Re: stat: standard deviation

[Allin C. <cot...@wf...>]

On Sat, 30 Aug 2014, Petr Mikulik wrote:

> In gnuplot, the "stat" command calculates "Std Dev:" and "STATS_stddev_x" as
>     sqrt( SumOfSquares / n )

That's the maximum likelihood estimator (MLE) of the population 
standard deviation. It happens to be biased, although it's 
consistent (converges in probability on the population standard 
deviation in large samples).

> In GNU R, OpenOffice et al, the function stddev() calculates
>     sqrt( SumOfSquares / (n-1) )

That's the "sample standard deviation", an unbiased estimator of the 
population standard deviation if the relevant degrees of freedom are 
indeed n - 1.

> while function stddevp() returns
>     sqrt( SumOfSquares / n )
>
> That's confusing. Why has gnuplot chosen the other possibility (this smaller
> stddev estimate means that the average value of the statistical ensemble
> is known).
>
> What to do with that?

If what you're saying is correct as a description of what gnuplot 
does then it's arguably idiosyncratic of gnuplot to give the MLE 
when most statistical software gives the sample standard deviation.

It woud be sufficient either to state in the documentation that 
gnuplot gives the MLE or to switch to the sample standard deviation. 
I don't see much to be said for more complicated options.

Allin Cottrell