Despite the recent “epistemic turn” in the philosophy of measurement, philosophers have ignored a nearly 80 year controversy about the relationship between statistical inference and measurement theory. Some scholars maintain that measurement theory places no constraints on statistics, whereas others argue that the measurement scale (e.g., ordinal or interval) of one’s data determines which statistical methods are “permissible.” I defend an intermediate position: even if existing measurement theory were irrelevant to statistical inference, it would be critical for scientific inference, which requires connecting statistical hypotheses to broader research hypotheses.