Tests of the relative performance of multiple forecasting models are sensitive to how the set of alternatives is defined. Evaluating one model against a particular set may show that it has superior predictive ability. However, changing the number or type of alternatives in the set may demonstrate otherwise. This paper focuses on forecasting models based on technical analysis and analyzes how much data snooping bias can occur in tests from restricting the size of forecasting model “universes” or ignoring alternatives used by practitioners and other researchers. A Monte Carlo simulation shows that false discoveries have an average increase of 0.72-2.5 percentage points each time one removes half of the prediction models from the set of relevant alternatives. A complementary empirical investigation suggests that at least 50% of positive findings reported in the literature concerned with trading rule overperformance may be false. Our results motivate several recommendations for applied researchers that would alleviate data snooping bias in some of the more popular statistical tests used in the literature.