Araştırmalarda Uygun İstatistiksel Tekniğin Belirlenmesinde Normallik ve Homojenlik İhlallerinin Etkisinin İlgili Literatür Bağlamında Değerlendirilmesi

Year 2024, Volume: 2 Issue: 2, 52 - 62, 01.10.2024

Ergul Demir , İrem Çelik , Sibel Urlu

https://doi.org/10.5281/zenodo.13865423

Abstract

Araştırmalarda uygun istatistiksel tekniğin belirlenmesi, araştırmanın metodolojik tasarımının yanı sıra analizin amacı, örneklem büyüklüğü ve yapısı, verilerin ve veri setinin karakteristiğinin de dikkate alınmasını gerektiren zorlayıcı bir aşamadır. Parametrik testler veya daha genel bir tanımlamayla doğrusal modeller, (1) normallik ve (2) varyansların homojenliği temel varsayımlarına duyarlı test ve modeller olarak değerlendirilmektedir. Ciddi düzeyde normallik ve homojenlik ihlallerinin görülmesi, bu testlerin kullanılmaması kararına yönlendirebilmektedir. Diğer taraftan, ciddi düzeyin ne olduğu, belirsizlik içeren ve tartışmalı bir konudur. Bu kapsamda bu çalışmanın amacı; uygun istatistiksel tekniğin belirlenmesinde normallik ve homojenlik ihlallerinin hangi durum ve koşullarda “ciddi” veya “ihmal edilebilir” olarak değerlendirilebileceğini, ayrıca bu tür durumlarda ne tür çözümlere başvurulabileceğini, ilgili araştırmalar ve temel kaynak kitaplar üzerinden tartışmak ve değerlendirmektir. Bu çalışma, ilgili literatürdeki temel kaynak kitaplar ve ilişkili araştırmaların ortaya koyduğu bulgular üzerinden yürütülen derleme niteliğinde kuramsal bir çalışmadır. Bu kapsamda alanda tanınırlığı yüksek olan 20 temel kaynak kitap ve varsayım ihlallerinin istatistiksel teknikler üzerindeki etkilerini inceleyen 25 makale belirlenmiştir. Araştırma soruları doğrultusunda tartışmalar yürütülmüştür. Sonuç olarak ilgili literatür, yeterli örneklem büyüklüğü ve gruplar arası denge sağlandığında, normallik ve homojenlik ihlallerinin, parametrik teknik ve modellerin kullanılmasında, ciddi düzeyde bir yanlılık oluşturmayacağını göstermektedir. Kullanılacak istatistiksel tekniğin karmaşıklık düzeyine bağlı olarak değişmekle birlikte genel olarak tek değişkenli tekniklerde 40 civarı, çok değişkenli tekniklerde ise 150 civarı ve üzeri örneklemler, ayrıca grup büyüklükleri arasında 4-5 katı geçmeyen oransal farklılıklar, normallik ve homojenlik ihlallerinin göz ardı edilebileceği koşullar olarak görülmektedir.

Keywords

çarpıklık, uçdeğer, varsayım, parametrik test, doğrusal modeller

Ethical Statement

Bu çalışma TÜBİTAK tarafından desteklenen 223K382 no’lu proje kapsamında hazırlanmıştır.

Supporting Institution

TÜBİTAK

Project Number

223K382

Evaluation of the Effect of Normality and Homogeneity Violations in Finding Appropriate Statistical Techniques in Research in the Context of Related Literature.

Abstract

Finding the appropriate statistical technique in research is a challenging step that requires taking into account the methodological design of the research, as well as the purpose of the analysis, sample size and structure, and the characteristics of the data and dataset. Parametric tests, or more generally linear models, are considered tests and models that are sensitive to the basic assumptions of (1) normality and (2) homogeneity of variances. Serious violations of normality and homogeneity may lead to the decision not to use these tests. On the other hand, what constitutes a serious level is an uncertain and controversial issue. In this context, the aim of this study is; to discuss and evaluate in which cases and conditions violations of normality and homogeneity can be considered "serious" or "negligible" in determining the appropriate statistical technique, and also what kind of solutions can be applied in such cases, based on relevant research and basic reference books. This study is a theoretical study in the form of a compilation conducted on the findings of basic reference books and related research in the relevant literature. In this context, 20 basic reference books with high recognition in the field and 25 articles examining the effects of assumption violations on statistical techniques were identified. Discussions were conducted in line with the research questions. As a result, the related literature indicates that, when sufficient sample size and balance between groups are ensured, violations of normality and homogeneity will not cause serious bias in the use of parametric techniques and models. Although it varies depending on the complexity level of the statistical technique to be used, in general, samples of around 40 in univariate techniques and around 150 and above in multivariate techniques, as well as proportional differences between group sizes not exceeding 4-5 times, are seen as conditions where violations of normality and homogeneity can be ignored.

Keywords

skewness, outliers, assumption, parametric test, linear models

Ethical Statement

This study was prepared within the scope of project number 223K382 supported by TÜBİTAK.

Supporting Institution

TÜBİTAK

Project Number

223K382

References

• Blanca, M. J., Alarcón, R., Arnau, J., Bono, R., & Bendayan, R. (2017). Non-normal data: Is ANOVA still a valid option? Psicothema, 29(4), 552-557. https://doi.org/10.7334/psicothema2016.383
• Çavuş, M. (2024). Comparison of one-way ANOVA tests under unequal variances in terms of median p-values. Communications in Statistics-Simulation and Computation, 53(4), 1619-1632.
• Cochran, W. G. (1977). Sampling techniques (3rd ed.). John Wiley & Sons.
• Cohen, B. H., & Lea, R. B. (2004). Essentials of statistics for the social and behavioral sciences. John Wiley & Sons, Inc.
• Cohen, R. J., & Swerdlik, M. (2010). Psychological testing and assessment: An introduction to tests and measurement. McGraw-Hill Book Co.
• Dancey, C. P., & Reidy, J. (2007). Statistics without math for psychology (5th ed.). Pearson.
• Davey, A., & Savla, J. (2010). Statistical power analysis with missing data: A structural equatic modeling approach. Routledge.
• DeCarlo, L. T. (1997). On the meaning and use of kurtosis. Psychological Methods, 2(3), 292-307.
• Delacre, M., Lakens, D., & Leys, C. (2017). Why psychologists should by default use Welch’s t-test instead of student’s t-test. International Review of Social Psychology, 30(1), 92-101.
• Douzenis, C., & Rakow, E. A. (1987) Outliers: A potential data problem. Mid-South Educational Research Association, Mobile, AL.
• Efron, B., & Tibshirani, R. J. (1993). An introduction to the bootstrap. Chapman & Hall
• Erceg-Hurn, D. M., & Mirosevich, V. M. (2008). Modern robust statistical methods: An easy way to maximize the accuracy and power of your research. American Psychologist, 63(7), 591-601.
• Field, A. (2013). Discovering statistics using IBM SPSS statistics. Sage Publications.
• Fox, J. (2015). Applied regression analysis and generalized linear models. Sage Publications.
• Gelman, A., Carlin, J. B., Stern, H. S., Dunson, D. B., Vehtari, A., & Rubin, D. B. (2013). Bayesian data analysis. CRC Press.
• Gelman, A., Hill, J., & Vehtari, A. (2021). Regression and other stories. Cambridge University Press.
• Hair, J. F., Black, W. C., Babin, B. J. & Anderson, R. E. (2010). Multivariate data analysis. Pearson Prentice Hall.
• Hayes, A. F., & Cai, L. (2007). Using heteroscedasdicity-consistent standard error estimators in OLS regression: An introduction and software implementation. Behavior Research Methods, 39(4), 709-722.
• Howell, D. C. (2010). Statistical methods for psychology. Wadsworth Cengage Learning.
• Hu, L. T., & Bentler, P. M. (1999). Cutoff criteria for fit indexes in covariance structure analysis: Conventional criteria versus new alternatives. Structural Equation Modeling: A Multidisciplinary Journal, 6(1), 1-55.
• Huberty, C. J., & Morris, J. D. (1989). Multivariate analysis versus multiple univariate analyses. Psychological Bulletin, 105(2), 302-308.
• Johnson, R. A., & Wichern, D. W. (2007). Applied multivariate statistical analysis (6th ed.). Prentice-Hall.
• Keselman, H. J., Algina, J., & Kowalchuk, R. K. (2001). The analysis of repeated measures designs: A review. British Journal of Mathematical and Statistical Psychology, 54(1), 1-20.
• Kirk, R. E. (1995). Experimental design: Procedures for the behavioral sciences (4th ed.). Sage Publications.
• Kish, L. (1965). Survey sampling. John Wiley & Sons.
• Kline, R. B. (2015). Principles and practice of structural equation modeling (4th ed.). Guilford Press.
• Knief, U., & Forstmeier, W. (2021). Violating the normality assumption may be the lesser of two evils. Behavior Research Methods, 53, 2576-2590. https://doi.org/10.3758/s13428-021-01587-5
• Kruschke, J. K. (2014). Doing Bayesian data analysis: A tutorial with R, JAGS, and Stan. Academic Press.
• Long, J. S., & Ervin, L. H. (2000). Using heteroscedasticity consistent standard errors in the linear regression model. The American Statistician, 54(3), 217-224.
• MacCallum, R. C., Widaman, K. F., Zhang, S., & Hong, S. (1999). Sample size in factor analysis. Psychological Methods, 4(1), 84-99.
• Mardia, K. V. (1974) Applications of some measures of multivariate skewness and kurtosis in testing normality and robustness studies. Sankhyā: The Indian J Statist, Series B 36, 115-28.
• Maxwell, S. E., & Delany, H. D. (2004). Designing experiments and analyzing data: A model comparison perspective (2nd ed.). Lawrence Erlbaum Associated, Publishers.
• Osborne, J. W., & Overbay, A. (2004). The power of outliers (and why researchers should ALWAYS check for them). Practical Assessment, Research & Evaluation, 9(6), 1-12.
• Pallant, J. (2016). A step by step guide to data analysis using IBM SPSS. McGraw Hill Education.
• Pek, J., Wong, O., & Wong, A. C. M. (2018). How to address non-normality: A taxonomy of approaches, reviewed, and illustrated. Frontiers in Psychology, 9, Article 2104. https://doi.org/10.3389/fpsyg.2018.02104
• Razali, N. M., & Wah, Y. B. (2011). Power comparisons of Shapiro-Wilk, Kolmogorov-Smirnov, Lilliefors and Anderson-Darling tests. Journal of Statistical Modeling and Analytics, 2(1), 22-33.
• Rousseeuw, P. J., & Leroy, A. M. (1987). Robust regression and outlier detection. Wiley.
• Ruxton, G. D. (2006). The unequal variance t-test is an underused alternative to Student's t-test and the Mann–Whitney U test. Behavioral Ecology, 17(4), 688-690.
• Sayago, A., & Asuero, A. A. (2004). Fitting straight lines with replicated observations by linear regression: Part II. Testing for homogeneity of variances. Critical Reviews in Analytical Chemistry, 34(3-4), 133-146.
• Stevens, J. P. (2009). Applied multivariate statistics for the social sciences. Routledge.
• Tabachnick, B, G., & Fidell, L. S. (2013). Using multivariate statistics. Pearson.
• Thompson, B. (2006). Foundations of behavioral statistics. The Guilford Press.
• Tukey, J. W. (1977). Exploratory data analysis. Addison-Wesley.
• Wilcox, R. R. (2009). Basic statistics: Understanding conventional methods and modern insights. Oxford University Press.
• Wilcox, R. R. (2012). Introduction to robust estimation and hypothesis testing (3rd ed.). Academic Press.
• Yang, K., Tu, J., & Chen, T. (2019). Homoscedasticity: An overlooked critical assumption for linear regression. General Psychiatry, 32(5) Article e100148. https://doi.org/10.1136/gpsych-2019-100148
• Zumbo, B. D., & Jennings, J. (2002). The robustness of validity and efficiency of the related samples t-test in the presence of outliers. Psicologica, 23, 415-450.