Political surveys often include multi-item scales to measure individual predispositions such as authoritarianism, egalitarianism, or racial resentment. Scholars use these scales to examine group differences in these predispositions, comparing women to men, rich to poor, or Republicans to Democrats. Such research implicitly assumes that, say, Republicans’ and Democrats’ responses to the egalitarianism scale measure the same construct in the same metric. This research rarely evaluates whether the data possess the characteristics necessary to justify this equivalence assumption. We present a framework to test this assumption and correct scales when it fails to hold. Examining 13 commonly-used scales on the 2012 and 2016 ANES, we find widespread violations of the equivalence assumption. These violations often lead to biased conclusions about the magnitude or direction of theoretically-important group differences. These results suggest we must reevaluate what we think we know about how authoritarianism and other predispositions are distributed in the mass public.