Abstract
TODD1 has proposed a series of tests for examining whether the spread of disease in a rectangular plantation of m rows and n columns is random or not. For an observed set s of diseased plants, he compared the expected and observed numbers of doublets formed from these plants, using for the variance of doublets the binomial approximation based on the probability of a single doublet. Todd extended his results to triplets and quadruplets, again using the binomial approximation. Finney2, however, showed that the binomial approximation over-estimates the variance for doublets, and under-estimates, rather considerably, the variance for triplets and for quadruplets. Krishna Iyer3 gave the correct expression for the variance of doublets by a characteristically new approach4. This note gives the expression for the variance of triplets. . If p and q = 1 – p the probabilities of a Plant being diseased and not diseased, the formula works out to be : where b = mn and a = m + n.
References
Todd, H., J. Roy. Stat. Soc., Supp. 7, 78 (1940).
Finney, D. J., J. Roy. Stat. Soc., Supp. 9, 99 (1947).
Krishna Iyer, P. V., Nature, 162, 333 (1948).
Krishna Iyer, P. V. [Nature, 164, 282 (1949)].
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SUKHATME, B. Variance of Triplets. Nature 164, 841 (1949). https://doi.org/10.1038/164841b0
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DOI: https://doi.org/10.1038/164841b0
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