Summary: Loosely speaking, a proximity-oblivious (property) tester is a randomized algorithm that makes a constant number of queries to a tested object and distinguishes objects that have a predetermined property from those that lack it. Specifically, for some threshold probability \(c\), objects having the property are accepted with probability at least \(c\), whereas objects that are \(\epsilon\)-far from having the property are accepted with probability at most \(c-F(\epsilon)\), where \(F: (0,1] \to (0,1]\) is some fixed monotone function. (We stress that, in contrast to standard testers, a proximity-oblivious tester is not given the proximity parameter.){ }The foregoing notion, introduced by the first author and D. Ron [in: Proceedings of the 41st annual ACM symposium on theory of computing, STOC ’09. New York, NY: Association for Computing Machinery (ACM). 141–150 (2009; Zbl 1304.05134)], was originally defined with respect to \(c = 1\), which corresponds to one-sided error (proximity-oblivious) testing. Here we study the two-sided error version of proximity-oblivious testers; that is, the (general) case of arbitrary \(c \in (0,1]\). We show that, in many natural cases, two-sided error proximity-oblivious testers are more powerful than one-sided error proximity-oblivious testers; that is, many natural properties that have no one-sided error proximity-oblivious testers do have a two-sided error proximity-oblivious tester.