Comments on: How to calculate correlation accurately http://www.johndcook.com/blog/2008/11/05/how-to-calculate-pearson-correlation-accurately/ The blog of John D. Cook Sat, 11 Feb 2012 22:42:11 -0500 http://wordpress.org/?v=2.8.4 hourly 1 By: browser http://www.johndcook.com/blog/2008/11/05/how-to-calculate-pearson-correlation-accurately/comment-page-1/#comment-13472 browser Tue, 17 Feb 2009 17:06:13 +0000 http://www.johndcook.com/blog/?p=795#comment-13472 Great set of articles here! I came across them looking for some justification for the "numerically stable" pseudocode given in the Wikipedia article on correlation. However, the pseudocode is currently marked "Citation needed". Anyone knows where that code comes from? Great set of articles here!

I came across them looking for some justification for the “numerically stable” pseudocode given in the Wikipedia article on correlation.

However, the pseudocode is currently marked “Citation needed”. Anyone knows where that code comes from?

]]> By: flashman http://www.johndcook.com/blog/2008/11/05/how-to-calculate-pearson-correlation-accurately/comment-page-1/#comment-10876 flashman Sat, 13 Dec 2008 04:46:18 +0000 http://www.johndcook.com/blog/?p=795#comment-10876 Thank Mr.John for quick reply. Now I have issues with the comparison macro block in two images so your information is very useful with me. Thanks again & best regards. Thank Mr.John for quick reply.
Now I have issues with the comparison macro block in two images so your information is very useful with me.
Thanks again & best regards.

]]> By: John http://www.johndcook.com/blog/2008/11/05/how-to-calculate-pearson-correlation-accurately/comment-page-1/#comment-10874 John Sat, 13 Dec 2008 03:58:27 +0000 http://www.johndcook.com/blog/?p=795#comment-10874 If sx is zero, all your x's are the same. If sy is zero, all your y's are the same. In either case, you have a degenerate situation. I suppose you could say the correlation is zero since a constant is independent of any random variable, but correlation coefficient implies there's a bivariate normal model in the background and that assumption is violated if one of the components is constant. If sx is zero, all your x’s are the same. If sy is zero, all your y’s are the same. In either case, you have a degenerate situation. I suppose you could say the correlation is zero since a constant is independent of any random variable, but correlation coefficient implies there’s a bivariate normal model in the background and that assumption is violated if one of the components is constant.

]]> By: flashman http://www.johndcook.com/blog/2008/11/05/how-to-calculate-pearson-correlation-accurately/comment-page-1/#comment-10873 flashman Sat, 13 Dec 2008 03:53:57 +0000 http://www.johndcook.com/blog/?p=795#comment-10873 Dear Mr.John Thank for your entry. What will happen if (sx==0) or (sy==0) in the first expression. Example I want to calculate the correlation of two arrays, and with the first array, all elements are equal. Could I use the first expression. Thanks! Dear Mr.John
Thank for your entry.

What will happen if (sx==0) or (sy==0) in the first expression.
Example I want to calculate the correlation of two arrays, and with the first array, all elements are equal. Could I use the first expression.

Thanks!

]]> By: Ravi http://www.johndcook.com/blog/2008/11/05/how-to-calculate-pearson-correlation-accurately/comment-page-1/#comment-10325 Ravi Fri, 28 Nov 2008 13:46:28 +0000 http://www.johndcook.com/blog/?p=795#comment-10325 Dear Karl and John, I could not completely understand the problem in computation of averages. Can you please guide to understand these kinds of problems that arise in various computaional algorithm. Regards, Gautam Dear Karl and John,

I could not completely understand the problem in computation of averages. Can you please guide to understand these kinds of problems that arise in various computaional algorithm.

Regards,

Gautam

]]> By: John http://www.johndcook.com/blog/2008/11/05/how-to-calculate-pearson-correlation-accurately/comment-page-1/#comment-9105 John Fri, 07 Nov 2008 00:54:04 +0000 http://www.johndcook.com/blog/?p=795#comment-9105 One of my favorite books on numerical computing is <a href="http://www.amazon.com/gp/product/0883854503?ie=UTF8&tag=theende-20&linkCode=xm2&camp=1789&creativeASIN=0883854503" rel="nofollow">Numerical methods that work</a> by Forman S. Acton. It's not specifically about statistics, and it's a little dated, but it's great on the fundamentals. One of my favorite books on numerical computing is Numerical methods that work by Forman S. Acton. It’s not specifically about statistics, and it’s a little dated, but it’s great on the fundamentals.

]]> By: Karl Ove Hufthammer http://www.johndcook.com/blog/2008/11/05/how-to-calculate-pearson-correlation-accurately/comment-page-1/#comment-9095 Karl Ove Hufthammer Thu, 06 Nov 2008 18:37:09 +0000 http://www.johndcook.com/blog/?p=795#comment-9095 Thanks for posting this. I enjoy reading about numerical issues in statistical computing. It’s surprising to many that calculating statistics from such simple formulas could be problematic. Even something as simple as calculating the sum or average of a set of numbers can be done in numerical ‘not so smart’ ways. For instance, sorting the values before adding them (and then adding the smaller numbers before the larger ones) should give more accurate results. I tried looking at source code for R, to find out how it calculated averages, and if it used this method. If I remember correctly (and read the code correctly), it first adds all the numbers and divides the sum by <i>n</i> to get a ‘naïve’ average, and then adds the average difference between the numbers and this average (which mathematically of course should be zero) to get a final value. Seems very clever. Do you know of any (easy to read, suitable for bedtime reading) books (or papers) on numerical calculations specifically for statistics? Thanks for posting this. I enjoy reading about numerical issues in statistical computing. It’s surprising to many that calculating statistics from such simple formulas could be problematic.

Even something as simple as calculating the sum or average of a set of numbers can be done in numerical ‘not so smart’ ways. For instance, sorting the values before adding them (and then adding the smaller numbers before the larger ones) should give more accurate results.

I tried looking at source code for R, to find out how it calculated averages, and if it used this method. If I remember correctly (and read the code correctly), it first adds all the numbers and divides the sum by n to get a ‘naïve’ average, and then adds the average difference between the numbers and this average (which mathematically of course should be zero) to get a final value. Seems very clever.

Do you know of any (easy to read, suitable for bedtime reading) books (or papers) on numerical calculations specifically for statistics?

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