当球性被侵犯时,重复测量ANOVA和调整的F测试:哪个程序是最好的?
María J Blanca1, Jaume Arnau2, F Javier García-Castro3
1Department of Psychobiology and Behavioral Sciences Methodology, University of Malaga, Málaga, Spain.
Frontiers in psychology
|September 15, 2023
概括
温室-Geisser (F-GG) 和Huynh-Feldt (F-HF) 调整的F测试控制了重复测量中的I型错误 ANOVA,当球性被破坏时. F-GG更保守,特别是在小样本大小和显著的球体性违规方面.
科学领域:
- 统计 统计 统计 统计
- 心理测量 心理测量 心理测量
- 生物统计学 生物统计学
背景情况:
- 单向重复测量 ANOVA 假定球形,这种条件在实践中经常被违反.
- 违反球性可以在标准F测试中增加I型错误率.
- 调整的F测试,如温室-Geisser (F-GG) 和Huynh-Feldt (F-HF),通常用于纠正球性违规.
研究的目的:
- 评估未经调整的F-统计,F-GG和F-HF在单向重复测量设计中的表现.
- 评估I型错误率和统计能力在不同条件下的球形性违规和样本大小.
- 根据球状性违规程度,为选择适当的调整F测试提供指导.
主要方法:
- 通过使用单向重复测量设计与正常数据进行了一个模拟研究.
- 对重复测量次数 (3,4,6) 和样本大小 (10至300) 进行了操纵.
- 违反球体性被系统地变化,以epsilon (ε) 值固定使用温室-盖塞程序.
主要成果:
- 未经调整的F统计数据显示,随着球形性违规的增加,I型错误率膨胀.
- 在测试条件下,F-GG和F-HF都有效控制了I型错误率.
- F-GG调整比F-HF更为保守,特别是在小样本大小和严重的球体性违规 (ε < 0.60) 的情况下.
结论:
- 建议在球状性被侵犯时进行调整的F-测试 (F-GG和F-HF),而不是未调整的F-统计.
- 对于低于0.60的epsilon (ε) 值,建议进行温室-盖塞 (F-GG) 调整,以更好地控制I型错误.
- 对于0.60或以上的epsilon (ε) 值,可以选择惠恩-费尔特 (F-HF) 调整,在错误控制和功率之间提供平衡.
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