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

Öz

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.

Anahtar Kelimeler

• skewness
• outliers
• assumption
• parametric test
• linear models

Destekleyen Kurum

TÜBİTAK

Proje Numarası

223K382

Etik Beyan

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

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

Öz

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.

Anahtar Kelimeler

• çarpıklık
• uçdeğer
• varsayım
• parametrik test
• doğrusal modeller

Destekleyen Kurum

TÜBİTAK

Proje Numarası

223K382

Etik Beyan

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

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