Averaging learning curves across and within participants
Averaging learning curves across and within participants
复制标题
DOI：
10.3758/bf03195493
复制
发表时间：
2003-02-01
期刊：
影响因子：
--
通讯作者：
Heathcote, A
中科院分区：
文献类型：
--
作者：
Brown, S;Heathcote, A
我们考察了最近的担忧，即平均学习曲线可能会呈现出个人学习的扭曲图景。对一系列范例的练习曲线数据的分析表明，当计算参与者的算术平均值时，对于幂函数和指数函数的拟合，这种担忧是有充分依据的。我们还证明，总体上，参与者的几何平均并不能避免扭曲。相比之下，我们证明了单独曲线的块平均和类似的平滑技术几乎或没有引起函数形式的扭曲，同时仍然提供了激励使用平均的降噪好处。我们的分析主要涉及平均化对指数函数和幂函数拟合的影响，但我们也定义了任何一组函数必须满足的一般条件，以避免平均化造成的扭曲。
We examine recent concerns that averaged learning curves can present a distorted picture of individual learning. Analyses of practice curve data from a range of paradigms demonstrate that such concerns are well founded for fits of power and exponential functions when the arithmetic average is computed over participants. We also demonstrate that geometric averaging over participants does not, in general, avoid distortion. By contrast, we show that block averages of individual curves and similar smoothing techniques cause little or no distortion of functional form, while still providing the noise reduction benefits that motivate the use of averages. Our analyses are concerned mainly with the effects of averaging on the fit of exponential and power functions, but we also define general conditions that must be met by any set of functions to avoid distortion from averaging.