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Carl-Erik Särndal, Bengt Swensson and Jan Wretman, Model Assisted Survey Sampling, Springer, 1992.

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Article

Roulette Model of Systematic Sampling

1Statistics and Information Department, Minister's Secretariat, Ministry of Health, Labour and Welfare, Kasumigaseki, Chiyoda-ku, Tokyo, JAPAN


American Journal of Applied Mathematics and Statistics. 2014, Vol. 2 No. 5, 344-351
DOI: 10.12691/ajams-2-5-8
Copyright © 2014 Science and Education Publishing

Cite this paper:
Fumito Muguruma. Roulette Model of Systematic Sampling. American Journal of Applied Mathematics and Statistics. 2014; 2(5):344-351. doi: 10.12691/ajams-2-5-8.

Correspondence to: Fumito  Muguruma, Statistics and Information Department, Minister's Secretariat, Ministry of Health, Labour and Welfare, Kasumigaseki, Chiyoda-ku, Tokyo, JAPAN. Email: muguruma-fumito@mhlw.go.jp

Abstract

Considering a natural model of systematic sampling, we can calculate the expectation of statistic exactly as it is without regarding it as any other sampling methods. I will demonstrate the details of calculation and get some results. It can be shown that the sample mean of systematic sampling is an unbiased estimator of population mean. Variance of sample mean can be described explicitly and depends on how to sort a population list. Sum of the variance of sample mean and the mean of sample variance is kept constant between random and systematic sampling. As the sample size becomes larger, the variance of sample mean converges to 0.

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