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Tamamlanmış Blok ve Tamamen Rasgele Tasarımdan Oluşan Bir Karma Tasarımda Genel Alternatif için Önerilen Testler

Yıl 2022, Cilt: 22 Sayı: 3, 560 - 569, 30.06.2022
https://doi.org/10.35414/akufemubid.1107460

Öz

Rasgele tamamlanmış blok ve tamamen rasgele bloktan oluşan bir karma tasarım altında, genel alternatifleri test etmek için iki parametrik olmayan test önerilmiştir. Bu makalede, önerilen testler Doksum testi, uyarlanmış Page testi ve Friedman testlerinin kombinasyonlarıdır. Farklı konum parametreleri ve örnek çapları altında 4 ve 5 işlem etkilerinin testlerinin güçlerini tahmin etmek için bir simülasyon çalışması yapılmıştır. Deneysel I. Tip hata oranı ve testin gücü bakımından testlerin performansları karşılaştırılmıştır. Simülasyon sonuçlarından, önerilen testlerden en az bir tanesinin diğer testlerden daha yüksek güç değerine sahip olduğu görülmüştür. Son olarak, önerilen testlerin kullanışlılığı, gerçek bir veri seti üzerinde uygulanmıştır.

Kaynakça

  • Best, D. J., Rayner, J. C. W., & Thas, O., 2009. Nonparametric tests for randomized block data with ties and ordered alternatives. Third Annual ASEARC Conference, 7-8.
  • Doksum, K., 1967. Robust procedures for some linear models with one observation per cell. The Annals of Mathematical Statistics, 38(3), 878-883.
  • Dubnicka, S. R., Blair, R. C., & Hettmansperger, T. P., 2002. Rank-based procedures for mixed paired and two-sample designs. Journal of Modern Applied Statistical Methods, 1(1), 6.
  • Friedman, M., 1937. The use of ranks to avoid the assumption of normality implicit in the analysis of variance. Journal of the American statistical association, 32(200), 675-701.
  • Gül, H. H., & Bayrak, H., 2021. Proposed nonparametric tests for the ordered alternative in a completely randomized and randomized block mixed design. Cumhuriyet Science Journal, 42(1), 191-200.
  • Hollander M., 1967. Rank tests for randomized blocks when the alternatives have a priori ordering. Annals of Mathematical Statistics, 38, 867-877.
  • Jonckheere A. R., 1954. A distribution-free k-sample test against. Biometrika, 41, (1/2), 133-145.
  • Kruskal W. H., & Wallis W. A., 1952. Use of ranks in one-criterion variance analysis. Journal of the American Statistical Association, 47(260), 583-621.
  • Magel, R. C., & Fu, R., 2014. Proposed nonparametric test for the mixed two-sample design. Journal of Statistical Theory and Practice, 8(2), 221-237.
  • Magel, R., Terpstra, J., Canonizado, K., & Park, J. I., 2010. Nonparametric tests for mixed designs. Communications in Statistics-Simulation and Computation, 39(6), 1228-1250.
  • Magel, R., Terpstra, J., & Wen, J., 2009. Proposed tests for the nondecreasing alternative in a mixed design. Journal of Statistics and Management Systems, 12(5), 963-977.
  • Page, E. B., 1963. Ordered hypotheses for multiple treatments: a significance test for linear ranks. Journal of the American Statistical Association, 58(301), 216-230.
  • Terpstra T. J., 1952. The asymptotic normality and consistency of Kendall’s test against trend, when ties are present in one ranking. Indications Mathematicae, 14, 327-333.

Proposed Tests for The General Alternative in A Mixed Design Consist of Completely Randomized and Randomized Block Design

Yıl 2022, Cilt: 22 Sayı: 3, 560 - 569, 30.06.2022
https://doi.org/10.35414/akufemubid.1107460

Öz

Two nonparametric tests are proposed in testing for a general alternative under a mixed design consisting of a randomized complete block portion and a completely randomized block portion. In this paper, the proposed tests are a combination of the Doksum test, Modified Page test and Friedman test. A simulation study is conducted to estimate the powers of the tests for 4 and 5 treatment effects under a variety of different location parameters and sample sizes. We compare the performance of the tests in terms of the empirical type I error rates and power of tests. The simulation results show that at least one of the proposed test versions generally has higher power than the other tests. Finally, the usefulness of proposed tests is implemented on a real data set.

Kaynakça

  • Best, D. J., Rayner, J. C. W., & Thas, O., 2009. Nonparametric tests for randomized block data with ties and ordered alternatives. Third Annual ASEARC Conference, 7-8.
  • Doksum, K., 1967. Robust procedures for some linear models with one observation per cell. The Annals of Mathematical Statistics, 38(3), 878-883.
  • Dubnicka, S. R., Blair, R. C., & Hettmansperger, T. P., 2002. Rank-based procedures for mixed paired and two-sample designs. Journal of Modern Applied Statistical Methods, 1(1), 6.
  • Friedman, M., 1937. The use of ranks to avoid the assumption of normality implicit in the analysis of variance. Journal of the American statistical association, 32(200), 675-701.
  • Gül, H. H., & Bayrak, H., 2021. Proposed nonparametric tests for the ordered alternative in a completely randomized and randomized block mixed design. Cumhuriyet Science Journal, 42(1), 191-200.
  • Hollander M., 1967. Rank tests for randomized blocks when the alternatives have a priori ordering. Annals of Mathematical Statistics, 38, 867-877.
  • Jonckheere A. R., 1954. A distribution-free k-sample test against. Biometrika, 41, (1/2), 133-145.
  • Kruskal W. H., & Wallis W. A., 1952. Use of ranks in one-criterion variance analysis. Journal of the American Statistical Association, 47(260), 583-621.
  • Magel, R. C., & Fu, R., 2014. Proposed nonparametric test for the mixed two-sample design. Journal of Statistical Theory and Practice, 8(2), 221-237.
  • Magel, R., Terpstra, J., Canonizado, K., & Park, J. I., 2010. Nonparametric tests for mixed designs. Communications in Statistics-Simulation and Computation, 39(6), 1228-1250.
  • Magel, R., Terpstra, J., & Wen, J., 2009. Proposed tests for the nondecreasing alternative in a mixed design. Journal of Statistics and Management Systems, 12(5), 963-977.
  • Page, E. B., 1963. Ordered hypotheses for multiple treatments: a significance test for linear ranks. Journal of the American Statistical Association, 58(301), 216-230.
  • Terpstra T. J., 1952. The asymptotic normality and consistency of Kendall’s test against trend, when ties are present in one ranking. Indications Mathematicae, 14, 327-333.
Toplam 13 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Bölüm Makaleler
Yazarlar

Hasan Hüseyin Gül 0000-0001-9905-8605

Hülya Bayrak 0000-0001-5666-4250

Yayımlanma Tarihi 30 Haziran 2022
Gönderilme Tarihi 22 Nisan 2022
Yayımlandığı Sayı Yıl 2022 Cilt: 22 Sayı: 3

Kaynak Göster

APA Gül, H. H., & Bayrak, H. (2022). Proposed Tests for The General Alternative in A Mixed Design Consist of Completely Randomized and Randomized Block Design. Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi, 22(3), 560-569. https://doi.org/10.35414/akufemubid.1107460
AMA Gül HH, Bayrak H. Proposed Tests for The General Alternative in A Mixed Design Consist of Completely Randomized and Randomized Block Design. Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi. Haziran 2022;22(3):560-569. doi:10.35414/akufemubid.1107460
Chicago Gül, Hasan Hüseyin, ve Hülya Bayrak. “Proposed Tests for The General Alternative in A Mixed Design Consist of Completely Randomized and Randomized Block Design”. Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi 22, sy. 3 (Haziran 2022): 560-69. https://doi.org/10.35414/akufemubid.1107460.
EndNote Gül HH, Bayrak H (01 Haziran 2022) Proposed Tests for The General Alternative in A Mixed Design Consist of Completely Randomized and Randomized Block Design. Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi 22 3 560–569.
IEEE H. H. Gül ve H. Bayrak, “Proposed Tests for The General Alternative in A Mixed Design Consist of Completely Randomized and Randomized Block Design”, Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi, c. 22, sy. 3, ss. 560–569, 2022, doi: 10.35414/akufemubid.1107460.
ISNAD Gül, Hasan Hüseyin - Bayrak, Hülya. “Proposed Tests for The General Alternative in A Mixed Design Consist of Completely Randomized and Randomized Block Design”. Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi 22/3 (Haziran 2022), 560-569. https://doi.org/10.35414/akufemubid.1107460.
JAMA Gül HH, Bayrak H. Proposed Tests for The General Alternative in A Mixed Design Consist of Completely Randomized and Randomized Block Design. Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi. 2022;22:560–569.
MLA Gül, Hasan Hüseyin ve Hülya Bayrak. “Proposed Tests for The General Alternative in A Mixed Design Consist of Completely Randomized and Randomized Block Design”. Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi, c. 22, sy. 3, 2022, ss. 560-9, doi:10.35414/akufemubid.1107460.
Vancouver Gül HH, Bayrak H. Proposed Tests for The General Alternative in A Mixed Design Consist of Completely Randomized and Randomized Block Design. Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi. 2022;22(3):560-9.