Re: "Mean" of Standard deviations
Date: Thu, 17 MAY 2001 13:01:06 +0200
From: Nasser Hosseini <[EMAIL PROTECTED]>
> I wonder, if anybody out there knows, how to calculate the "mean" Standard
> deviation, if you have a number of Mean and Standard deviation based on
> DIFFERENT number of measurment:
>
> Subject 1: N1 (no. of measurment), M1 (mean), S1 (Standard deviation)
> Subject 2: N2 , M2 , S2
> ...
> Subject m: Nm , M2 , Sm
>
> i.e. Stotal = F(S1,S2,...,Sm; N1,N2,...,Nm)???
I don't have the exact expression handy, but you can derive it yourself.
Define
N = sum(i=1,m){ Ni }
M = (1/N)*sum(j=1,N){ xj } = (1/N)*sum(i=1,m){ Ni*Mi }
St = [1/(N-1)] sum(j=1,N){ (xj-M)^2 }
= Sb + Sw
where the between-group and within-group variances are proportional
to Sb0 and Sw0 given by
Sb0 = [1/(m-1)] SUM(i=1,m){ (Mi-M)^2 }
Sw0 = [1/(N-m)] sum(i=1,m)( (Ni-1)*Si }
Greg
Hope this helps.
Gregory E. Heath [EMAIL PROTECTED] The views expressed here are
M.I.T. Lincoln Lab (781) 981-2815not necessarily shared by
Lexington, MA(781) 981-0908(FAX) M.I.T./LL or its sponsors
02420-9185, USA
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Re: "Mean" of Standard deviations
If they are independent then the expectation of the mean is the mean of the expectations. Note that the usual estimate of the standard deviation is slightly biased (its expectation is not sigma). The sum of squared deviations from the sample mean, divided by n-1 is unbiased for the variance, but a slight bias is introduced when you take the square root. Details are widely available, but my library is at the office, and I do not have access to news groups there. Nasser Hosseini wrote: > > Hi everybody! > > I wonder, if anybody out there knows, how to calculate the "mean" Standard > deviation, if you have a number of Mean and Standard deviation based on > DIFFERENT number of measurment: > > Subject 1: N1 (no. of measurment), M1 (mean), S1 (Standard deviation) > Subject 2: N2 , M2 , S2 > ... > Subject m: Nm , M2 , Sm > > i.e. Stotal = F(S1,S2,...,Sm; N1,N2,...,Nm)??? > > Thanks > > /Nasser Hosseini = Instructions for joining and leaving this list and remarks about the problem of INAPPROPRIATE MESSAGES are available at http://jse.stat.ncsu.edu/ =
Re: "Mean" of Standard deviations
That's the pooled sd. If all the data were in one column then you would
have to consider the mean differences between sets or you will
underestimate the variance. To find the standard deviation for the combined
groups use
{[[sum(n(i)(M(i)**2 + var(i))] / sum(n(i))] - grand means**2} and then take
the square root.
formula from McNemar, 1969
At 11:33 PM 5/17/01 -0400, dennis roberts wrote:
>
>
>sounds like you want the overall sd ... as though you had ALL the data in
>ONE column and were calculating the sd on THAT one column
>
>the formula for TWO groups would be:
>
>variance (weighted or pooled)=
>
>[(n1-1)* var1] + [(n2-1)*var2] all divided by ... n1 + n2 -2
>
>then take the square root to get the overall sd
>
>if you have more than two groups ... just follow the same pattern
>
>
>
>=
>Instructions for joining and leaving this list and remarks about
>the problem of INAPPROPRIATE MESSAGES are available at
> http://jse.stat.ncsu.edu/
>=
>
Paul R. Swank, PhD.
Professor
UT-Houston School of Nursing
Center for Nursing Research
Phone (713)500-2031
Fax (713) 500-2033
soon to be moving to the Department of Pediatrics
UT Houston School of Medicine
=
Instructions for joining and leaving this list and remarks about
the problem of INAPPROPRIATE MESSAGES are available at
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Re: "Mean" of Standard deviations
sounds like you want the overall sd ... as though you had ALL the data in ONE column and were calculating the sd on THAT one column the formula for TWO groups would be: variance (weighted or pooled)= [(n1-1)* var1] + [(n2-1)*var2] all divided by ... n1 + n2 -2 then take the square root to get the overall sd if you have more than two groups ... just follow the same pattern = Instructions for joining and leaving this list and remarks about the problem of INAPPROPRIATE MESSAGES are available at http://jse.stat.ncsu.edu/ =
Re: "Mean" of Standard deviations
Do you want a pooled standard deviation or a total standard devation? One ignores mean differences, the other does not. At 01:01 PM 5/17/01 +0200, Nasser Hosseini wrote: >Hi everybody! > >I wonder, if anybody out there knows, how to calculate the "mean" Standard >deviation, if you have a number of Mean and Standard deviation based on >DIFFERENT number of measurment: > >Subject 1: N1 (no. of measurment), M1 (mean), S1 (Standard deviation) >Subject 2: N2 , M2 , S2 >... >Subject m: Nm , M2 , Sm > >i.e. Stotal = F(S1,S2,...,Sm; N1,N2,...,Nm)??? > >Thanks > >/Nasser Hosseini > > > > > >= >Instructions for joining and leaving this list and remarks about >the problem of INAPPROPRIATE MESSAGES are available at > http://jse.stat.ncsu.edu/ >= > Paul R. Swank, PhD. Professor UT-Houston School of Nursing Center for Nursing Research Phone (713)500-2031 Fax (713) 500-2033 soon to be moving to the Department of Pediatrics UT Houston School of Medicine = Instructions for joining and leaving this list and remarks about the problem of INAPPROPRIATE MESSAGES are available at http://jse.stat.ncsu.edu/ =
"Mean" of Standard deviations
Hi everybody! I wonder, if anybody out there knows, how to calculate the "mean" Standard deviation, if you have a number of Mean and Standard deviation based on DIFFERENT number of measurment: Subject 1: N1 (no. of measurment), M1 (mean), S1 (Standard deviation) Subject 2: N2 , M2 , S2 ... Subject m: Nm , M2 , Sm i.e. Stotal = F(S1,S2,...,Sm; N1,N2,...,Nm)??? Thanks /Nasser Hosseini = Instructions for joining and leaving this list and remarks about the problem of INAPPROPRIATE MESSAGES are available at http://jse.stat.ncsu.edu/ =
