In this post, I focus on the logic underlying statistical inference based on fMRI research designs. This consists of (1) modelling the hemodynamic response; (2) "first-level" within-subject analysis of time series; (3) "second-level" population inferences drawn from a random sample of participants; and (4) dealing with familywise error. This is part of a line of teaching-oriented posts aimed at explaining fundamental concepts in statistics, neuroscience, and psychology.