**Date:** Sat, 22 Mar 2003 12:05:04 -0500
**Reply-To:** Art@DrKendall.org
**Sender:** "SPSSX(r) Discussion" <SPSSX-L@LISTSERV.UGA.EDU>
**From:** "Arthur J. Kendall" <Art@DRKENDALL.ORG>
**Organization:** Social Research Consultants
**Subject:** Re: Turning SD into SE
**Content-Type:** text/plain; charset=us-ascii; format=flowed
Try running this piece of syntax and use the output to go through the
comments below.

new file.
input program.
loop #i = 1 to 43.
compute x = rnd(rv.normal(50,10)).
end case.
end loop.
end file.
end input program.
execute.
compute constant = 1.
aggregate outfile = 'c:\temp\temp.sav' /break= constant
/xmean = mean(x).
match files file=* /table = 'c:\temp\temp.sav' /by constant.
compute square = (x-xmean)**2.
descriptives variables=x square /stats = sum mean variance stdev semean.

Note the following in the resulting output.
The sum of squares is 4597.

The sample Variance (mean square) is (4597 / (43-1)) = 109.452.
Note the mean square not adjusted for sampling bias is (4597 / (43)) =
106.91.

The Standared deviation = sqrt(sample variance) = root mean square =
sqrt(109.452) = 10.462

The Standard Error (sd of similar sample means) = (standard deviation /
sqrt (N) = (10.462 / sqrt(43)) = 1.60.

scaling the standard deviation to a standard error AS IF N was 600
instead of 43 = (standard deviation / sqrt (N)) = (10.462 / sqrt(600))
= .427.

the standard error or the difference of two means = the denominator of a
t-test = sqrt( (first standard error**2) + (second standard error**2) )
= sqrt( (1.60**2) + (0**2)) = 1.60 with a constant as second mean
or
= sqrt( (1.60**2) + (.427**2)) = 1.66 using the first sd as the second
sd but scaled to 600 cases.
= sqrt( (1.60**2) + (Exner se**2)) = ????

In all three instances, the numerator of the t would be the difference
in the means.
the three t's would differ only to the degree that the three
denominators differed.

Cut-and-paste and run the syntax at the top of this message.
Use the output to walk through the comments above.

If the original responder gets Exner's SD and writes the ONEWAY syntax
for this demo, perhaps (s)he would share it with the list.

Hope this helps.

Art
Art@DrKendall.org
Social Research Consultants
University Park, MD USA
(301) 864-5570

Dirk Enzmann wrote:
> Art,
>
> In your reply to Lana ("I need help!!!") you wrote (Thu, 20 Mar 2003
> 08:37:47 -0500):
>
> (snip)
>
>>a kludge: If you cannot get Exner's SD, use yours for the second mean
>>but turn it into a SE using 600 df.
>
> (snip)
>
> and
>
> (snip)
>
>>3) with your sum of squares scaled as if you had 600 df.
>>The two means remain the same in each of the 3 runs.
>
> (snip)
>
> Question:
> How do you turn a SD into a SE using a certain df? And how do you scale
> the sums of squares as if you had a certain df?
>
> Dirk
>
> *************************************************
> Dr. Dirk Enzmann
> Criminological Research Institute of Lower Saxony
> Luetzerodestr. 9
> D-30161 Hannover
> Germany
>
> phone: +49-511-348.36.32
> fax: +49-511-348.36.10
> email: ENZMANN@KFN.uni-hannover.de
>
> http://www.kfn.de
> *************************************************
>
>
>