute difference in strength.
Based on the above calculation, there really is no way that a symmetrical Bell Curve centered on 50% of the maximum strength and which is based on absolute strength differences can be supported in any way.
I happen to be one of those who find it interesting. In any case a massive debate has arisen as to whether the Bell Curve implies that the strongest channeler is only twice as strong as the average channeler. Here I have simple proof that this is not the case:
Firstly, the only reasonably sized channeler sample that we have some in depth knowledge of is the White Tower. This sample consists of 1000 channelers.
Normally you would think that a random sample - if it is large enough - accurately reflects the general population it is drawn from. But in the case of the White Tower, RJ has specifically refuted this, by saying that 37.5% of female channelers are too weak to be tested for the shawl.
That means that the Tower sample exludes the weakest 37.5% of the channeling population. Therefore, the White Tower sample is clearly biased to the stronger side of the general channeling populations's strength range.
In other words, the average Aes Sedai is stronger than the average woman. This makes sense, since the average population's mean strength would be dragged down by the 37.5% of women who are too weak to be included in the Tower. The Tower does not have a similar exclusion on the upper side of the strength scale, which means that it is more heavily weighted in favour of stronger women at the expense of the 37.5% of weaker women.
So the one fact we can take from this is that the average Aes Sedai is stronger than the average Randland woman.
Right.
Now, if the Bell Curve was perfectly proportioned and centered on a strength of 50 (with Lanfear on 100 and the weakest woman on 0), then you would expect the average woman to sit on a strength of 50.
And that would mean that the average woman is exactly half as strong as the strongest possible woman (Lanfear in this case.)
However, if the average woman is placed at 50, then it means that the average Aes Sedai must be higher than 50, based on the the fact that the Tower sample is skewed in favour of stronger women.
And if an average Aes Sedai is higher than 50 (let's for the moment leave out the magnitude of the difference) then a strong Aes Sedai like Moiraine must be even further above 50.
And if that's the case then how strong must Egwene be - who according to Aviendha is stronger than Amys and Melaine combined?
Amys is stated as being equal to Moiriane in strength, and Melaine is stated to be as strong as a strong Aes Sedai.
Both are significantly stronger than the average Aes Sedai, who in turn is stronger than the average woman - who in a symmetrical Bell Curve is supposed to be half as strong as Lanfear.
If that's the case, then Egwene must be significantly stronger than Lanfear, the strongest woman! Clearly, this disproves the notion that the Bell Curve is centered at 50% of the strongest woman's strength.
I have deliberately left estimated strengths for the likes of Egwene, Moiraine and the average Aes Sedai out of this post, as I wanted to prove the concept first. But we have very good evidence for assigning comparative strengths to these various levels as well, should the debate go into that direction.
All I wanted to achieve with this first post is to prove once and for all that the Bell Curve that RJ referred to cannot be a normal distribution centered on the halfway mark between the weakest and strongest woman's strengths. At least, not in absolute terms.
It is far more likely that it is a relative distribution, where the distance from the mean depicts a proportional increase or decrease in strength, rather than an absolute difference in strength.
Based on the above calculation, there really is no way that a symmetrical Bell Curve centered on 50% of the maximum strength and which is based on absolute strength differences can be supported in any way.