ANOM ve ANOMTR Testlerinin Performansları Bakımından Karşılaştırılması

Year 2019, Volume: 6 Issue: 2, 193 - 198, 30.06.2019

Soner Yiğit

https://doi.org/10.19159/tutad.524099

Abstract

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.

Keywords

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

Comparison of ANOM and ANOMTR Tests with Regard to Performances

Abstract

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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