Averaging learning curves across and within participants

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.