newsletter service. Do you’ve any? Kindly allow me understand in order that

I could subscribe. Thanks. ]]>

I was meaning to comment on this earlier and got side tracked by RL.

Take home part:

The use of n − 1 instead of n in the formula for the sample variance is known as Bessel’s correction, which corrects the bias in the estimation of the sample variance, and some, but not all of the bias in the estimation of the sample standard deviation.

The problem arises because of taking the square-root of a random variable, and it is that which introduces the bias. Since the square-root is a “compressive nonlinearity”, that causes the square-root of an unbiased estimator of variance (Bessel’s variance) to be biased low.

It is this which leads to an underestimation of the true error of the mean, and in turn to a too-high of a false rejection rate.

]]>Thanks for the article – I’ve had a read and very interesting. I’ll try his revised calculation out. This is the “bias-corrected estimator suggested by Doran et al (1992)”.

For the standard deviation of the sample I am using the 1/(N-1) version, i.e. Bessel’s correction. In Matlab this is simply the function std().

]]>You once wrote, why did the editor post an article at tAV? You may remember that it was an obviously confused individual with a post that would be shredded by the readers. I think you may have answered your own question with these baby step posts into stats.

The fun is in the puzzle and the intent is for clarity to those who don’t have the backgrounds to find it.

]]>Wikipedia’s article on error of the mean has a reference to Bence that relates to this, which I downloaded and briefly read over.

James R. Bence (1995) Analysis of short time series: Correcting for autocorrelation. Ecology 76(2): 628 – 639

He does similar comparisons to what you did. I didn’t look at the article closely to see how much agreement there was being your results and his, but it might be a good article to look at to track down the breakdown of the formal results for small *N*.