プランクトン採集数の信頼区間

概要

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The fiducial limits of the catch provided by a single plankton sample may be estimated by the repeated sample. In order to estimate the limits (TFL), traditionally, the data were transformed to logarithms. The log-transform was expected to have the effect of removing the correlation between variance and mean, thus stabilizing the variance to more-or-less constant value, so that valid analysis of variance could be applied to the data. Although the data are transformed to logarithms, the catches of anchovy eggs and pre-larvae taken with ten repeated hauls show that the variances apparently depend upon the means, es-pecially provided the sample size is small (100 or less), so that the analysis of variance may be misleading. New fiducial limits (NFL) are made with a pair of catches, C1 and C2. Suppose that C1 and C2 are sampled from a hypothetical population following a negative binomial distribution with a constant 1/k. Then the NFL |D| can be expressed by means of the formula, |D|≤tp√(1/m-1/k)/2 where m=(C1+ C2)/2, D=(C1-C2)/(C1+C2) and tp is the value for p% in the standard normal distribution. Compairing NFL with TFL by m-D diagram for anchovy data, it was proved that NFL fitted better than TFL when the sample sizes are widely distributed. Using m-D diagram, moreover, only two repeated samples on each station give much information on the distribution of catches there.