Expected Mean Squares for the Random Effects One-Way ANOVA Model when Sampling from a Finite Population

Authors

  • Teerawat Simmachan Department of Mathematics and Statistics, Faculty of Science and Technology, Thammasat University, Pathum Thani 12120, Thailand.
  • John J. Borkowski Department of Mathematical Sciences, Montana State University, Bozeman, MT 5971, USA.
  • Kamon Budsaba Department of Mathematics and Statistics, Faculty of Science and Technology, Thammasat University, Pathum Thani 12120, Thailand.

Keywords:

expected mean squares, finite population, finite population correction, random effects model, variance components

Abstract

The purpose of this work is to determine the expected value of the mean square error (MSE) and the expected value of the treatment mean square (MStrt) for the random effects one-way ANOVA model assuming a finite population.

For the case of balanced data (equal sample sizes), both the expected value of the mean square error and the expected value of the treatment mean square for the finite population are the same as that for the infinite population.

For the case of unbalanced data, the expected value of MSE for the finite population is equal to that for the infinite population which is also the same as the expected value for the balanced case. On the other hand, the expected value of MStrt for the finite population is different from that for the infinite population because of the different multiplier values of the population variance (στ2).

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How to Cite

Simmachan, T., Borkowski, J. J., & Budsaba, K. (2015). Expected Mean Squares for the Random Effects One-Way ANOVA Model when Sampling from a Finite Population. Thailand Statistician, 10(1), 121–128. Retrieved from https://ph02.tci-thaijo.org/index.php/thaistat/article/view/34241

Issue

Vol. 10 No. 1 (2012): JANUARY

Section

Articles