A labor-saving sampling method for estimating a normally distributed population by using a local median

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  • Wada Takashi
    National Agricultural Research Center for Kyushu Okinawa Region
  • Urano Satoru
    National Agricultural Research Center for Kyushu Okinawa Region
  • Yamamura Kohji
    National Institute for Agro-Environmental Science

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  • Labor Saving Sampling Method for Estimating a Normally Distributed Population by Using a Local Median

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We propose a sampling method using a median (random-median sampling) for estimating the mean and variance of a normally distributed population. First, a sampling unit is selected at random, and then two sampling units adjacent to the selected sampling unit are drawn. These three units are compared and only the unit with the median quantity among the three units, which we call the local median, is adopted. This procedure is repeated for a given sample size. A computer simulation was conducted to compare the required sample size for random-median sampling with that for simple random sampling for homogeneous populations. The sample size required to attain a given precision of estimates by random-median sampling relative to that by random sampling (=100) was shown to be constant, i.e. about 45%, irrespective of the mean and standard deviation of the population; therefore, this principle is generally applicable for any normally distributed populations. The discrimination limit (DL) is defined as 10% of the mean of the population when considering practical field selection of the median by eye. Random-median sampling with a DL in which samples are randomly selected among candidates when the difference between three or two, candidates is smaller than the DL, also decreased the sample size significantly. The sample sizes required by random-median sampling were 45–60% of those required by simple random sampling when the DL ratio (=standard deviation of the population/DL) was greater than 1.5. Therefore, in field sampling, when selection of a median is not time-consuming, for example, when examining soybean yield, random-median sampling with a DL saves labor in comparison with random sampling, at least for homogeneous populations. Unbiased variances of samples from random-median sampling and random-median sampling with a DL were about 45% and 45–60% of those from random sampling, respectively. Thus, it is possible to estimate the variance of the population using both random-median methods.

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