Linganisha mbinu

	Vipimo vya Takwimu Visivyo vya Parametrik	Utohozi wa Kitakwimu wa Kibayesi
Nyanja	Takwimu za Utafiti	Takwimu za Utafiti
Familia	Process / pipeline	Process / pipeline
Mwaka wa asili	1947	1763
Mwanzilishi	Henry Mann and Donald Whitney	Thomas Bayes
Aina	Method	Method
Chanzo asilia	Mann, H. B., & Whitney, D. R. (1947). On a test of whether one of two random variables is stochastically larger than the other. Annals of Mathematical Statistics, 18(1), 50–60.	Bayes, T. (1763). An essay towards solving a problem in the doctrine of chances. Philosophical Transactions of the Royal Society, 53, 370–418.
Majina mbadala	rank-based tests, Mann-Whitney U, Kruskal-Wallis, distribution-free	Bayes theorem, Bayesian inference, posterior probability
Zinazohusiana	3	3
Muhtasari	Nonparametric (distribution-free) tests are statistical methods for hypothesis testing that do not assume data follow a specific probability distribution (e.g., normal), making them robust to departures from normality, outliers, and ordinal data. The Mann-Whitney U test (1947) and Kruskal-Wallis test (1952) extend hypothesis testing beyond the constraints of parametric assumptions. Essential in biology, medicine, psychology, and any field where data are non-normal, highly skewed, or measured on ordinal scales (rankings, ratings), nonparametric tests provide valid inference when parametric assumptions fail.	Bayesian inference is a statistical framework using Bayes' theorem to update beliefs about parameters or hypotheses as data accumulate. Published posthumously in 1763, Thomas Bayes' work lay dormant until the 20th century, when computational advances (Gibbs sampling, Markov Chain Monte Carlo) made Bayesian methods practical. Unlike frequentist inference (which treats parameters as fixed unknowns), Bayesian analysis treats parameters as random variables with probability distributions, enabling direct probability statements about parameters, incorporation of prior knowledge, and sequential updating. Essential in precision medicine, adaptive trials, complex hierarchical models, and any context where prior information enriches inference.