Barlow, M. C. (1928). A learning curve equation as fitted to learning records. Psychological Review, 35(2), 142-160.
http://dx.doi.org/10.1037/h0070275
By the mathematical justification and use of certain formulae on empirical data the author concludes that he has confirmed the fact that hyperbolic equations furnish a reasonably satisfactory fit to the form of the learning curve. An hyperbolic equation has been fitted to the same set of learning scores by the methods of inspection, averages, and least squares, each of which yields the necessary constants of the hyperbolic equation by following the procedure developed in the mathematical portion of the article. The method of least squares is preferred to the other two. Predicted limits of training correlate more highly with practical training limits than do any other values used as scores in this investigation. While the learning curve forms under consideration fail to show exact agreement with the forms of the learning curve equation, there is sufficient similarity between them to justify the use of the latter for representing the former in certain mental traits, as multiplication and syllable learning, and for predicting limiting practice achievements from the results of early practice in those traits. (PsycINFO Database Record (c) 2016 APA, all rights reserved)