Stdev of RMS running average?

[Lance Norskog <go...@gmail.com>]

How should an Root-Mean-Square running average calculate the Standard
Deviation?
Should it tot up the raw samples and return as the standard version?
Or should it tot up the squares and return the square root?

-- 
Lance Norskog
goksron@gmail.com

Re: Stdev of RMS running average?

[Ted Dunning <te...@gmail.com>]

If you change RunningAverageAndStdDev so that you can set the mean to a
fixed value, then the standard deviation that comes out *is* RMS error.

On Sat, Mar 19, 2011 at 2:30 PM, Lance Norskog <go...@gmail.com> wrote:

> More precisely: if I make a variant of the RunningAverage classes to
> do RMS instead of simple mean, what should the StDev subclass do? And
> clearly the answer is 'simple standard deviation'.
>
> On Sat, Mar 19, 2011 at 8:45 AM, Ted Dunning <te...@gmail.com>
> wrote:
> > You can turn it into the standard deviation by doing RMS deviation from
> the
> > estimated mean.
> > And I am totally on-board with Sean in being a bit confused about the use
> of
> > the sd of a real RMS error.
> >
> > On Sat, Mar 19, 2011 at 2:28 AM, Sean Owen <sr...@gmail.com> wrote:
> >>
> >> If you're asking if root-mean-square is actually just the standard
> >> deviation of something, because it sort of looks like a population
> >> standard deviation formula -- no it isn't just the standard deviation
> >> of something.
> >
>
>
>
> --
> Lance Norskog
> goksron@gmail.com
>

Re: Stdev of RMS running average?

[Sean Owen <sr...@gmail.com>]

Well there are three activities here:

1) Construct some series of real numbers
2) Calculate statistics on that series, like mean or variance /
standard deviation (or higher moments like skew or kurtosis...)
3) Do something else with those numbers

Root-mean-square has meaning in the context of evaluating error of
predictions from reality, and plays out as:

1) In a series of predictions, square each difference between
prediction and reality
2) Calculate the mean
3) Take the square root of that mean

RunningAverage does #2, and its subclass RunningAverageAndStdDev also
does #2 but calculates the standard deviation too (square root of
second moment).

RunningAverage does not do #1-#3, and shouldn't. RMS is not another
statistic you calculate on a series -- it's not an nth moment of a
series. What are you trying to do then?

On Sat, Mar 19, 2011 at 9:30 PM, Lance Norskog <go...@gmail.com> wrote:
> More precisely: if I make a variant of the RunningAverage classes to
> do RMS instead of simple mean, what should the StDev subclass do? And
> clearly the answer is 'simple standard deviation'.

Re: Stdev of RMS running average?

[Lance Norskog <go...@gmail.com>]

More precisely: if I make a variant of the RunningAverage classes to
do RMS instead of simple mean, what should the StDev subclass do? And
clearly the answer is 'simple standard deviation'.

On Sat, Mar 19, 2011 at 8:45 AM, Ted Dunning <te...@gmail.com> wrote:
> You can turn it into the standard deviation by doing RMS deviation from the
> estimated mean.
> And I am totally on-board with Sean in being a bit confused about the use of
> the sd of a real RMS error.
>
> On Sat, Mar 19, 2011 at 2:28 AM, Sean Owen <sr...@gmail.com> wrote:
>>
>> If you're asking if root-mean-square is actually just the standard
>> deviation of something, because it sort of looks like a population
>> standard deviation formula -- no it isn't just the standard deviation
>> of something.
>



-- 
Lance Norskog
goksron@gmail.com

Re: Stdev of RMS running average?

[Ted Dunning <te...@gmail.com>]

You can turn it into the standard deviation by doing RMS deviation from the
estimated mean.

And I am totally on-board with Sean in being a bit confused about the use of
the sd of a real RMS error.

On Sat, Mar 19, 2011 at 2:28 AM, Sean Owen <sr...@gmail.com> wrote:

> If you're asking if root-mean-square is actually just the standard
> deviation of something, because it sort of looks like a population
> standard deviation formula -- no it isn't just the standard deviation
> of something.
>

Re: Stdev of RMS running average?

[Sean Owen <sr...@gmail.com>]

Root-mean-square means the square root of the mean of the squared
differences between the correct answer and observed answer.

If you want to calculate the standard deviation of those squared
differences, sure you can do that in the usual way. I don't know of a
statistical use for that figure.

If you're asking if root-mean-square is actually just the standard
deviation of something, because it sort of looks like a population
standard deviation formula -- no it isn't just the standard deviation
of something.

On Sat, Mar 19, 2011 at 4:04 AM, Lance Norskog <go...@gmail.com> wrote:
>
> How should an Root-Mean-Square running average calculate the Standard
> Deviation?
> Should it tot up the raw samples and return as the standard version?
> Or should it tot up the squares and return the square root?