Akademik Veri Yönetim Sistemi
VI. International Applied Statistics Congress (UYIK – 2025) , Ankara, Türkiye, 14 - 16 Mayıs 2025, ss.53, (Özet Bildiri)
This study introduces the NO Test, a novel nonparametric method for comparing two independent samples by examining differences not just in central tendency but across distributional quantiles, particularly in the tails. The proposed method combines the Navruz–Özdemir (NO) quantile estimator, the Mahalanobis distance, and a percentile bootstrap approach. It evaluates whether the 2.5th, 50th, and 97.5th percentiles differ significantly between groups by examining how the vector of quantile differences is nested within the distribution of bootstrapped differences. This approach yields a global p-value for determining distributional equality. Simulation studies covering symmetric, skewed, and heavy-tailed distributions show that the NO Test provides superior power to detect differences, especially when conventional tests like Kolmogorov– Smirnov, Anderson–Darling, or Cramér–von Mises may fail. Moreover, the test reliably maintains Type I error rates under various continuous and discrete distribution settings. Compared to other quantile-based approaches, it offers robustness even in small samples and settings with tied values. The NO Test thus offers a powerful and flexible alternative for detecting subtle distributional differences, making it especially valuable in fields where tail behavior matters, such as finance, biomedical research, and environmental studies.