Random median sampling to enhance the precision of population estimates
2007
Yamamura, Kohji | Wada, Takashi | Urano, Satoru
We describe the characteristics of a sampling procedure called random median sampling that was proposed to enhance the precision of population estimates. In performing random median sampling, we first select a sampling item at random from the sampling area. We roughly compare the abundance of individuals in the selected item with that of the adjacent two items in order to identify the item that has median abundance, i.e., the item that has the second largest abundance among the three items. We count the number of individuals of the item having the median abundance. This procedure is repeated n times in the sampling area (i = 1, 2, ..., n). Let m i be the ith median abundance. The estimates of the mean abundance per sampling item and the variance of estimates are given by Σm i /n and Σ(m i -Σm i /n)²/n(n - 1), respectively. This method is a local application of the median ranked set sampling that was proposed by Muttlak (J Appl Stat Sci 6:245-255, 1997). Random median sampling is effective when the correlation coefficient between adjacent items is small. If the correlation coefficient is close to zero, random median sampling reduces the variance of estimates to 45 or 32% of that in simple random sampling when the distribution follows a normal distribution or a Laplace distribution, respectively. The sample size required to achieve a given precision of estimate decreases accordingly. The effectiveness of random median sampling, however, is small if the correlation coefficient is large. The condition in which random median sampling is superior to simple random sampling is also discussed.
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