ANOM ve ANOMTR Testlerinin Performansları Bakımından Karşılaştırılması

Bu çalışmada, tek yönlü Ortalamaların Analizi (ANOM) ve Transforme Edilmiş Ranklara Dayalı Ortalamaların Analizi (ANOMTR) testleri varyansları homojen normal olmayan dağılımlarda 1. tip hata olasılığı ve testin gücü bakımından karşılaştırılmıştır. Yapılan 100000 simülasyon denemesi sonucunda, dikkate alınan deneme koşulları ne olursa olsun ANOMTR testi bakımından gerçekleşen 1. tip hata olasılıkları % 4.50-5.50 içinde kalmıştır. Ancak ANOM testi bakımından gerçekleşen 1. tip hata olasılıklarının genel olarak bu sınırlar içerisinde kalmadığı görülmüştür. ANOM testinin dağılımın eğriliğinden ziyade, dikliğinden oldukça olumsuz etkilendiği tespit edilmiştir. Varyanslar homojen olduğu sürece, dağılımın şekli ve tekerrür sayısı ne olursa olsun ANOMTR testi oldukça güvenilir sonuçlar vermiştir.

Anahtar Kelimeler:

ANOM, ANOMTR, 1. tip hata, testin gücü, simülasyon

Comparison of ANOM and ANOMTR Tests with Regard to Performances

In this study, one-way ANOM (Analysis of Means) and ANOMTR (Analysis of Means Based on Transformed Ranks) tests were compared in non-normal distributions with homogeneous variances in terms of the Type I error rate and test power. As a result of 100.000 simulation experiments conducted, regardless of the experimental conditions considered, actual Type I error rates occurred in ANOMTR was within the limits of 4.50-5.50%. However, it was observed that actual Type I error rates occurred in ANOM test was generally not within these limits. The ANOM test was found to be affected quite negatively by the kurtosis rather than the skewness of the distribution. As long as the variances were homogeneous, the ANOMTR test has given very reliable results regardless of the shape of the distribution and the number of replications.

Keywords:

ANOM, ANOMTR, type I error rate, test power, simulation,

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