The Methods Used in Nonparametric Covariance Analysis

Şengül Cangür; Mehmet Ali Sungur; Handan Ankaralı

doi:10.18678/dtfd.424774

Research Article

Parametrik Olmayan Kovaryans Analizinde Kullanılan Metotlar

Year 2018, Volume: 20 Issue: 1, 1 - 6, 03.08.2018

Şengül Cangür Mehmet Ali Sungur Handan Ankaralı

https://doi.org/10.18678/dtfd.424774

Cited By: 15

Abstract

Amaç: Parametrik kovaryans analizi (ANCOVA) varsayımlarının sağlanamaması ve/veya bağımlı değişkenin iki değerli/sıralayıcı ölçekli olması durumunda, parametrik olmayan ANCOVA yaklaşımlarından yararlanılmaktadır. Parametrik olmayan ANCOVA metodolojisinde Quade, Puri & Sen ve McSweeney & Porter metotları, Ranklı ANCOVA yöntemleri olarak bilinmektedir. Ancak yaygın kullanılan programlarda, bu metotların uygulanmasına yönelik modül(ler) bulunmamaktadır. Bu çalışmanın amacı Ranklı ANCOVA yaklaşımlarını tanıtmak, yazarlar tarafından geliştirilen web tabanlı bir programda uygulamasını yapmak ve bu yaklaşımların avantajlarından bahsetmektedir.

Gereç ve Yöntemler: Ranklı ANCOVA yaklaşımlarının teorik özellikleri ve uygulama adımları tanımlanmış ve her bir yaklaşımın uygulanmasına yönelik web tabanlı bir program oluşturulmuştur. Sigara kullanma durumunun biyokimyasal tetkik sonuçları üzerindeki etkisinin incelendiği sağlık alanındaki bir çalışmadan simüle edilen veriler yardımıyla web tabanlı bir program üzerinde her bir yaklaşımın uygulamasına da yer verilmiştir.

Bulgular: Her ne kadar, bu çalışmada açıklanan yaklaşımlar için yaygın kullanılan istatistik programlarında özel bir modül olmasa da, bu yaklaşımların kolaylıkla uygulanabileceği simüle verilerle oluşturulmuş klinik bir çalışma üzerinde gösterilmiş, yaklaşımların sonuçları verilmiştir.

Sonuç: Birçok araştırmada örneklem genişliğinin kısıtlı olması ve/veya bağımlı değişkenin normal dağılım göstermemesi durumunda, faktöriyel modeller için parametrik yöntemlerin kullanılması, Tip I hata oranının artmasına ve testin gücünün azalmasına neden olmaktadır. Bu hatayı azaltmak için çalışmada önerilen yaklaşımların kullanılması tavsiye edilmektedir. Bu yaklaşımların, web tabanlı program sayesinde de yaygın kullanıma ulaşacağı düşünülmektedir.

Keywords

Ranklı ANCOVA, kovaryans, parametrik olmayan, Quade, Puri & Sen, McSweeney & Porter

References

1. Huitema BE. The Analysis of Covariance and Alternatives Statistical Methods for Experiments, Quasi-Experiments, and Single-Case Studies. 2nd ed. NJ: Wiley; 2011.
2. Cooper DJ, Plewes K, Grigg MJ, Rajahram GS, Piera KA, William T, et al. The effect of regularly dosed paracetamol versus no paracetamol on renal function in Plasmodium knowlesi malaria (PACKNOW): study protocol for a randomised controlled trial. Trials. 2018; 19(1): 250. doi: 10.1186/s13063-018-2600-0.
3. Mochizuki T, Amagai T, Tani A. Effects of soil water content and elevated CO2 concentration on the monoterpene emission rate of Cryptomeria japonica. Science of the Total Environment. 2018; 634: 900-8.
4. Focht BC, Lucas AR, Grainger E, Simpson C, Fairman CM, Thomas-Ahner JM, et al. Effects of a Group-Mediated Exercise and Dietary Intervention in the Treatment of Prostate Cancer Patients Undergoing Androgen Deprivation Therapy: Results from the IDEA-P Trial. Ann Behav Med. 2018; 52(5): 412-28.
5. Kononova A, McAlister A, Oh HJ. Screen overload: Pleasant multitasking with screen devices leads to the choice of healthful over less healthful snacks when compared with unpleasant multitasking. Computers in Human Behavior. 2018; 80: 1-11
6. Barrett TJ. Computations using analysis of covariance. WIREs Computational Statistics. 2011; 3(3): 260-8.
7. Rheinheimer DC, Penfield DA. The effects of type I error rate and power of the ANCOVA F Test and selected alternatives under nonnormality and variance heterogeneity. J Exp Educ. 2001; 69(4): 373-91.
8. Olejnik SF, Algina J. Parametric ANCOVA and the Rank Transform ANCOVA When the Data are Conditionally Non-Normal and Heteroscedastic. Journal of Educational and Behavioral Statistics. 1984; 9(2): 129-49.
9. Olejnik SF, Algina J. A review of nonparametric alternatives to analysis of covariance. Evaluation Rev. 1985; 9(1): 51-83.
10. Rutherford A. Alternatives to traditional analysis of covariance. British Journal of Mathematical and Statistical Psychology. 1992; 45(2): 197-223.
11. Quade D. Rank analysis of covariance. J Am Stat Assoc. 1967, 62(320): 1187-200.
12. Puri ML, Sen PK. Analysis of covariance based on general rank scores. Ann Math Stat. 1969; 40(2): 610-8.
13. McSweeny M, Porter AC. Small sample properties of nonparametric index of response and rank analysis of covariance. Occasional paper No. 16, Office of Research Consultation. East Lansing, MI: State University; 1971.
14. Burnett TD, Barr DR. A nonparametric analogy of analysis of covariance. Educational and Psychological Measurement. 1977; 37(2): 341-8.
15. Conover WJ, Inman RL. Analysis of covariance using the rank transformation. Biometrics. 1982; 38(3): 715-24.
16. Hettmansperger TP, McKean JW. A geometric interpretation of inferences based on ranks in the linear model. Journal of the American Statistical Association. 1983; 78(384): 885-93.
17. Hettmansperger TP. Statistical inference based on ranks. New York: Wiley; 1984.
18. Nakonezny PA, Shull RD. Hettmansperger and Mckean Linear Model Aligned Rank Test for the Single Covariate and One-Way ANCOVA Case (SAS). Journal of Modern Applied Statistical Methods. 2007; 6(1): 336-40.
19. Hamilton BL. A Monte Carlo test of robustness of parametric and nonparametric analysis of covariance against unequal regression slopes. J Am Stat Assoc. 1976; 71(356): 864-9.
20. Winer BJ. Statistical Principles in Experimental Design. New York: Mcgraw-Hill Book; 1962.
21. Harwell MR, Serlin RC. A nonparametric test statistic for the general linear model. Journal of Educational Statistics. 1989; 14(4): 351-71.

The Methods Used in Nonparametric Covariance Analysis

Year 2018, Volume: 20 Issue: 1, 1 - 6, 03.08.2018

Şengül Cangür Mehmet Ali Sungur Handan Ankaralı

https://doi.org/10.18678/dtfd.424774

Cited By: 15

Abstract

Aim: Nonparametric covariance analysis (ANCOVA) methods are used when the assumptions of parametric ANCOVA are not met and/or the dependent variable has bivariate/ordinal scale. In the nonparametric ANCOVA methodology, Quade, Puri & Sen and McSweeney & Porter methods are known as Ranked ANCOVA methods. However, commonly used programs do not have module(s) for applying these methods. The objective of this study is to introduce the ranked ANCOVA methods, to apply it in a web-based program developed by the authors and to present the advantages of these methods.

Material and Methods: The theoretical features and application steps of the Ranked ANCOVA methods are defined and a web-based program for the application of each method has been established. The application of each method on this program with the help of simulated data taken from the health field study, where the effect of cigarette smoking on biochemical tests was examined has also been included.

Results: Although there is no specific module in the widely used statistical programs for the methods described in this study, it is shown on a clinical study constituted with simulated data that these methods can easily be applied and the results of the methods are given.

Conclusion: The use of parametric methods for factorial models leads to an increase in Type-I error rate and a decrease in test power in many studies, where the sample size is limited and/or the dependent variable does not have normal distribution. To reduce this error, we recommend using the methods suggested in the study. These methods are also expected to reach widespread use thanks to the web-based program.

Keywords

Ranked ANCOVA, covariance, nonparametric, Quade, Puri & Sen, McSweeney & Porter

References

1. Huitema BE. The Analysis of Covariance and Alternatives Statistical Methods for Experiments, Quasi-Experiments, and Single-Case Studies. 2nd ed. NJ: Wiley; 2011.
2. Cooper DJ, Plewes K, Grigg MJ, Rajahram GS, Piera KA, William T, et al. The effect of regularly dosed paracetamol versus no paracetamol on renal function in Plasmodium knowlesi malaria (PACKNOW): study protocol for a randomised controlled trial. Trials. 2018; 19(1): 250. doi: 10.1186/s13063-018-2600-0.
3. Mochizuki T, Amagai T, Tani A. Effects of soil water content and elevated CO2 concentration on the monoterpene emission rate of Cryptomeria japonica. Science of the Total Environment. 2018; 634: 900-8.
4. Focht BC, Lucas AR, Grainger E, Simpson C, Fairman CM, Thomas-Ahner JM, et al. Effects of a Group-Mediated Exercise and Dietary Intervention in the Treatment of Prostate Cancer Patients Undergoing Androgen Deprivation Therapy: Results from the IDEA-P Trial. Ann Behav Med. 2018; 52(5): 412-28.
5. Kononova A, McAlister A, Oh HJ. Screen overload: Pleasant multitasking with screen devices leads to the choice of healthful over less healthful snacks when compared with unpleasant multitasking. Computers in Human Behavior. 2018; 80: 1-11
6. Barrett TJ. Computations using analysis of covariance. WIREs Computational Statistics. 2011; 3(3): 260-8.
7. Rheinheimer DC, Penfield DA. The effects of type I error rate and power of the ANCOVA F Test and selected alternatives under nonnormality and variance heterogeneity. J Exp Educ. 2001; 69(4): 373-91.
8. Olejnik SF, Algina J. Parametric ANCOVA and the Rank Transform ANCOVA When the Data are Conditionally Non-Normal and Heteroscedastic. Journal of Educational and Behavioral Statistics. 1984; 9(2): 129-49.
9. Olejnik SF, Algina J. A review of nonparametric alternatives to analysis of covariance. Evaluation Rev. 1985; 9(1): 51-83.
10. Rutherford A. Alternatives to traditional analysis of covariance. British Journal of Mathematical and Statistical Psychology. 1992; 45(2): 197-223.
11. Quade D. Rank analysis of covariance. J Am Stat Assoc. 1967, 62(320): 1187-200.
12. Puri ML, Sen PK. Analysis of covariance based on general rank scores. Ann Math Stat. 1969; 40(2): 610-8.
13. McSweeny M, Porter AC. Small sample properties of nonparametric index of response and rank analysis of covariance. Occasional paper No. 16, Office of Research Consultation. East Lansing, MI: State University; 1971.
14. Burnett TD, Barr DR. A nonparametric analogy of analysis of covariance. Educational and Psychological Measurement. 1977; 37(2): 341-8.
15. Conover WJ, Inman RL. Analysis of covariance using the rank transformation. Biometrics. 1982; 38(3): 715-24.
16. Hettmansperger TP, McKean JW. A geometric interpretation of inferences based on ranks in the linear model. Journal of the American Statistical Association. 1983; 78(384): 885-93.
17. Hettmansperger TP. Statistical inference based on ranks. New York: Wiley; 1984.
18. Nakonezny PA, Shull RD. Hettmansperger and Mckean Linear Model Aligned Rank Test for the Single Covariate and One-Way ANCOVA Case (SAS). Journal of Modern Applied Statistical Methods. 2007; 6(1): 336-40.
19. Hamilton BL. A Monte Carlo test of robustness of parametric and nonparametric analysis of covariance against unequal regression slopes. J Am Stat Assoc. 1976; 71(356): 864-9.
20. Winer BJ. Statistical Principles in Experimental Design. New York: Mcgraw-Hill Book; 1962.
21. Harwell MR, Serlin RC. A nonparametric test statistic for the general linear model. Journal of Educational Statistics. 1989; 14(4): 351-71.

There are 21 citations in total.

Details

Primary Language	English
Subjects	Health Care Administration
Journal Section	Research Article
Authors	Şengül Cangür Mehmet Ali Sungur Handan Ankaralı
Publication Date	August 3, 2018
Submission Date	May 18, 2018
Published in Issue	Year 2018 Volume: 20 Issue: 1

Cite

APA	Cangür, Ş., Sungur, M. A., & Ankaralı, H. (2018). The Methods Used in Nonparametric Covariance Analysis. Duzce Medical Journal, 20(1), 1-6. https://doi.org/10.18678/dtfd.424774
AMA	Cangür Ş, Sungur MA, Ankaralı H. The Methods Used in Nonparametric Covariance Analysis. Duzce Med J. August 2018;20(1):1-6. doi:10.18678/dtfd.424774
Chicago	Cangür, Şengül, Mehmet Ali Sungur, and Handan Ankaralı. “The Methods Used in Nonparametric Covariance Analysis”. Duzce Medical Journal 20, no. 1 (August 2018): 1-6. https://doi.org/10.18678/dtfd.424774.
EndNote	Cangür Ş, Sungur MA, Ankaralı H (August 1, 2018) The Methods Used in Nonparametric Covariance Analysis. Duzce Medical Journal 20 1 1–6.
IEEE	Ş. Cangür, M. A. Sungur, and H. Ankaralı, “The Methods Used in Nonparametric Covariance Analysis”, Duzce Med J, vol. 20, no. 1, pp. 1–6, 2018, doi: 10.18678/dtfd.424774.
ISNAD	Cangür, Şengül et al. “The Methods Used in Nonparametric Covariance Analysis”. Duzce Medical Journal 20/1 (August 2018), 1-6. https://doi.org/10.18678/dtfd.424774.
JAMA	Cangür Ş, Sungur MA, Ankaralı H. The Methods Used in Nonparametric Covariance Analysis. Duzce Med J. 2018;20:1–6.
MLA	Cangür, Şengül et al. “The Methods Used in Nonparametric Covariance Analysis”. Duzce Medical Journal, vol. 20, no. 1, 2018, pp. 1-6, doi:10.18678/dtfd.424774.
Vancouver	Cangür Ş, Sungur MA, Ankaralı H. The Methods Used in Nonparametric Covariance Analysis. Duzce Med J. 2018;20(1):1-6.