Research Article
BibTex RIS Cite

Uzunlamasına Verilerin Yer Aldığı Faktöriyel Tasarımlar için Parametrik Olmayan Yaklaşım

Year 2012, Volume: 9 Issue: 3, 17 - 29, 14.12.2012

Abstract

Uzunlamasına verilerin analizinde parametrik yöntemler oldukça yaygın olarak kullanılsa da bu yöntemlerin kullanımı, belirli varsayımların sağlanmasına bağlıdır. Son yıllarda parametrik test varsayımlarının sağlanmadığı verilerde ve/veya sıralı kategorik değişkenler kullanılarak yapılan değerlendirmelerde birden çok faktörün etkisini incelemek üzere parametrik olmayan yöntemler geliştirilmiştir. Bu çalışmanın amacı, uzunlamasına verilerin analizinde Brunner ve arkadaşları tarafından geliştirilen parametrik olmayan yöntemin tanıtılması ve Fiziksel Tıp ve Rehabilitasyon alanından bir veri seti üzerinde uygulamasının yapılmasıdır. Uzunlamasına verilerin parametrik olmayan yöntemlerle analizinde, parametre tahminlerinin elde edilmesinde ve test edilmek istenen hipotezlerin oluşturulmasında marjinal dağılımlar kullanılır. Hipotezlerin test edilmesinde örneklem büyüklüğüne bağlı olarak ANOVA tipi veya Wald tipi istatistik kullanılırken; tanımlayıcı istatistik olarak göreli deneme/marjinal etkileri yorumlanır. Uygulama için tedavi öncesi, tedavi sırasında ve tedaviden 3 ay sonra elde edilen Duruöz El İndeksi değerleri bağımsız iki grupta (tedavi ve kontrol) FI-LD-FI tasarımı kullanılarak karşılaştırılmıştır. Brunner ve arkadaşları tarafından geliştirilen yöntem, uzunlamasına verilerin analizinde ortaya çıkabilecek farklı deneme tasarımlarına çözüm sunmaktadır. Herhangi bir test varsayımı gerektirmemesi ve örneklem büyüklüğü bakımından kısıtı olmaması yöntemin avantajları olarak özetlenebilir.

References

  • Bonferroni, Abdi, H., Sidak, 2007. Corrections for Multiple Comparisons. In: Salkind NJ ed. Encyclopedia of Measurement and Statistics. 1st ed. Thousand Oaks, CA: Sage; p.103-107.
  • Akritas, M., G., Brunner, E., 1997. A Unified Approach to Ranks Tests in Mixed Models. Journal of Statistical Planning and Inference. 61 (2): 249 - 77.
  • Albus, C., Theissen, P., Hellmich, M., Griebenow, R., Wilhelm, B., Aslim, D., et al., 2009. Long term Effects of a Multimodal Behavioral Intervention on Myocardial Perfusion - a Randomized Controlled Trial. International Journal of Behavioral Medicine. 16 (3): 219 - 26. DOI 10.1007/s12529-008-9030-4.
  • Ateş. C., 2010. Nonparametric Analysis of Longitudinal Data in Factorial Experiments. M.Sc. Thesis. Ankara Üniversitesi Sağlık Bilimleri Enstitüsü, p. 66-70.
  • Brunner, E., 2002. Domhof S, Langer F. Nonparametric Analysis of Longitudinal Data in Factorial Experiments. 1st ed. New York: John Wiley & Sons; p. 21-32, 35-42, 67-80.
  • Brunner, E., Neumann, N., 1982. Rank Tests for Correlated Random Variables. Biometrical Journal, 24 (4): 373 - 89.
  • Brunner, E., Puri, M., L., 2002. A Class of Rank-score Tests in Factorial Designs. Journal of Statistical Planning and Inference. 103 (1-2): 331- 60.
  • Brunner, E., Puri M., L., 2001 Nonparametric Methods in Factorial Designs. Statistical papers, 42 (1): 1-52.
  • Duruöz, M., T., Poiraudeau, S., Fermanian, J., et al., 1996. Development and Validation of a Rheumatoid Hand Functional Disability Scale That Assesses Functional Handicap. Journal of Rheumatology, 23 (7): 1167 - 72.
  • Gao, O., H., Holmen, B., A., Niemeier, D., A., 2005. Nonparametric Factorial Analysis of Daily Weigh-in-motion Traffic: İmplieations Fort the Ozone "Weekend Effeet" in Southern California. Atmospheric Environment, 39 (9): 1669 - 82.
  • Gao, Y., 2004. Rank Based Methods in the Factorial Designs for Longitudinal Data with Application to Liver Cancer Studies. M.sc. Thesis. Graduate Faculty of Texas Tech University, p. 36 - 45.
  • Hafız, M., 2010. Impact of Corticosteroid Phonophoresia in Carpal Tunnel Syndrome on Pain and Hand Functions: Randomised Controlled Study. Phd Thesis. Ankara Üniversitesi Tıp Fakültesi Fiziksel Tıp ve Rehabilitasyon Anabilim Dalı, p. 10 - 25.
  • Hollander, M., Pledger, G., Lin, P., E., 1974. Robustuess of the Wilcoxon Test to a Certain Dependency Between Samples. Ann. Statist. 2 (1):177- 81.
  • Kamburoglu, K., Murat, S., Yüksel, S. P., Cebeci, A. R., Paksoy, C. S., 2010. Occlusal Caries Detection by Using a Cone-beam CT with Different Voxel Resolutions and a Digital Intraoral Sensor. Oral Surg. Oral Med. Oral Pathol, Oral Radiol Endod., 109(5): 63-9. DOI:10.1016/j.tripleo.2009.12.048.
  • Kruskal, W., H., 1952. A Nonparametric Test for the Several Sample Problems. Annals of Mathematical Statistics, 23 (4): 525 - 40.
  • Munzel, U., Bandelow, B., 1998. The Use of Parametric vs. Nonparametric Tests in the Statistical Evaluation of Rating Scales. Pharmacopsychiatry, 31 (6): 222 - 24.
  • Munzel, U., Brunner, E,, 2000. Nonparametric Methods in Multivariate Factorial Designs. Journal of statistical Planning and Inference, 88 (1): 117 - 32.
  • Ruymgaart, F., H., 1980. A Unified Approach to the Asymptotic Distribution Theory of Certain Midrank Statistics. In J.P. Raoult ed. Statistique non Parametrique Asymptotique. Lecture Notes on Mathematics No: 821. Berlin, Springer: p. 1-18.
  • Shah, D., A., Madden, L., V., 2003. Nonparametric Analysis of Ordinal Data in Design Factorial Experiments. Phytopathology, 94 (1): 33-43.
  • Thompson, G., L., 1991. A Unified Approach to Rank Tests of Multivariate and Repeated Measures Designs. Journal of the American Statistical Association, 86 (414): 410 9.
  • Thompson, G., L., 1990. Asymptotic Distribution of Rank Statistics Under Dependencies with Multivariate Application. Journal of Multivariate Analysis, 183-211.

Nonparametric Approach for Factorial Designs with Longitudinal Data

Year 2012, Volume: 9 Issue: 3, 17 - 29, 14.12.2012

Abstract

Although parametric methods are commonly used for longitudinal data, the use of these methods depends on several assumptions. In recent years, nonparametric methods have been developed to investigate the effect of multiple factors for the longitudinal data that do not meet parametric test assumptions and/or that include ordinal variables. The aim of this study is to introduce the nonparametric method for the analysis of longitudinal data which was developed by Brunner and colleagues and to implement it on a data set from the field of physical medicine and rehabilitation. Marginal distributions are used for obtaining parameter estimates and hypothesis testing, in the analysis of longitudinal data with nonparametric methods. While ANOVA or Wald type statistics are used to test the hypotheses depending on the sample size, relative treatment/marginal effects are used
as descriptive statistics. For the application, Duruöz Hand Index (DHl) scores are compared between two independent groups (control and treatment) at three time points; pre-treatment, during treatment and after 3 months of treatment, by using the FI-LD-FI design. The method developed by Brunner and colleagues offers solutions to different trial designs which may arise in the analyses of longitudinal data. Not requiring any test assumptions and any constraints in terms of sample size can be summarized as the advantages of this method.

References

  • Bonferroni, Abdi, H., Sidak, 2007. Corrections for Multiple Comparisons. In: Salkind NJ ed. Encyclopedia of Measurement and Statistics. 1st ed. Thousand Oaks, CA: Sage; p.103-107.
  • Akritas, M., G., Brunner, E., 1997. A Unified Approach to Ranks Tests in Mixed Models. Journal of Statistical Planning and Inference. 61 (2): 249 - 77.
  • Albus, C., Theissen, P., Hellmich, M., Griebenow, R., Wilhelm, B., Aslim, D., et al., 2009. Long term Effects of a Multimodal Behavioral Intervention on Myocardial Perfusion - a Randomized Controlled Trial. International Journal of Behavioral Medicine. 16 (3): 219 - 26. DOI 10.1007/s12529-008-9030-4.
  • Ateş. C., 2010. Nonparametric Analysis of Longitudinal Data in Factorial Experiments. M.Sc. Thesis. Ankara Üniversitesi Sağlık Bilimleri Enstitüsü, p. 66-70.
  • Brunner, E., 2002. Domhof S, Langer F. Nonparametric Analysis of Longitudinal Data in Factorial Experiments. 1st ed. New York: John Wiley & Sons; p. 21-32, 35-42, 67-80.
  • Brunner, E., Neumann, N., 1982. Rank Tests for Correlated Random Variables. Biometrical Journal, 24 (4): 373 - 89.
  • Brunner, E., Puri, M., L., 2002. A Class of Rank-score Tests in Factorial Designs. Journal of Statistical Planning and Inference. 103 (1-2): 331- 60.
  • Brunner, E., Puri M., L., 2001 Nonparametric Methods in Factorial Designs. Statistical papers, 42 (1): 1-52.
  • Duruöz, M., T., Poiraudeau, S., Fermanian, J., et al., 1996. Development and Validation of a Rheumatoid Hand Functional Disability Scale That Assesses Functional Handicap. Journal of Rheumatology, 23 (7): 1167 - 72.
  • Gao, O., H., Holmen, B., A., Niemeier, D., A., 2005. Nonparametric Factorial Analysis of Daily Weigh-in-motion Traffic: İmplieations Fort the Ozone "Weekend Effeet" in Southern California. Atmospheric Environment, 39 (9): 1669 - 82.
  • Gao, Y., 2004. Rank Based Methods in the Factorial Designs for Longitudinal Data with Application to Liver Cancer Studies. M.sc. Thesis. Graduate Faculty of Texas Tech University, p. 36 - 45.
  • Hafız, M., 2010. Impact of Corticosteroid Phonophoresia in Carpal Tunnel Syndrome on Pain and Hand Functions: Randomised Controlled Study. Phd Thesis. Ankara Üniversitesi Tıp Fakültesi Fiziksel Tıp ve Rehabilitasyon Anabilim Dalı, p. 10 - 25.
  • Hollander, M., Pledger, G., Lin, P., E., 1974. Robustuess of the Wilcoxon Test to a Certain Dependency Between Samples. Ann. Statist. 2 (1):177- 81.
  • Kamburoglu, K., Murat, S., Yüksel, S. P., Cebeci, A. R., Paksoy, C. S., 2010. Occlusal Caries Detection by Using a Cone-beam CT with Different Voxel Resolutions and a Digital Intraoral Sensor. Oral Surg. Oral Med. Oral Pathol, Oral Radiol Endod., 109(5): 63-9. DOI:10.1016/j.tripleo.2009.12.048.
  • Kruskal, W., H., 1952. A Nonparametric Test for the Several Sample Problems. Annals of Mathematical Statistics, 23 (4): 525 - 40.
  • Munzel, U., Bandelow, B., 1998. The Use of Parametric vs. Nonparametric Tests in the Statistical Evaluation of Rating Scales. Pharmacopsychiatry, 31 (6): 222 - 24.
  • Munzel, U., Brunner, E,, 2000. Nonparametric Methods in Multivariate Factorial Designs. Journal of statistical Planning and Inference, 88 (1): 117 - 32.
  • Ruymgaart, F., H., 1980. A Unified Approach to the Asymptotic Distribution Theory of Certain Midrank Statistics. In J.P. Raoult ed. Statistique non Parametrique Asymptotique. Lecture Notes on Mathematics No: 821. Berlin, Springer: p. 1-18.
  • Shah, D., A., Madden, L., V., 2003. Nonparametric Analysis of Ordinal Data in Design Factorial Experiments. Phytopathology, 94 (1): 33-43.
  • Thompson, G., L., 1991. A Unified Approach to Rank Tests of Multivariate and Repeated Measures Designs. Journal of the American Statistical Association, 86 (414): 410 9.
  • Thompson, G., L., 1990. Asymptotic Distribution of Rank Statistics Under Dependencies with Multivariate Application. Journal of Multivariate Analysis, 183-211.
There are 21 citations in total.

Details

Primary Language Turkish
Subjects Statistics
Journal Section Research Articles
Authors

Can Ateş

Yasemin Genç This is me

Meliha Hafız This is me

Derya Öztuna This is me

Şehim Kutlay This is me

Bülent Seçkin This is me

Publication Date December 14, 2012
Published in Issue Year 2012 Volume: 9 Issue: 3

Cite

APA Ateş, C., Genç, Y., Hafız, M., Öztuna, D., et al. (2012). Uzunlamasına Verilerin Yer Aldığı Faktöriyel Tasarımlar için Parametrik Olmayan Yaklaşım. İstatistik Araştırma Dergisi, 9(3), 17-29.