The Combination of Estimates from Different Experiments

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Abstract
The problem considered here is that of combining estimates of a parameter which are obtained from different expts. The expts. may differ in size or in precision and interactions may exist among expts., i.e., each expt. might not estimate exactly the same parameter value. Methods are given first for testing homogeneity of variances. If variances are then assumed equal, different procedures are followed depending on whether the expts. are the same size and on whether interaction is present. The same problems are considered for the case in which variances are not uniform. For all these situations recommendations are made for the use of unweighted, semiweighted or weighted means based on the principle of minimum error. Methods for computing standard errors are also discussed. Detailed examples are given which illustrate most of the situations encountered in practice.