Repealing the power law: the case for an exponential law of practice

The power function is treated as the law relating response time to practice trials. However, the evidence for a Power Law is flawed because it is based on averaged data. We report a survey that assessed the form of the practice function for individual learners and learning conditions in paradigms that have shaped theories of skill acquisition. We fit power and exponential functions to 40 sets of data representing 7910 learning series from 475 subjects in 24 experiments. The exponential function fit better than the power in all the unaveraged data sets. Averaging produced a bias in favour of the power function. A new practice function based on the exponential, the APEX function, fit better than a power function with an extra, pre-experimental practice, parameter. Clearly, the best candidate for the Law of Practice is the exponential or APEX function, not the generally accepted power function. Theoretical implications are discussed.