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While parameters are crucial components of cognitive models, relatively little importance has been given to their units. We show that this has lead to some parameters to be contaminated, introducing an artifactual correlation between them. We also show that this has led to the illegal comparison of parameters with different units of measurement – this may invalidate parameter comparisons across participants, conditions, groups, or studies. We demonstrate that this problem affects two related models: Stevens’ Power Law and Rachlin’s delay discounting model. We show that it may even affect models which superficially avoid the incompatible units problem, such as hyperbolic discounting. We present simulation results to demonstrate the extent of the issues caused by the muddled units problem. We offer solutions in order to avoid the problem in the future or to aid in re-interpreting existing datasets.