Bias in exponential and power function fits due to noise: comment on Myung, Kim and Pitt

Myung, Kim and Pitt (2000) demonstrated that simple power functions almost always provide a better fit than simple exponential functions to purely random data. This result has important implications because it suggests that high noise levels, which are common in psychological, may cause a bias favouring power functions. We replicate their result, and extend it by showing strong bias for realistic sample sizes. We also show that biases occur for data that contain both random and systematic components, as may be expected in real data. We then demonstrate that these biases disappear for two- or three- parameter functions that include linear parameters (in at least parameterisation).