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| ノンパラメトリック統計検定× | 分散分析（ANOVA）× | |
|---|---|---|
| 分野 | 研究統計 | 研究統計 |
| 系統 | Process / pipeline | Process / pipeline |
| 提唱年≠ | 1947 | 1925 |
| 提唱者≠ | Henry Mann and Donald Whitney | Ronald A. Fisher |
| 種類 | Method | Method |
| 原典≠ | 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. DOI ↗ | Fisher, R. A. (1925). Statistical Methods for Research Workers. Oliver and Boyd. link ↗ |
| 別名≠ | rank-based tests, Mann-Whitney U, Kruskal-Wallis, distribution-free | ANOVA, F-test |
| 関連≠ | 3 | 4 |
| 概要≠ | 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. | ANOVA is a parametric statistical method developed by Ronald A. Fisher in 1925 that tests whether means differ significantly across three or more independent groups. By partitioning total variance into between-group and within-group components, ANOVA determines whether observed differences are likely due to treatment effects or random variation, making it fundamental to comparative research across medicine, psychology, agriculture, and engineering. |
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