In neurophysiology, psychophysics, optical imaging and functional imaging studies, the investigator seeks a relationship between a high-dimensional variable, such as an image, and a categorical variable, such as the presence or absence of a spike or a behavior. The usual analysis strategy is fundamentally identical across these contexts--it amounts to calculating the average value of the high-dimensional variable for each value of the categorical variable and comparing these results by subtraction. Though intuitive and straightforward, this procedure may be inaccurate or inefficient and may overlook important details. Sophisticated approaches have been developed within these several experimental contexts, but they are rarely applied beyond the context in which they were developed. Recognition of the relationships among these contexts has the potential to accelerate improvements in analytic methods and to increase the amount of information that can be gleaned from experiments.