Never say "not": Impact of negative wording in probability phrases on imprecise probability judgments

A reanalysis of Budescu et al.’s (2009) data on numerical interpretations of the Intergovernmental Panel on Climate Change (IPCC 2007) fourth report’s verbal probability expressions (PE’s) revealed that negative wording has deleterious effects on lay judgements. Budescu et al. asked participants to interpret PE’s in IPCC report sentences, by asking them to provide lower, “best” and upper estimates of the probabilities that they thought the authors intended. There were four experimental conditions, determining whether participants were given any numerical guidelines for translating the PE’s into numbers. The first analysis presented here focuses on six sentences in Budescu et al. that used the PE “very likely” or “very unlikely”. A mixed beta regression (Verkuilen & Smithson, in press) modelling the three numerical estimates revealed a less regressive mean and less dispersion for positive than for negative wording in all three estimates. Negative wording therefore resulted in more regressive estimates and less consensus regardless of experimental condition. The second analysis focuses on two statements that were positive-negative duals. Appropriate pairs of responses were assessed for conjugacy and additivity. A large majority of respondents were appropriately superand sub-additive in their lower and upper probability estimates. A mixed beta regression model of these three variables revealed that the P (A) and P (A) pairs adhered most closely to conjugacy. Also, the greatest dispersion occurred for P (A) + P (A), followed by P (A) + P (A). These results were driven by the dispersion in the estimates for the negativelyworded statement. This paper also describes the effects of the experimental conditions on conjugacy and dispersion.