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.
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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