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Program
Explanation
This page is a simple utility to combine multiple groups of n, mean, and SD into a single group using the following algorithm.
This algorithm must be used with care, as the statistical assumption is that all the groups are merely sub-samples of a single group, and combining them merely restore them back into the original single group. In many cases this assumption is faulty, as the groups may be from different populations, and sampled under different environments. It is much safer therefore to combine groups using the meta-analysis algorithm, using the Random Effect Model, available in the Meta-analysis for Comparing Two Unpaired Groups Program Page , using the mean and Standard Error of the mean for each group. The Standard Error of the mean is calculated as SE = SD / sqrt(n) of each group. After combining them using the Random Effect Model, the Standard Deviation can be recalculated as SD = SE * sqrt(tn), where tn is the sum of sample sizes from all the groups. References : This program is a re-engineering of the standard mean and Standard Deviation formula, so there is no reference to this procedure. However, the standard formula for mean and Standard Deviation is available in just about all basic statistical texts. If you must have a reference for it, I used the following Altman DG, Machin D, Bryant TN and Gardner MJ. (2000) Statistics with Confidence Second Edition. BMJ Books ISBN 0 7279 1375 1. p. 28-31 |