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discuss Algorithm II and AlexC's similar algorithm |
Algorithm III does not compute |
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I have derived and added the update formulas (only the results) for the unbiased/biased variance. The clearly shown that the (old) second algorithm which was in dispute was wrong, so I removed it. I have also removed the example which just shows some numbers (was it a weak numerical proof?) and does not provide any insight on how the formulas work. It was not clear whether the algorithms were for biased or unbiased estimators, so I added comments on it. BurkayDonderici
== Algorithm III does not compute ==
Hi,
In the mathematical equation for m(new), I don't agree with (n+1) in the denominator. I believe that the denominator should be simply (n).
I didn't want to edit the entry since I am not a mathematician. CAN SOMEONE WHO IS PLEASE MAKE THE APPROPRIATE COMMENTS .
If you plug some numbers into the equation shown, and compare your results to what a spreadsheet calculator gives, you will see that there is a significant error.
I tested the show equation in MS Excel. I used a population of 404 values generated by the RANDBETWEEN(0,1000) function.
I used 4 methods to calculate the average at each point through the population.
Method 1) (Cumulative total)/(Number of samples) [this calculation was done for each sample for tracking purposes
Method 2) Previous average + new contribution. M(new) = M(old) + ( (M(old)-X(new))/n )
Method 3) Previous average + new contribution. M(new) = M(old) + ( (M(old)-X(new))/(n+1) )
Method 4) I then used the Average function on the total population.
Methods 1 and 2 produced the same results all the way through the population and matched Method 4's result for the whole population.
However, Method 3 always produced a lower result, and the error (which started significatly) reduced as the number of samples grew.
Regards,
Napoleon BlownApart
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