Re: stat: standard deviation

[sfeam <sf...@us...>]

On Saturday, 30 August 2014 07:39:57 AM pl...@pi... wrote:
> On 08/30/14 02:10, Allin Cottrell wrote:
> > 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
> 
> 
> This should be clearly stated up front without the need for digging the doc.
> 
> If gnuplot is calculating the "sample standard deviation" ( which would 
> seem to be the most appropriate when given a sample of data ) then that 
> is what it should label it as when outputting the result, rather than 
> just 'std dev'.  The note about degrees of freedom assumption could go 
> in the doc.

Gnuplot "stats" is not calculating the sample standard deviation.
That is exactly the point being raised.

The standard deviation, skew and kurtosis values all use a full-population
assumption rather than being corrected for finite sampling.

I definitely agree this should be clearly stated in the documentation,
and I'll work on editing gnuplot.doc to include the relevant equation
for each variable STATS_*.

However that does not resolve the question of whether gnuplot should 
be reporting the finite-sampling assumption values instead of, or in
addition to, what it reports now.

By the way, this same point came up a while back with regard to the
calculation of the bandwidth in "smooth kdensity".
The code  currently uses the population standard deviation, but arguably
should use the sample-based standard deviation instead.
The question did not generate any discussion at that time.     

	Ethan

> Uneducated used of these kind of statistics is pretty common, perhaps 
> more so in population that are going to depend on a plotting program to 
> provide them, rather than having existing knowledge and software to 
> provide the stats.  It would be good to be as clear as possible about 
> what is being output with an assumption that user probably has little 
> knowledge of the subject.
> 
> A link to some starting point to further understanding as a note in help 
> may be valuable.
> 
> Peter.