Researchers commonly use analysis of variance (ANOVA) to statistically test results of factorial designs. Performing an a priori power analysis is crucial to ensure that the ANOVA is sufficiently powered, however, it often poses a challenge and can result in large sample sizes, especially if the expected effect size is small. Due to the high prevalence of small effect sizes in psychology, studies are frequently underpowered as it is often economically unfeasible to gather the necessary sample size for adequate Type-II error control. Here, we present a more efficient alternative to the fixed ANOVA, the so-called sequential ANOVA that we implemented in the R package "sprtt." The sequential ANOVA is based on the sequential probability ratio test (SPRT) that uses a likelihood ratio as a test statistic and controls for long-term error rates. SPRTs gather evidence for both the null and the alternative hypothesis and conclude this process when a sufficient amount of evidence has been gathered to accept one of the two hypotheses. Through simulations, we show that the sequential ANOVA is more efficient than the fixed ANOVA and reliably controls long-term error rates. Additionally, robustness analyses revealed that the sequential and fixed ANOVAs exhibit analogous properties when their underlying assumptions are violated. Taken together, our results demonstrate that the sequential ANOVA is an efficient alternative to fixed sample designs for hypothesis testing. (PsycInfo Database Record (c) 2024 APA, all rights reserved).

中文翻译：

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方差的序贯分析：提高假设检验的效率。


研究人员通常使用方差分析 (ANOVA) 来统计检验因子设计的结果。执行先验功效分析对于确保方差分析具有足够的功效至关重要，但是，它通常会带来挑战，并且可能会导致样本量较大，特别是在预期效应量较小的情况下。由于心理学中小效应量的普遍存在，研究常常力度不足，因为收集足够的样本量来进行充分的 II 型误差控制通常在经济上不可行。在这里，我们提出了一种比固定方差分析更有效的替代方案，即我们在 R 包“sprtt”中实现的所谓顺序方差分析。序贯方差分析基于序贯概率比检验 (SPRT)，该检验使用似然比作为检验统计量并控制长期错误率。 SPRT 收集原假设和备择假设的证据，并在收集到足够数量的证据来接受这两个假设之一时结束此过程。通过模拟，我们表明顺序方差分析比固定方差分析更有效，并且可以可靠地控制长期错误率。此外，稳健性分析表明，当其基本假设被违反时，顺序方差分析和固定方差分析表现出类似的特性。综上所述，我们的结果表明，序贯方差分析是假设检验固定样本设计的有效替代方案。 （PsycInfo 数据库记录 (c) 2024 APA，保留所有权利）。