Reducing A Random Sample To A Smaller Set, With Applications
A transformation matrix is given for reducing a random sample of size n to a smaller set of m uncorrelated variables, with the same mean and minimum common variance. This transformation may be applied to the classic Behrens-Fisher problem to obtain a solution similar to Scheffé's. An indication of the loss of information is also given. The transformation is also used to obtain an exact test of whether two regression planes are parallel, when the variances and sample sizes are unequal. Also a test of whether two regression planes are identical, when they are assumed parallel, can be derived easily by this method, and the results are similar to a recent solution by Potthoff. Some possible applications of the transformation to randomization tests concerning means is also given, the idea being to reduce the sample so that the amount of computations required would be feasible. © Taylor & Francis Group, LLC.
L. J. Bain, "Reducing A Random Sample To A Smaller Set, With Applications," Journal of the American Statistical Association, vol. 62, no. 318, pp. 510 - 519, Taylor and Francis Group; Taylor and Francis; American Statistical Association, Jan 1967.
The definitive version is available at https://doi.org/10.1080/01621459.1967.10482924
Mathematics and Statistics
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01 Jan 1967