Comparing Conditional Probability Matrices

In a wide variety of tasks, a persons performance may be characterized by a conditional probability matrix having one row for each possible stimulus, one column for each possible response, and with each cell entry being a conditional probability of the form P responsestimulus. This paper describes a method for measuring how close one persons conditional probability matrix is either to another persons matrix, to the persons own matrix in another condition, or to the matrix predicted by a model. We describe a method for defining an inner product on the space of all SxR matrices. The inner product of two persons conditional probability matrices measures their trial-by-trial response agreement. This inner product induces a distance metric on the space of all SxR matrices. We then describe a method for empirically estimating the inner product of two persons matrices. From inner-product estimates, a distance estimate may be calculated.