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| 贝叶斯双因素方差分析× | 贝叶斯单因素方差分析× | |
|---|---|---|
| 领域 | 统计学 | 统计学 |
| 方法族 | Hypothesis test | Hypothesis test |
| 起源年份≠ | 1961 (foundations); 2012 (default Bayes factor formulation) | 1961 (foundations); 2012 (ANOVA Bayes factors) |
| 提出者≠ | Harold Jeffreys (foundational); modern default-prior form by Jeffrey N. Rouder et al. | Harold Jeffreys (foundations); Jeffrey Rouder et al. (default priors for ANOVA) |
| 类型 | Bayesian hypothesis test | Bayesian hypothesis test |
| 开创性文献 | Rouder, J. N., Morey, R. D., Speckman, P. L., & Province, J. M. (2012). Default Bayes factors for ANOVA designs. Journal of Mathematical Psychology, 56(5), 356–374. DOI ↗ | Rouder, J. N., Morey, R. D., Speckman, P. L., & Province, J. M. (2012). Default Bayes factors for ANOVA designs. Journal of Mathematical Psychology, 56(5), 356–374. DOI ↗ |
| 别名 | Bayesian factorial ANOVA, Bayes factor two-way ANOVA, Bayesian 2×k ANOVA, Bayesian two-factor ANOVA | Bayesian ANOVA, BF ANOVA, Bayes factor one-way ANOVA, Bayesian F-test |
| 相关≠ | 4 | 3 |
| 摘要≠ | Bayesian two-way ANOVA extends the classical two-way analysis of variance by replacing p-values with Bayes factors and posterior distributions. It quantifies evidence for or against main effects and their interaction using prior-weighted model comparison, yielding conclusions that are directly interpretable in probabilistic terms rather than relying on a fixed significance threshold. | Bayesian one-way ANOVA tests whether the means of three or more independent groups differ by computing a Bayes factor — a ratio that quantifies how much more likely the data are under a model that allows group differences than under the null model that assumes equal means. Unlike the classical F-test, it provides direct evidence for or against the null hypothesis rather than merely rejecting or retaining it. |
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