Game theorists typically assume that changing a game's payoff levels - by adding the same constant to, or subtracting it from, all payoffs - should not affect behavior. While this invariance is an implication of the theory when payoffs mirror expected utilities, it is an empirical question when "payoffs" are actually money amounts. Loss avoidance is a phenomenon where payoff-level changes matter when they change the signs of payoffs: gains become losses or vice versa. We report the results of a human-subjects experiment designed to test for two types of loss avoidance: certain-loss avoidance (avoiding a strategy leading to a sure loss, in favor of an alternative that might lead to a gain) and possible-loss avoidance (avoiding a strategy leading to a possible loss, in favor of an alternative that leads to a sure gain). Subjects in the experiment play three versions of Stag Hunt, which are identical up to the level of payoffs, under a variety of treatments. We find strong evidence of behavior consistent with certain-loss avoidance in the experiment. We also find evidence of possible-loss avoidance, though weaker than that for certain-loss avoidance. Our results carry implications for theorists modeling real-life situations with game theory, and for experimenters attempting to test theory and interpret observed behavior in terms of theory.