Testing curvatures of learning functions on individual trial and block average data

Many models offer different explanations of learning processes, some of them predicting equal learning rates between conditions. The simplest method by which to assess this equality is to evaluate the curvature parameter for each condition, followed by a statistical test. However, this approach is highly dependent on the fitting procedure, which may come with built-in biases difficult to identify Averaging the data per block of training would help reduce the noise present in the trial data, but averaging introduces a severe distortion on the curve, which can no longer be fitted by the original function. In this article, we first demonstrate what is the distortion resulting from block averaging. The block average learning function, once known, can be used to extract parameters when the performance is averaged over blocks or sessions. The use of averages eliminates an important part of the noise present in the data and allows good recovery of the learning curve parameters. Equality of curvatures can be tested with a test of linear hypothesis. This method can be performed on trial data or block average data, but it is more powerful with block average data.