Normality Testing in Medical Data: Classical vs. Adapted Jarque-Bera

The principle of normality stands as a crucial component for statistical procedure specifically in medical research since parametric methods such as t-tests ANOVA and regression analysis depend on normally distributed data for proper inference. Real medical data databases deviate from normal distribution patterns when researchers observe skews and outliers or heavy-tailed distributions because such variations negatively impact statistical research outcomes. A performance evaluation examines classical and modified normality tests for medical data distribution assessment. Two proposed adaptations known as First Adapted Jarque-Bera (JB*) alongside Second Adapted Jarque-Bera (JB**) join a comparison with traditional tests that include Shapiro-Wilk, Anderson-Darling, Kolmogorov-Smirnov and Jarque-Bera and Lilliefors and Shapiro-Francia tests and D’Agostino’s skewness and Anscombe-Glynn kurtosis and Pearson Chi-Square Test results alongside JBa, JBσ2 , JBa,σ2 tests. The study carries out a detailed simulation analysis with 20,000 replicates among different sample sizes (10, 20, 30, 50, 100) to evaluate these tests against symmetric and asymmetric distributions. Standard testing techniques demonstrate good performance at large sample levels but show limitations when dealing with small sample-based and non-normal data which causes erroneous type I or type II detection rates. The JB* and JB** tests prove to be robust since they sustain stronger error control together with superior detection capabilities in multiple distributional environments. A correct assessment of normality remains essential for valid statistical inference in clinical trials together with biomedical studies. The presented study enhances medical statistics methodology by developing reliable statistical analyses for healthcare decisions making.