Quantitative theories with free parameters often gain credence when they closely fit data. This is a mistake. A good fit reveals nothing about the flexibility of the theory (how much it cannot fit), the variability of the data (how firmly the data rule out what the theory cannot fit), or the likelihood of other outcomes (perhaps the theory could have fit any plausible result), and a reader needs all 3 pieces of information to decide how much the fit should increase belief in the theory. The use of good fits as evidence is not supported by philosophers of science nor by the history of psychology; there seem to be no examples of a theory supported mainly by good fits that has led to demonstrable progress. A better way to test a theory with free parameters is to determine how the theory constrains possible outcomes (i.e., what it predicts), assess how firmly actual outcomes agree with those constraints, and determine if plausible alternative outcomes would have been inconsistent with the theory, allowing for the variability of the data.Many quantitative psychological theories with free parameters are supported mainly or entirely by demonstrations that they can fit data-that the parameters can be adjusted so that the output of the theory resembles actual results. The similarity is often shown by a graph with two functions: one labeled observed (or data) and the other labeled predicted (or theory or simulated). That the theory fits data is supposed to show that the theory should be taken seriously-should be published, for example. This type of argument is common; judging from a search of Psychological Abstracts , the research literature probably contains thousands of examples. Early instances involved sensory processes (Hecht, 1931) and animal learning (Hull, 1943), but this reasoning is now used in many areas. Here are three examples.1. Cohen, Dunbar, and McClelland (1990) proposed a parallel distributed processing model to explain the Stroop effect and related data. The model was meant to embody a "continuous" view of automaticity, in contrast to an "all-or-none" view (Cohen et al.,