Score Test for Homogeneity of Variances in Normal Distributions

Aksoy S., GÖKPINAR F., GÖKPINAR E.

Gazi University Journal of Science, cilt.38, sa.3, ss.1503-1516, 2025 (ESCI) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 38 Sayı: 3
  • Basım Tarihi: 2025
  • Doi Numarası: 10.35378/gujs.1604187
  • Dergi Adı: Gazi University Journal of Science
  • Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI), Scopus, Academic Search Premier, Aerospace Database, Aquatic Science & Fisheries Abstracts (ASFA), Communication Abstracts, Metadex, Civil Engineering Abstracts, TR DİZİN (ULAKBİM)
  • Sayfa Sayıları: ss.1503-1516
  • Anahtar Kelimeler: Computational approach test, Homogeneity of variances, Score test
  • Gazi Üniversitesi Adresli: Evet

Özet

In this study, we suggest a novel test statistic based on the Score statistic for evaluating the homogeneity of variances in normal distributions. In addition to the conventional chi-square approximation of the Score statistic, we introduce a parametric bootstrap technique known as the Computational Approach Test (CAT). Through a simulation study, we evaluate the proposed test’s CAT approach (referred to as CS) and assess its performance against established methods under varying group sizes and sample sizes. The results show that, regardless of the number of groups, the CAT approach of the Score test performs well when sample sizes and variances are directly proportional, even with a minimum sample size of three. Furthermore, when sample sizes and variances are inversely proportional, the proposed test significantly outperforms alternative methods. To demonstrate the application of the discussed methods, we provide two numerical examples.