global sd as you call it: [var1(n1-1) + var2(n2-1)] / n1+n2 ... then take the sq root of it all
NOTE: the denominator MAY be n1-1 + n2-1 ...
just extend to 3 or more groups
At 12:57 PM 11/27/2002, David Robinson wrote:
I've searched for this, and failed to come up with an answer. It's not a homework question, or even a purely accademic 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. . . ================================================================= Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at: . http://jse.stat.ncsu.edu/ . =================================================================
_________________________________________________________ dennis roberts, educational psychology, penn state university 208 cedar, AC 8148632401, mailto:[EMAIL PROTECTED] http://roberts.ed.psu.edu/users/droberts/drober~1.htm . . ================================================================= Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at: . http://jse.stat.ncsu.edu/ . =================================================================
