 "Mark R. Diggory" <mdiggory@latte.harvard.edu>
wrote:
> Well, I think should step back and ask a few design
> questions concerning the objects that will use these
> Sample/Population variances and that will assist us
> in their own design.
>
> 1.) Is it the case that a covariance matrix could be
> built off of "either" Sample or Population
Variances?
Yes. With the remark that the whole matrix is filled
with either sample (co)variances or population
(co)variances.
> 2.) Are there other applications of Sample/Pop
> Variances which we want to implement, if so what are
> they? Are they interchangeable in these cases?
>
> 3.) Do we want to add methods to the
> Descriptive/Summary/StatUtils stats
> to capture both cases?
I can not answer these two questions. However, I do
know that you can calculate any method that uses
(co)variances with either population or sample
estimates. So, my suggestion would be to incorperate
it such a way that it deploys a default (my preference
would be sample) but leaves the option open to use
population versions instead, without calling a
complete new class. Essentially, as soon as you go
with the population variance, all derived methods have
to go with that to, including correlations,
regressions pca, GLM etc.
> What this and the Remedian case are somewhat
> convincing me of is that, in the SummaryStatistics
> case; you need to know what your want before you
> start adding values to the Statistic, which
> constitutes a sort of configuration environment,
> while in the "DescriptiveStatistics" case, one can
> choose these aspects afterward, as the statistic is
> calculated after all the values are known.
>
> This means that you either have to calculate both
> the PopulationVariance and SampleVariance in the
> SummaryStatistics case, or configure it to use one
or
> the other. While in the DescriptiveStatistics case,
> you can just call the appropriate method to return
> that statistic.
If you want to set it very blunt, the only difference
is the N/(N1) (or reciprocal of that) factor, which
always can be added.
That is also why I think that incorporating is the
best way.
With the median, this might be different.
Cheers,
Kim
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