Center for Cognitive Neuroscience, Duke University, Durham, North Carolina 27708, USA.
Behav Res Methods. 2012 Sep;44(3):788-94. doi: 10.3758/s13428-011-0172-y.
Research in cognitive science has documented numerous phenomena that are approximated by linear relationships. In the domain of numerical cognition, the use of linear regression for estimating linear effects (e.g., distance and SNARC effects) became common following Fias, Brysbaert, Geypens, and d'Ydewalle's (1996) study on the SNARC effect. While their work has become the model for analyzing linear effects in the field, it requires statistical analysis of individual participants and does not provide measures of the proportions of variability accounted for (cf. Lorch & Myers, 1990). In the present methodological note, using both the distance and SNARC effects as examples, we demonstrate how linear effects can be estimated in a simple way within the framework of repeated measures analysis of variance. This method allows for estimating effect sizes in terms of both slope and proportions of variability accounted for. Finally, we show that our method can easily be extended to estimate linear interaction effects, not just linear effects calculated as main effects.
认知科学的研究已经记录了许多可以用线性关系来近似的现象。在数值认知领域，线性回归被用于估计线性效应（例如距离效应和 SNARC 效应），这一方法在 Fias、Brysbaert、Geypens 和 d'Ydewalle（1996）对 SNARC 效应的研究之后变得很常见。虽然他们的工作已经成为该领域分析线性效应的典范，但它需要对个体参与者进行统计分析，并且不能提供可变性解释比例的度量（参见 Lorch 和 Myers，1990）。在本方法说明中，我们使用距离效应和 SNARC 效应作为示例，演示了如何在重复测量方差分析的框架内以简单的方式估计线性效应。该方法允许以斜率和可变性解释比例的形式估计效应大小。最后，我们表明，我们的方法可以轻松扩展到估计线性交互效应，而不仅仅是作为主效应计算的线性效应。
