New Zealand Journal of Crop and Horticultural Science abstracts

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Estimating a binomial proportion from several independent samples

C. G. Qiao

Centre for Social Research and Evaluation
Ministry of Social Development
P.O. Box 12 136
Wellington, New Zealand
email: chungui.qiao001@msd.govt.nz

G. R. Wood

Department of Statistics
Macquarie University, Sydney
NSW 2109, Australia

C. D. Lai

Institute of Information Sciences and Technology
Massey University
Private Bag 11 222
Palmerston North, New Zealand

Abstract  This paper addresses the problem of estimating a binomial proportion from several independent samples in agricultural research, where the arithmetic average is widely used. The penalties of using a suboptimal estimator, the arithmetic estimator, relative to the preferred best estimator, the weighted average, are theoretically and empirically investigated, using numerical illustrations and simulation studies. Raw count data from a study of the proportion of inoculated transgenic hairy roots expressing resistance to cyst nematode in soybean (Glycine max) cultivars and a set of 10 examples of proportion estimation involving several independent samples are used for a practical evaluation of the findings. Results show that using the arithmetic average estimator can inflate variance and widen large sample confidence intervals of the estimates. The weighted average is recommended.

Keywords  arithmetic average estimator; weighted average estimator; binomial proportion; confidence interval; penalty; variance ratio

H05008; Online publication date 22 July 2005 Received 27 January 2005; accepted 14 April 2005
New Zealand Journal of Crop and Horticultural Science, 2005, Vol. 33: 293-302
0014-0671/05/3303-0293 © The Royal Society of New Zealand 2005

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