Although it is often assumed that the natural language expressions 'some' and 'or' are interpreted according to their first-order logic counterparts, in certain contexts, they receive a narrower interpretation: 'some' is strengthened to 'some, but not all', and 'or' to 'A or B, but not both'. This process is typically explained as an instance of scalar inference. To test this scalar implicature hypothesis, we collect experimental evidence for the effects and interactions of three factors that should affect the robustness of the scalar inferences of 'some' and 'or': the relevance of the stronger alternative, the speaker's competence about the alternative, and the prior probability that the alternative is true. We find that the interpretation of both triggers was affected by speaker competence, but only 'some' was also affected by prior probability, while relevance did not affect either trigger. Ultimately, our results suggest that the interdependence of the three factors is more complex than just the sum of their effects.