Ambiguous probabilities: when does p =0.3 reflect a possibility, and when does it express a doubt?

Verbal phrases denoting uncertainty are usually held to be more vague than numerical probability statements. They are, however, directionally more precise, in the sense that they are either positive, suggesting the occurrence of a target outcome, or negative, drawing attention to its non‐occurrence. A numerical probability will, in contrast, sometimes be perceived as positive and sometimes as negative. When asked to complete sentences such as ‘The operation has a 30% chance of success, because’ some people will give reasons for success (‘the doctors are expert surgeons’), whereas others will give reasons for failure (‘it is a difficult operation’). It is shown in two experiments that positive reasons are given more often than negative ones, even for p values below 0.5, especially when the probability is higher than expected, and the target outcome is non‐normal, undesirable, and phrased as a negation. We conclude that the directionality of numerical probabilities (as opposed to verbal phrases) is context‐dependent, but biased towards a positive interpretation. Copyright © 2000 John Wiley & Sons, Ltd.