A novel modification approach for the one sample Kolmogorov-Smirnov test in large sample size

This study aims to propose and evaluate a modified version of the One-Sample Kolmogorov-Smirnov (K-S) test that addresses its current limitations in large sample groups, with the goal of improving its accuracy and reliability in assessing normality assumptions in medical research data. In addition to the classical K-S test, a logarithmic modification was applied to reduce the impact of sample size. This modification replaces the sample size in the test calculation with a logarithmic formula (ln n²) to prevent z-values from becoming excessively small in large samples. Statistical analyses were conducted using Microsoft 365/Excel, SPSS 21.0 and STATA/MP18 with a geometric approach employed to assess data normality using the Geometric Approach to Normality Testing. The study analyzed real-world laboratory data obtained from the complete blood count (CBC) results of 122,310 adult patients (aged ≥18 years) who were treated at Cerrahpaşa Medical Faculty Hospital throughout 2022. The modified K-S test with the proposed logarithmic modification (ln n²) reduced the tendency to reject normality solely due to large sample size. The modified test was able to confirm that some hematological parameters did indeed fit normal distribution models, while discriminating those that did not. In particular, analysis of the data set trimmed by 0.5% showed further improvement in test performance. Consequently, the proposed modification is shown to provide a more sensitive method for assessing the assumption of normal distribution in large data sets. The method can be easily integrated into existing statistical software, making it accessible for routine use in large-scale data analysis.