You could try to simulate the solution as follows. Pick a data distribution type. Then generate data of the appropriate size samples each with its own mean and standard deviation. You likely will next need to message the data with a Ax + B transformation to get the exact mean and standard deviation for each sample. Then combine the data and compute the global mean and global standard deviation.
This is fairly easy using MINITAB; and I imagine also with other packages.
Howard Kaplon
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| Howard S. Kaplon | Mathematics Department |
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-----Original Message-----
From: David Robinson [mailto:[EMAIL PROTECTED]]
Sent: Wednesday, November 27, 2002 12:57 PM
To: [EMAIL PROTECTED]
Subject: unanswerable question? combining standard deviations
I've searched for this, and failed to come up with an answer. It's not
a homework question, or even a purely academic question - I'm trying
to combine psychoacoustic data from a number of sources, because I
need to calculate the percentage of the population who are able to
detect certain sounds.
Here's the problem:
I have several measurements of the SAME QUANTITY from different tests.
For each test, I have:
number of subjects, mean value, standard deviation (or standard error
of the mean.)
(All standard errors will be converted to standard deviations - I know
they don't quite mean the same thing (even when divided by root N),
but I believe SD is more appropriate in this context).
I want to combine all the data, to get a global mean, and a global
standard deviation. The results I want for these two values should be
the results I would get if I had ALL the original data from all the
tests, and simply calculated the mean and standard deviation over all
the data.
(I do not have all the original data - some of it does not exist
anymore)
I can calculate the global mean easily (n1*x_bar1 + n2*x_bar2 +
...)/n_total
I do not know how to calculate the global standard deviation. Please
can you help?
(I don't understand it, but from what I have read I believe the usual
technique of simply adding the squares of the SDs is not appropriate
because I have (hopefully) correlated data, and different sample
sizes)
Cheers,
David.
http://www.David.Robinson.org/
P.S. The SD is AS IMPORTANT as the mean for this work, because I will
integrate the resulting gaussian to give a psychometric function.
(Well, I have the integrated form giving a psychometric function, and
I can put the numbers in!) I have some real measured psychometric
functions to compare with, and these match the psychometric formula
predictions (from mean and SD values) very well.
.
.
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