Turkiye Klinikleri Journal of Biostatistics

.: ORIGINAL RESEARCH
Etkileşimleri Test Etmek İçin Hizalanmış Sıra Sayıları Dönüşüm Yöntemleri
Aligned Rank Transform Methods for Testing Interactions
İsmet DOĞANa, Nurhan DOĞANa
aAfyonkarahisar Sağlık Bilimleri Üniversitesi Tıp Fakültesi, Biyoistatistik ve Tıbbi Bilişim ABD, Afyonkarahisar, TÜRKİYE
Turkiye Klinikleri J Biostat. 2021;13(1):120-30
doi: 10.5336/biostatic.2020-79049
Article Language: TR
Full Text
ÖZET
 Amaç: Bu makalenin amacı, normallik varsayımının sağ-lanmadığı faktöriyel deneme desenlerinde etkileşim teriminin önemlilik testi için uygulaması kolay ve etkili olan hizalanmış sıra sayıları dönüşümü işlemini tanıtmaktır. Gereç ve Yöntemler: Bir-çok istatistiksel testin geçerliliği, gözlemlerin normal dağıldığı var-sayımına bağlıdır. Ancak incelenen birçok karmaşık özellik, normal olmayan dağılımlara sahiptir. Dağılımın normal olmadığı durum-larda kullanılan çeşitli yaklaşımlar mevcuttur. Normallik veya varyansların homojenliğini ihlal eden verilerin söz konusu olduğu durumlarda, başlangıçta sıra sayısı dönüşümleri alternatif olarak önerilmiştir. Sıra sayıları dönüşüm işleminin dikkate alındığı çalış-malarda önce orijinal gözlemler sıra sayılarına dönüştürülmekte, ardından da sıra sayıları üzerinde parametrik bir istatistik hesap-lanmaktadır. Bulgular: Hem en küçük kareler tekniğine hem de sıra dönüşüm işlemine alternatif bir yöntem, hizalanmış sıra sayıları dönüşüm işlemidir. Hizalanmış sıralama dönüşümü, hem normallik gibi varsayım ihlallerinin etkisini en aza indirmekte hem de sırala-ma dönüşümü için bir sorun olan etkileşim terimlerinin önemlilik testine olanak sağlamaktadır. Hizalanmış sıra sayıları işlemine da-yalı testler sağlam ve güçlü testlerdir. Bu işlem, varsayım ihlalleri-ne ve aykırı değerlere karşı duyarlı değildir. Sonuç: Hizalanmış sıra sayıları dönüşüm işlemlerinin klasik varyans analizi işlemlerine karşı bilinen en iyi alternatifler olduğu ve normallik varsayımlarının şüpheli olduğu durumlarda kullanılması gerektiği sonucuna varıl-mıştır.

Anahtar Kelimeler: İstatistiksel analiz; nonparametrik etkileşim testleri; hizalanmış sıra sayısı testi; faktöriyel analiz
ABSTRACT
 Objective: The purpose of this article is to introduce aligned rank transform which is easy and effective to apply for the significance test of interaction term in factorial experimental design where normality assumption is not provided. Material and Meth-ods: The validity of many statistical tests depends on the assump-tion that observations are normally distributed. But, many complex traits studied have non-normal distributions. Several approaches exist to respond to non-normality. Rank transformations were ini-tially proposed as an alternative when dealing with data that violat-ed normality or homogeneity of variances. In studies where the rank transformation is taken into consideration, the original obser-vations are first converted into ranks, and then a parametric statis-tics is calculated on the ranks. Results: An alternative method to both the least squares technique and the rank transform process is the aligned rank transform procedure. The aligned rank transform minimizes the effect of violations of assumptions such as normality, but does not suffer some of the same problems of the rank trans-form, such as introducing interactions when they are not present or removing interactions when they are present. The aligned rank transform is a robust and powerful technique. This method is not sensitive to outliers and violations of assumptions on error distribu-tion. Conclusion: It concluded that the aligned rank transform pro-cedures appear to be the best known alternatives to the classical analysis of variance procedures, and should be used in situations where the assumptions of normality is suspect.

Keywords: Statistical analysis; nonparametric interaction tests; aligned rank test; factorial analysis
REFERENCES:
  1. Leys C, Schumann S. A nonparametric method to analyze interactions: The adjusted rank transform test. Journal of Experimental Social Psychology. 2010;46(4):684-8. [Crossref] 
  2. Durner E. Effective analysis of interactive effects with non-normal data using the aligned rank transform, ARTool and SAS® University edition. Horticulturae. 2019;5(3):57; doi: 10.3390/ horticulturae5030057. [Crossref] 
  3. Higgins JJ, Tashtoush S. An aligned rank transform test for interaction. Nonlinear World, 1994; 1 (2): 201-11. [Link] 
  4. Saste SV, Sananse SL, Sonar CD. On parametric and nonparametric analysis of two factor factorial experiment. Int J Appl Res. 2016;2(7):653-6. [Link] 
  5. Higgins JJ, Blair RC, Tashtoush S. The aligned rank transform procedure. 2nd Annual Conference Proceedings. Conference on Applied Statistics in Agriculture. New Prairie Press; 1990. p.185-95 [Crossref] 
  6. Beasley TM, Zumbo BD. Aligned rank tests for interactions in split-plot designs: distributional assumptions and stochastic heterogeneity. Journal of Modern Applied Statistical Methods. 2009;8(1):16-50. [Crossref] 
  7. Salter KC, Fawcett RF. The art test of interaction: a robust and powerful rank test of interaction in factorial models. Communications in Statistics-Simulation and Computation. 1993;22(1):137-53. [Crossref] 
  8. Beasley TM. Multivariate aligned rank test for interactions in multiple group repeated measures designs. Multivariate Behavioral Research. 2002;37(2):197-226. [Crossref] 
  9. Peterson K. Six modifications of the aligned rank transform test for interaction. Journal of Modern Applied Statistical Methods. 2002;1(1):100-9. [Crossref] 
  10. Lei X, Holt JK, Beasley TM. Aligned rank tests as robust alternatives for testing interactions in multiple group repeated measures designs with heterogeneous covariances. Journal of Modern Applied Statistical Methods. 2004;3(2):462-75. [Crossref] 
  11. Richter SJ, Payton ME. An improvement to the aligned rank statistic for two factor analysis of variance. J Appl Stat Sci. 2005;14(3/4):225-35. [Link] 
  12. Mansouri H. Multifactor analysis of variance based on the aligned rank transform technique. Computational Statistics & Data Analysis. 1999;29(2):177-89. [Crossref] 
  13. Mansouri H, Paige RL, Surles JG. Aligned rank transform techniques for analysis of variance and multiple comparisons. Communications in Statistics-Theory and Methods. 2004;33(9):2217-32. [Crossref] 
  14. Sawilowsky SS. Nonparametric tests of interaction in experimental design. Review of Educational Research. 1990;60(1):91-126. [Crossref] 
  15. Feys J. New nonparametric rank tests for interactions in factorial designs with repeated measures. Journal of Modern Applied Statistical Methods. 2016;15(1): 78-99. [Crossref] 
  16. Oliver-Rodríguez JC, Wang XT. Non-parametric three-way mixed ANOVA with aligned rank tests. Br J Math Stat Psychol. 2015;68(1):23-42. [Crossref]  [PubMed] 
  17. Blair RC, Sawilowsky SS, Higgins JJ. Limitations of the rank transform statistic in tests for interactions. Communications in Statistics-Simulation and Computation. 1987;16(4):1133-45. [Crossref] 
  18. Richter SJ, Payton ME. Nearly exact tests in factorial experiments using the aligned rank transform. Journal of Applied Statistics. 1999;26(2):203-17. [Crossref] 
  19. Bryan JJ. Rank transforms and tests of interaction for for repeated measures experiments with various covariance structures. PhD Thesis. Stillwater: Oklahoma State University; 2009.
  20. Akritas MG, Arnold SF, Brunner E. Nonparametric hypotheses and rank statistics for unbalanced factorial designs. Journal of the American Statistical Association. 1997;92(437):258-65. [Crossref] 
  21. Salazar-Alvarez MI, Tercero Gómez VG, Temblador MDC, Cordero Franco AE, Conover W. Nonparametric analysis of interactions: A review and gap analysis. In: Guan Y, Liao H, eds. Proceedings of Proceedings of the 2014 Industrial and Systems Engineering Research Conference. Vol. 1. Montreal, Canada: Curran Associates, Inc; 2014. p.2910-7.
  22. Wobbrock JO, Findlater L, Gergle D, Higgins JJ. The aligned rank transform for nonparametric factorial analyses using only ANOVA procedures. In: Proceeding of ACM CHI 2011. Conference on Human Factors in Computing Systems. 2011. p.143-6. [Crossref] 
  23. Luepsen H. The aligned rank transform and discrete variables: A warning. Communications in Statistics-Simulation and Computation. 2017;46(9):6923-36. [Crossref] 
  24. Sawilowsky SS, Blair RC, Higgins JJ. An investigation of the type I error and power properties of the rank transform procedure in factorial ANOVA. Journal of Educational Statistics. 1989;14(3):255-67. [Crossref] 
  25. Luepsen H. Comparison of nonparametric analysis of variance methods: a vote for van der Waerden. Communications in Statistics-Simulation and Computation. 2018;47(9):2547-76. [Crossref] 
  26. Mangiafico SS. How should we analyze Likert item data? Journal of the NACAA. 2019;12(2): 1-8. [Link] 

.: Up To Date

.: Process List

Login

 Forgot your password?

 New Registration  

Contact

Ortadoğu Reklam Tanıtım Yayıncılık Turizm Eğitim İnşaat Sanayi ve Ticaret A.Ş.

.: Address

Turkocagi Caddesi No:30 06520 Balgat / ANKARA
Phone: +90 312 286 56 56
Fax: +90 312 220 04 70
E-mail: info@turkiyeklinikleri.com

.: Manuscript Editing Department

Phone: +90 312 286 56 56/ 2
E-mail: yaziisleri@turkiyeklinikleri.com

.: English Language Redaction

Phone: +90 312 286 56 56/ 145
E-mail: tkyayindestek@turkiyeklinikleri.com

.: Marketing Sales-Project Department

Phone: +90 312 286 56 56/ 142
E-mail: reklam@turkiyeklinikleri.com

.: Subscription and Public Relations Department

Phone: +90 312 286 56 56/ 118
E-mail: abone@turkiyeklinikleri.com

.: Customer Services

Phone: +90 312 286 56 56/ 118
E-mail: satisdestek@turkiyeklinikleri.com

1. TERMS OF USE

1.1. To use the web pages with http://www.turkiyeklinikleri.com domain name or the websites reached through the sub domain names attached to the domain name (They will be collectively referred as "SITE"), please read the conditions below. If you do not accept these terms, please cease to use the "SITE." "SITE" owner reserves the right to change the information on the website, forms, contents, the "SITE," "SITE" terms of use anytime they want.

1.2. The owner of the "SITE" is Ortadoğu Advertisement Presentation Publishing Tourism Education Architecture Industry and Trade Inc. (From now on it is going to be referred as "Turkiye Klinikleri", shortly) and it resides at Turkocagi cad. No:30, 06520 Balgat Ankara. The services in the "SITE" are provided by "Turkiye Klinikleri."

1.3. Anyone accessing the "SITE" with or without a fee whether they are a natural person or a legal identity is considered to agree these terms of use. In this contract hereby, "Turkiye Klinikleri" may change the stated terms anytime. These changes will be published in the "SITE" periodically and they will be valid when they are published. Any natural person or legal identity benefiting from and reaching to the "SITE" are considered to be agreed to any change on hereby contract terms done by "Turkiye Klinikleri."

1.4. The "Terms of Use" hereby is published in the website with the last change on March 30th 2014 and the "SITE" is activated by enabling the access to everyone. The "Terms of Use" hereby is also a part of the any "USER Contract" was and/or will be done with the users using "Turkiye Klinikleri" services with or without a fee an inseparable.

2. DEFINITIONS

2.1. "SITE": A website offering different kind of services and context with a certain frame determined by "Turkiye Klinikleri" and it is accessible on-line on http://www.turkiyeklinikleri.com domain name and/or subdomains connected to the domain name.

2.2. USER: A natural person or a legal identity accessing to the "SITE" through online settings.

2.3. LINK: A link enabling to access to another website through the "SITE", the files, the context or through another website to the "SITE", the files and the context.

2.4. CONTEXT: Any visual, literary and auditory images published in the "Turkiye Klinikleri", "SITE" and/or any website or any accessible information, file, picture, number/figures, price, etc.

2.5. "USER CONTRACT": An electronically signed contract between a natural or a legal identity benefiting from special services "Turkiye Klinikleri" will provide and "Turkiye Klinikleri".

3. SCOPE OF THE SERVICES

3.1. "Turkiye Klinikleri" is completely free to determine the scope and quality of the services via the "SITE".

3.2. To benefit the services of "Turkiye Klinikleri" "SITE", the "USER" must deliver the features that will be specified by "Turkiye Klinikleri". "Turkiye Klinikleri" may change this necessity any time single-sided.

3.3. Not for a limited number, the services "Turkiye Klinikleri" will provide through the "SITE" for a certain price or for free are;

- Providing scientific articles, books and informative publications for health industry.

- Providing structural, statistical and editorial support to article preparation stage for scientific journals.

4. GENERAL PROVISIONS

4.1. "Turkiye Klinikleri" is completely free to determine which of the services and contents provided in the "SITE" will be charged.

4.2. People benefiting from the services provided by "Turkiye Klinikleri" and using the website can use the "SITE" only according to the law and only for personal reasons. Users have the criminal and civil liability for every process and action they take in the "SITE". Every USER agrees, declares and undertakes that they will not proceed by any function or action infringement of rights of "Turkiye Klinikleri"s and/or other third parties', they are the exclusive right holder on usage, processing, storage, made public and revealing any written, visual or auditory information reported to Turkiye Klinikleri" and/or "SITE" to the third parties. "USER" agrees and undertakes that s/he will not duplicate, copy, distribute, process, the pictures, text, visual and auditory images, video clips, files, databases, catalogs and lists within the "SITE", s/he will not be using these actions or with other ways to compete with "Turkiye Klinikleri", directly or indirectly.

4.3. The services provided and the context published within the "SITE" by third parties is not under the responsibility of "Turkiye Klinikleri", institutions collaborated with "Turkiye Klinikleri", "Turkiye Klinikleri" employee and directors, "Turkiye Klinikleri" authorized salespeople. Commitment to accuracy and legality of the published information, context, visual and auditory images provided by any third party are under the full responsibility of the third party. "Turkiye Klinikleri" does not promise and guarantee the safety, accuracy and legality of the services and context provided by a third party.

4.4. "USER"s cannot act against "Turkiye Klinikleri", other "USER"s and third parties by using the "SITE". "Turkiye Klinikleri" has no direct and/or indirect responsibility for any damage a third party suffered or will suffer regarding "USER"s actions on the "SITE" against the rules of the hereby "Terms of Use" and the law.

4.5. "USER"s accept and undertake that the information and context they provided to the "SITE" are accurate and legal. "Turkiye Klinikleri" is not liable and responsible for promising and guaranteeing the verification of the information and context transmitted to "Turkiye Klinikleri" by the "USER"s, or uploaded, changed and provided through the "SITE" by them and whether these information are safe, accurate and legal.

4.6. "USER"s agree and undertake that they will not perform any action leading to unfair competition, weakening the personal and commercial credit of "Turkiye Klinikleri" and a third party,  encroaching and attacking on personal rights within the "SITE" in accordance with the Turkish Commercial Code Law.

4.7. "Turkiye Klinikleri" reserves the right to change the services and the context within the "SITE"  anytime. "Turkiye Klinikleri" may use this right without any notification and timelessly. "USER"s have to make the changes and/or corrections "Turkiye Klinikleri" required immediately. Any changes and/or corrections that are required by "Turkiye Klinikleri", may be made by "Turkiye Klinikleri" when needed. Any harm, criminal and civil liability resulted or will result from changes and/or corrections required by "Turkiye Klinikleri" and were not made on time by the "USER"s belongs completely to the users.

4.8. "Turkiye Klinikleri" may give links through the "SITE" to other websites and/or "CONTEXT"s and/or folders that are outside of their control and owned and run by third parties. These links are provided for ease of reference only and do not hold qualification for support the respective web SITE or the admin or declaration or guarantee for the information inside. "Turkiye Klinikleri" does not hold any responsibility over the web-sites connected through the links on the "SITE", folders and context, the services or products on the websites provided through these links or their context.

4.9. "Turkiye Klinikleri" may use the information provided to them by the "USERS" through the "SITE" in line with the terms of the "PRIVACY POLICY" and "USER CONTRACT". It may process the information or classify and save them on a database. "Turkiye Klinikleri" may also use the USER's or visitor's identity, address, e-mail address, phone number, IP number, which sections of the "SITE" they visited, domain type, browser type, date and time information to provide statistical evaluation and customized services.

5. PROPRIETARY RIGHTS

5.1. The information accessed through this "SITE" or provided by the users legally and all the elements (including but not limited to design, text, image, html code and other codes) of the "SITE" (all of them will be called as studies tied to "Turkiye Klinikleri"s copyrights) belongs to "Turkiye Klinikleri". Users do not have the right to resell, process, share, distribute, display or give someone permission to access or to use the "Turkiye Klinikleri" services, "Turkiye Klinikleri" information and the products under copyright protection by "Turkiye Klinikleri". Within hereby "Terms of Use" unless explicitly permitted by "Turkiye Klinikleri" nobody can reproduce, process, distribute or produce or prepare any study from those under "Turkiye Klinikleri" copyright protection.

5.2. Within hereby "Terms of Use", "Turkiye Klinikleri" reserves the rights for "Turkiye Klinikleri" services, "Turkiye Klinikleri" information, the products associated with "Turkiye Klinikleri" copyrights, "Turkiye Klinikleri" trademarks, "Turkiye Klinikleri" trade looks or its all rights for other entity and information it has through this website unless it is explicitly authorized by "Turkiye Klinikleri".

6. CHANGES IN THE TERMS OF USE

"Turkiye Klinikleri" in its sole discretion may change the hereby "Terms of Use" anytime announcing within the "SITE". The changed terms of the hereby "Terms of Use" will become valid when they are announced. Hereby "Terms of Use" cannot be changed by unilateral declarations of users.

7. FORCE MAJEURE

"Turkiye Klinikleri" is not responsible for executing late or never of this hereby "Terms of Use", privacy policy and "USER Contract" in any situation legally taken into account as force majeure. Being late or failure of performance or non-defaulting of this and similar cases like this will not be the case from the viewpoint of "Turkiye Klinikleri", and "Turkiye Klinikleri" will not have any damage liability for these situations. "Force majeure" term will be regarded as outside of the concerned party's reasonable control and any situation that "Turkiye Klinikleri" cannot prevent even though it shows due diligence. Also, force majeure situations include but not limited to natural disasters, rebellion, war, strike, communication problems, infrastructure and internet failure, power cut and bad weather conditions.

8. LAW AND AUTHORISATION TO FOLLOW

Turkish Law will be applied in practicing, interpreting the hereby "Terms of Use" and managing the emerging legal relationships within this "Terms of Use" in case of finding element of foreignness, except for the rules of Turkish conflict of laws. Ankara Courts and Enforcement Offices are entitled in any controversy happened or may happen due to hereby contract.

9. CLOSING AND AGREEMENT

Hereby "Terms of Use" come into force when announced in the "SITE" by "Turkiye Klinikleri". The users are regarded to agree to hereby contract terms by using the "SITE". "Turkiye Klinikleri" may change the contract terms and the changes will be come into force by specifying the version number and the date of change on time it is published in the "SITE".

 

30.03.2014

Privacy Policy

We recommend you to read the terms of use below before you visit our website. In case you agree these terms, following our rules will be to your favor. Please read our Terms of Use thoroughly.

www.turkiyeklinikleri.com website belongs to Ortadoğu Advertisement Presentation Publishing Tourism Education Architecture Industry and Trade Inc. and is designed in order to inform physicians in the field of health

www.turkiyeklinikleri.com cannot reach to user’s identity, address, service providers or other information. The users may send this information to the website through forms if they would like to. However, www.turkiyeklinikleri.com may collect your hardware and software information. The information consists of your IP address, browser type, operating system, domain name, access time, and related websites. www.turkiyeklinikleri.com cannot sell the provided user information (your name, e-mail address, home and work address, phone number) to the third parties, publish it publicly, or keep it in the website. Gathered information has a directing feature to be a source for the website’s visitor profile, reporting and promotion of the services.

www.turkiyeklinikleri.com uses the taken information:

-To enhance, improve and maintain the quality of the website

-To generate visitor’s profile and statistical data

-To determine the tendency of the visitors on using our website

-To send print publications/correspondences

-To send press releases or notifications through e-mail

-To generate a list for an event or competition

By using www.turkiyeklinikleri.com you are considered to agree that;

-Ortadoğu Advertisement Presentation Publishing Tourism Education Architecture Industry and Trade Inc. cannot be hold responsible for any user’s illegal and immoral behavior,

-Terms of use may change from time to time,

-It is not responsible for other websites’ contents it cannot control or the harms they may cause although it uses the connection they provided.

Ortadoğu Advertisement Presentation Publishing Tourism Education Architecture Industry and Trade Inc. may block the website to users in the following events:

-Information with wrong, incomplete, deceiving or immoral expressions is recorded to the website,

-Proclamation, advertisement, announcement, libelous expressions are used against natural person or legal identity,

-During various attacks to the website,

-Disruption of the website because of a virus.

Written, visual and audible materials of the website, including the code and the software are under protection by legal legislation.

Without the written consent of Ortadoğu Advertisement Presentation Publishing Tourism Education Architecture Industry and Trade Inc. the information on the website cannot be downloaded, changed, reproduced, copied, republished, posted or distributed.

All rights of the software and the design of the website belong to Ortadoğu Advertisement Presentation Publishing Tourism Education Architecture Industry and Trade Inc.

Ortadoğu Advertisement Presentation Publishing Tourism Education Architecture Industry and Trade Inc. will be pleased to hear your comments about our terms of use. Please share the subjects you think may enrich our website or if there is any problem regarding our website.

info@turkiyeklinikleri.com