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Re: Chi Square Areas

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  • Subject: [mg110956] Re: Chi Square Areas
  • From: Bill Rowe <readnews at>
  • Date: Wed, 14 Jul 2010 05:35:11 -0400 (EDT)

On 7/13/10 at 5:26 AM, s123 at (Steve) wrote:

>Norbert provided a particularly elegant solution and also pointed
>out a small inconsistency in my question. The values I needed
>returned were the critical values not the areas as I had stated at
>the beginning of my post.

>Below is a parameter-consistent comparison of my solution and

>DOF = 8;
>confidence = .90;
>p = (1 - confidence)/2
>ChiPDF = PDF[ChiSquareDistribution[DOF], x]
>Plot[ChiPDF, {x, 0, 50}]
>guessvalue = 2.5;
>stevesolution =
>FindRoot[NIntegrate[ChiPDF, {x, CriticalValue, Infinity}] ==
>p, {CriticalValue, guessvalue}];
>stevesolution = stevesolution[[1, 2]]
>norbertsolution =
>InverseCDF[ChiSquareDistribution[DOF], confidence + p]
>difference = stevesolution - norbertsolution

In case you are not aware of it, the difference between a
solution using FindRoot and NIntegrate and one using either
InverseCDF or Quantile is due to small differences in rounding
resulting from different algorithms and machine precision
numbers. FindRoot and NIntegrate are general purpose root
finding and numerical integration tools. Quantile and InverseCDF
are more specialized and are certain to be more optimized for
doing this particular computation. Consequently, these will
execute faster and will yield better results.

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