Research Article: Verbal probabilities: Very likely to be somewhat more confusing than numbers

Date Published: April 17, 2019

Publisher: Public Library of Science

Author(s): Bonnie C. Wintle, Hannah Fraser, Ben C. Wills, Ann E. Nicholson, Fiona Fidler, Eldad Yechiam.


People interpret verbal expressions of probabilities (e.g. ‘very likely’) in different ways, yet words are commonly preferred to numbers when communicating uncertainty. Simply providing numerical translations alongside reports or text containing verbal probabilities should encourage consistency, but these guidelines are often ignored. In an online experiment with 924 participants, we compared four different formats for presenting verbal probabilities with the numerical guidelines used in the US Intelligence Community Directive (ICD) 203 to see whether any could improve the correspondence between the intended meaning and participants’ interpretation (‘in-context’). This extends previous work in the domain of climate science. The four experimental conditions we tested were: 1. numerical guidelines bracketed in text, e.g. X is very unlikely (05–20%), 2. click to see the full guidelines table in a new window, 3. numerical guidelines appear in a mouse over tool tip, and 4. no guidelines provided (control). Results indicate that correspondence with the ICD 203 standard is substantially improved only when numerical guidelines are bracketed in text. For this condition, average correspondence was 66%, compared with 32% in the control. We also elicited ‘context-free’ numerical judgements from participants for each of the seven verbal probability expressions contained in ICD 203 (i.e., we asked participants what range of numbers they, personally, would assign to those expressions), and constructed ‘evidence-based lexicons’ based on two methods from similar research, ‘membership functions’ and ‘peak values’, that reflect our large sample’s intuitive translations of the terms. Better aligning the intended and assumed meaning of fuzzy words like ‘unlikely’ can reduce communication problems between the reporter and receiver of probabilistic information. In turn, this can improve decision making under uncertainty.

Partial Text

It is well established that verbal descriptors of uncertainty, such as ‘very likely’, are interpreted in different ways by different people (e.g., [1–6]). Verbal probabilities are more ambiguous than numerical ones, and two people can, and often do, have very different numbers in mind when they hear or read words of estimative probability. People also intuitively use different lexicons, or sets of words, to describe their uncertainty [7]. When information about uncertainty is ambiguous, people’s interpretations are particularly sensitive to context, including how memorable or severe a hazard’s consequences are (e.g. probability of infection versus probability of death) (e.g., [1, 3, 4, 8, 9]). Not only can this mismatch create communication problems between the reporter and receiver of probabilistic information [10], it can also compromise predictive accuracy [11, 12] and undermine decision-making.

For the main experiment, we included data from all participants who responded to at least one experimental item (Control, n = 236; Tooltip, n = 225; Table, n = 231; Brackets, n = 232). Results from the Bayesian hierarchical model (Fig 3) show that all three treatment conditions resulted in participant interpretations of verbal probabilities that were, to varying extents, more consistent with the ICD 203 guidelines than the control, indicated by the improvement in percentage overlap with the guidelines ranges. However, the only condition showing a statistically significant and substantial improvement over the average percentage overlap was the Brackets condition (as the 95% credible intervals do not overlap 0). The model output also shows that, overall, people were least consistent when estimating the phrase Unlikely, followed by Very Unlikely, Likely, and Very Likely.

Our results suggest that people do not reliably refer to guidelines unless they are directly in front of them (e.g. translated numerically in text). Just under half of participants in the Table condition accessed a clickable link to the guidelines table, and just under half of participants in the Tooltip condition reported accessing the tooltip guidelines function, despite being instructed to. The improvements in consistency when we restricted our analysis to those active participants suggest that accessing the guidelines through these formats does make a difference. Moreover, the slightly better consistency scores in the Tooltip condition over the Table condition may be explained by active participants accessing the guidelines more frequently in a Tooltip format (4.5 of 8 possible items) than in a click to Table format (2 of 8 possible items).

The experimental results of our study uncontroversially demonstrated that consumers of words of estimative probability in intelligence reports show high variability when translating these words into numbers. This variability can be substantially reduced by using in-text numerical guidelines. It is difficult to encourage attention to numerical translation guidelines when they are presented in other ways (specifically, in mouse-over tool tips or in accompanying guidelines tables, even if they are easy to access). Our study adds to the evidence that variability and potential biases in interpreting verbal probabilities can only effectively be reduced if numerical translations are highly visible alongside verbal expressions in reports. This would produce less ambiguous forecasts that can be interpreted more consistently, leading to more informed decision making.




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