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10-27-2012, 11:36 AM
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Originally Posted by barneyg View Post
Why the hell do you think the bolded creates a bell curve? Please explain. You keep arguing two points at once. One of those is completely wrong, the other is likely right:

a) the adjustment leads to a bell curve (completely wrong)
b) the adjustment shouldn't be uniform (likely right).

You should drop a) because it's just not true. If anything, the ONLY thing we can be mathematically sure of is that the adjustment retains the shape of the distribution (relevant). Iain's adjusted graph is not any closer to a bell curve than the original data is.

Again, the only reason why your "mathematical eye" was able to con you into thinking the adjustment creates a bell curve (other than perhaps your mind looking for a bell curve) is the arbitrary bins used to create the frequency graph. If the adjusted data graph used [4*F,7*F], [8*F,11*F] and so on instead of [4,7], [8,11], you would clearly see that the shape of the adjusted graph is exactly the same as the original.
If the graph is not acurate for whatever then perhaps that should have been the initial response to my complaint about it. I guess its useless in this debate.

You take every NHL season ever and adjust all the stats to 82gp and 6gpg (skaters). What is that? What have you done to the seasons?

I alter every result in a set of test scores so everyone gets 60%. Someone asks to audit the tests. Now I have to go in and alter the mark for each question. What happens to the 0's and 100%'s achieved for individual questions? If the original result was 40% on a particular test, do I just add 50% to each individual question?

I can show you that graph.
---------------------------- 60%
____________________ 40%

It doesn't matter how I shape it, the two graphs would be parallel in some geometry. But now I'm giving value to 0's. I'm creating value where none existed before.

If I use some multiplier so as not alter the 0's and perhaps the 100's then I've completely changed the relationship between the grades on individual questions. My graphed results for a single test would look like two uniquely formed pieces of string with the ends tied together. Perhaps even a circle. There may be some visible correlation since the new curve comes from the values of the first curve but the shape would clearly be distorted.

Both these methods fail to maintain either the integrity or relationship of the grades recieved for each question on each individual test.

Now suppose that to prevent cheating I have more than one test. They have different questions and even different numbers of questions. Some of the questions are not changed however except perhaps the wording.

I need different formulae if I want to keep the 0's. In that case people who got identical results on questions that every test had might now have different results.

If I don't care about 0's then many would have different results on questions that they originally had identical results.

Making all the tests have the same final result only leads to errors on the individual test questions.

Call it whatever you want but making all the seasons exactly equal with respect to gp, gpg, players per team can only lead to errors.

The only reason to even do this is a misplaced notion of bell curving. The belief that there exists an average. The refusal to accept extreme outliers as a possible real outcome. The 'bell curve' is a way of thinking that permeates evaluation and prediction of productivity.

You need to read that study or read it differently. Ignore the data and read what the authors purpose was and how the results support it.

If you are averaging and making all the seasons have the same values, if you are forcing the outliers to conform to average then you are bell curving whether you see the physical thing or not.

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