Permütasyon testlerinin doğrusal regresyonda kullanılabilirliğinin irdelenmesi

Genellikle F ve t testleri deneysel veri analizinde doğrusal modellerin ve/veya parametrelerin önemini test etmek için kullanılır. Bu testler çoğu durumda oldukça etkili olsa da modelin ihtiyaç duyduğu bir ya da daha fazla varsayım sağlanamadığında etkilerini kaybetmektedir. Bu durumda, varsayımlardan etkilenmeyen permütasyon testleri parametrik olmayan bir yöntem olarak uygulanabilmektedir. Bu çalışmada, doğrusal regresyon analizi için permütasyon testleri incelendi. Testin regresyon tekniği ile birlikte kullanımı biyolojik çalışmalardan elde edilen ve yapay olarak üretilen veri kümeleri üzerinde gerçekleştirildi. Ayrıca, permütasyon testlerinin iki türü (ham verinin tam permütasyonu ve kalıntıların permütasyonu) Normal, Ki-kare ve Poisson dağılışları gibi farklı dağılışa sahip veri setleri için karşılaştırılmalı olarak incelendi. Sonuç olarak, bu çalışmada ilgilenilen tüm dağılışlarda permütasyon testlerinin I. Tip hatayı engellemek için kullanılabileceği anlaşıldı.

Anahtar Kelimeler:

hayvan deneyleri, doğrusal modeller, matematiksel modeller, istatistiksel analizler, regresyon analizleri

To examine the usability of permutation tests on linear regression

Generally, F and t tests are used to test significance of linear models and/or their parameters in experimental data analysis. Although these tests are considerably effective in most cases they may be ineffective for some data sets when one or more of the assumptions belongs to the model are not satisfied. In these cases, permutation tests that are not affected by the assumptions can be applied as non-parametric test methods. In this paper, the permutation tests for linear regressions were introduced, and their uses were demonstrated on real biometrical and hypothetically produced data sets. Additionally, two types of permutation (permutation of raw data and permutation of residuals) were also compared for data sets which have Normal, Chi-square, Poisson distributions. As a result, it was obtained that permutation tests can be used to avoid Type I error for linear regression models in all forms of distributions concerned in this study.

Keywords:

animal experiments, linear models, mathematical models, statistical analysis, regression analysis,

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