A Revisit to Satterthwaite Approximation to the Distribution   of a Linear Combination of Sample Mean Squares

V.T. Prabhakaran

doi:10.56093/jisas.v76i1.172106

Authors

V.T. Prabhakaran 346, DDA SFS, Pocket-2, Dwarka Sec.-19, New Delhi

https://doi.org/10.56093/jisas.v76i1.172106

Keywords:

Linear combination of mean squares, Satherthwaite approximation.

Abstract

Linear combinations of mean squares occur in many areas of research like statistical hypothesis testing, design of experiments, and statistical genetics. The present paper demonstrates how the Satterthwaite approximation dating back to early nineteenth century is still a potential tool to reduce complicated problems to a solvable format. Significantly, a new derivation of the distribution of a linear combination of ‘Between sires’ and ‘Between dams within sires’ mean squares under certain restrictions is proposed which is quite simple compared the Graybill (1956) approach to the problem.

Downloads

Download data is not yet available.

References

Cochran, W.G., and Cox, G., M. (1950). Experimental Designs. John Wiley, New York.

Kempthorne, O. (1967). Design and Analysis of Experiments. Wiley Eastern, New Delhi.

Graybill, F.A., Martin, F., and Godfrey, G. (1956). Confidence intervals for measures of heritability. Biometrics, 12, 99-108.

Prabhakaran, V.T. and Jain, J.P. (1987a). Probability of inadmissible estimates of heritability from regression and half-sib analyses. Biom. J., 29, 219-230.

Prabhakaran, V.T. (1987b). Probability of obtaining negative estimates of heritability from full-sib analysis under a general model of gene action. Biom. J., 29, 461-469.

Prabhakaran, V.T. (1987c). A procedure for obtaining the probability of negative estimates of heritability from sib analysis. The Statistician, 36, 409-411.

Prabhakaran, V.T. and Jain, J.P. (1988). Probability of inadmissible estimates of heritability from full-sib analysis under a general model of gene action. Biom. J., 30, 47-57.

Prabhakaran, V.T. and Jain, J.P. (1990). Logistic transformation regression estimators of heritability. Biom. J., 32(3), 361-366.

Prabhakaran, V.T. and Seema Jaggi (1996). On the estimation of intra sire regression heritability subject to linear constraint. Biom. J., 38, 455-460.

Prabhakaran, V.T. and Sharma, B.S. (1994). Probability of heritability estimates from full-sib analysis exceeding unity, based on underlying theoretical distribution. Biom. J., 36(3), 341-352.

Prabhakaran, V.T. and Sharma, B.S. (1995). On improved estimation of heritability. Indian Journal of Animal Genetics and Breeding, 17(1,2), 33-37.

Satterthwaite, F.E. (1941). Synthesis of variance. Psychometrika, 6, 309-316.

Satterthwaite, F.E. (1946). An approximate distribution of estimates of variance components. Biometrics Bulletin, 2, 110-114.

Shukla, R.K. (1993). Some investigations on effects of genetico-statistical assumptions on the estimates of genetic parameters. Ph.D. Thesis, IARI, New Delhi.

Singh, Jogendra (1992). Some contributions to the estimation of heritability. Ph.D. Thesis, IARI, New Delhi.

Bodmer, W. (2003). R.A. Fisher, statistician and geneticist extraordinary: a personal view. International Journal of Epidemiology, 32, 938-942.