1.2 Three themes: randomization inference, conGLYPH<133>dence intervals with interference, ine⁄ective trials In this case-study, we reanalyze a randomized experiment in cognitive neuroscience with a view to illustrating three ideas, one very old idea, one somewhat new idea, and one idea that has evolved gradually over more than half a century. In many cognitive neuroscience experiments, a moderate number of subjects are repeatedly exposed to many randomly selected stimuli intended to elicit cognitive activity of a speciGLYPH<133>c type together with its characteristic neurological activity visible with, say, fMRI. Three dilemmas arise in these experiments. First, because a few thoughtful, complex human subjects are observed many times performing simple repetitive tasks, subjects become familiar with the tasks, perhaps increasingly bored or skillful or distracted or fatigued or aware of the purpose of the experiment, so the situation is unlike a study of a single response elicited from each of many separated, unrelated subjects, and also unlike a stationary time series or a repeated measures model with dependence within subjects represented by additive subject parameters. In such a context, one might wish to draw inferences about treatment e⁄ects on many brain regions without relying on a model GLYPH<133>tted to just a few people. Second, for reasons both biological and cognitive, rapid-GLYPH<133>re stimuli are likely to interfere with one another, in part because the neurological response to one stimulus is expected to last well beyond the presentation of the next stimulus, and in part because learning and boredom and surprise are global cognitive responses to long segments of a sequence of stimuli not responses to a single stimulus. If 100 treatment/control tasks are presented to one subject in ten minutes, then it is unrealistic to characterize the e⁄ect of the treatment versus control in terms of response to single trials, because the response to each trial is a⁄ected by many previous trials. We need to characterize the di⁄ering responses to treated and control stimuli without assuming the mind and brain are born anew after 3