Showing papers on "Resampling published in 1966"

Some Monte Carlo results on the power of the F-test under permutation in the simple randomized block design*

Abstract: Randomization models and tests in the analysis of randomized experiments have been discussed by Scheff6 (1959, pp. 291-330) who concludes that under fairly wide conditions the normal theory analysis of variance F-test offers a good approximation to the size of the permutation test. Hoeffding (1952, pp. 177-80) has shown that the usual variance-ratio test on treatments in the simple randomized block design is, under permutation, asymptotically (as the number of blocks tend to infinity for a fixed number of treatments) as powerful as the normal theory analysis of variance test of the same size. Kempthorne, Zyskind, Addelman, Throckmorton & White (1961) have investigated the power characteristics of a 'fixed cut-off point' test, i.e. a test which employs normal theory rejection rules but uses a permutation probability basis. In the design studied, a randomized block design with two treatments, they found reasonably good agreement between the power of this test under all possible permutations and normal theory for a given size, ac. The authors have attempted in the present paper to extend the work of Kempthorne et al. (1961). Specifically, we study the power under permutation of the usual F-test of null treatment effects for two randomized block designs with one observation per cell-a three treatment by eight-block design and a three treatment by fifteen-block design. Both the size and the power of the F-test under permutation for these designs were estimated by Monte Carlo methods.

Logic for a randomization test

Abstract: Dr. Ray calls attention to a neglected statistical tool and describes a way in which it may be more easily used.