Abstract
MOST research workers have had occasion, during the course of several investigations, to combine two groups of quantitative results which show no statistically significant difference either in their means(m1 and m2) or in their variances (V1 and V2) and standard errors (e1 and e2). It is usually irksome to have to go back to the original data of both groups in order to calculate the new variance and standard error. Worse still, the original values may not be always available, and lengthy retrograde calculations of the sums of squares would then be required before the combined standard error could be obtained. Evidently, a simple expression relating the new standard error (e3) to the original standard errors and means would be most useful for both research workers and statisticians. We have therefore investigated this problem and have found the following simple relationship: where n1, n2 refer to the number of observations in the first and second group respectively, and n= n1 + n2.
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BAKER, R., NISSIM, J. Expressions for Combining Standard Errors of Two Groups and for Sequential Standard Error. Nature 198, 1020 (1963). https://doi.org/10.1038/1981020a0
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DOI: https://doi.org/10.1038/1981020a0
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