Journal of the Korea Safety Management & Science (대한안전경영과학회지)

Korea Safety Management & Science (대한안전경영과학회)
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Pooling Variance Tests Using Expected Mean Square in Split-Plot Designs

분할법에서 EMS알고리즘을 이용한 풀링분산검정

  • Published : 2008.09.30
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Abstract

The research proposes three ANOVA(Analysis of Variance) tests using expected mean square(EMS) algorithms in various split-plot designs. The variance tests consist of Never-Pool test, Sometimes-Pool test and Always-Pool test. This paper also presents two EMS algorithms such as standard method and easy method. These algorithms are useful to make a decision rule for pooling. Numerical examples are illustrated for various split-plot designs such as split-plot designs, split-split-plot designs, repetition split-plot designs, and nested designs. Pragmatically, the results are summarized and compared with popular ANOVA spreadsheets and data model equations.

Keywords

References

  1. 박동권, 실험계획법, 자유아카데미, 1995
  2. 박성현 외, SPSS와 SAS분석을 통한 실험계획법의 이해, 민영사, 2005
  3. 박성현, 현대실험계획법, 민영사, 2003
  4. 이우선, 최신실험설계, 영풍문고, 1998
  5. 최성운, "$k^n$요인배치법에서 포화실험에 의한 요인효과의 검정", 대한안전경영과학회 춘계학술논문발표집, (2008) 295-299
  6. Bozivich H., Bancroft T.A., Hartley H.O., "Power of Analysis of Variance Test Procedures for Certain Incompletely Specified Models, I", The Annals of Mathematical Statistics, 27(4)(1956) 1017-1043 https://doi.org/10.1214/aoms/1177728071
  7. Harter H.L., "On the Analysis of Split-Plot Experiments", Biometrics, 17(1)(1961) 144-149 https://doi.org/10.2307/2527501
  8. Hines W.G.S., "Pragmatics of Pooling in ANOVA Tables", The American Statistician, 50(1996) 127-139 https://doi.org/10.2307/2684424
  9. Janky D.G., " Sometimes Pooling for Analysis of Variance Hypothesis Tests : A Review and Study of a Split-Plot Model", The American Statistician, 54(4)(2000) : 269-279 https://doi.org/10.2307/2685778
  10. Mead R., Bancroft T.A., Han C., "Power of Analysis of Variance Test Procedures for Incompletely Specified Fixed Models", The Annals of Statistics, 3(1975) 797-808 https://doi.org/10.1214/aos/1176343183
  11. Merrington M., Thompson C.M., "Tables of Percentage Points of the Inverted Beta(F) Distribution", Biometrika, 33(1)(1943) 73-88 https://doi.org/10.1093/biomet/33.1.73
  12. Paull A.E., "On a Preliminary Test for Pooling Mean Squares in the Analysis of Variance", Annals of Mathematical Statistics, 21(1950) 539-556 https://doi.org/10.1214/aoms/1177729750
  13. Rao C.V., Saxena K.P., " A Study of Power of a Test Procedure Based on Two Preliminary Tests of Significance", Estadistica, 33(1979) 201-2214
  14. Wolde-Tsadik G., Afifi A.A., " A Comparision of the 'Sometimes-Pool', 'Sometimes-Switch', and 'Never-Pool', Procedures in the Two-Way ANOVA Random Effects Model", Technometrics, 22(1980) 363-373