## Statistical Science

- Statist. Sci.
- Volume 5, Number 1 (1990), 1-158

### Quantifying Probabilistic Expressions

Frederick Mosteller and Cleo Youtz

#### Abstract

For 20 different studies, Table 1 tabulates numerical averages of opinions on quantitative meanings of 52 qualitative probabilistic expressions. Populations with differing occupations, mainly students, physicians, other medical workers, and science writers, contributed. In spite of the variety of populations, format of question, instructions, and context, the variation of the averages for most of the expressions was modest, suggesting that they might be useful for codification. One exception was possible, because it had distinctly different meanings for different people. We report new data from a survey of science writers. The effect of modifiers such as very or negation (not, un-, im-, in-) can be described approximately by a simple rule. The modified expression has probability meaning half as far from the appropriate boundary (0 or 100) as that of the original expression. This paper also reviews studies that show stability of meanings over 20 years, mild effects of translation into other languages, context, small order effects, and effects of scale for reporting on extreme values. The stem probability with modifiers gives a substantial range 6% to 91% and the stem chance might do as well if tried with very. The stems frequent, probable, likely, and often with modifiers produce roughly equivalent sets of means, but do not cover as wide a range as probability. Extreme values such as always and certain fall at 98% and 95%, respectively, and impossible and never at 1%. The next step will be to offer codifications and see how satisfactory people find them.

#### Article information

**Source**

Statist. Sci. Volume 5, Number 1 (1990), 2-12.

**Dates**

First available: 19 April 2007

**Permanent link to this document**

http://projecteuclid.org/euclid.ss/1177012242

**JSTOR**

links.jstor.org

**Digital Object Identifier**

doi:10.1214/ss/1177012242

**Mathematical Reviews number (MathSciNet)**

MR1054855

**Zentralblatt MATH identifier**

0955.62514

#### Citation

Mosteller, Frederick; Youtz, Cleo. Quantifying Probabilistic Expressions. Statistical Science 5 (1990), no. 1, 2--12. doi:10.1214/ss/1177012242. http://projecteuclid.org/euclid.ss/1177012242.

#### See also

- See Comment: Herbert H. Clark. [Quantifying Probabilistic Expressions]: Comment. Statist. Sci., Volume 5, Number 1 (1990), 12--16.Project Euclid: euclid.ss/1177012243
- See Comment: Norman Cliff. [Quantifying Probabilistic Expressions]: Comment. Statist. Sci., Volume 5, Number 1 (1990), 16--18.Project Euclid: euclid.ss/1177012244
- See Comment: Joseph B. Kadane. [Quantifying Probabilistic Expressions]: Comment: Codifying Chance. Statist. Sci., Volume 5, Number 1 (1990), 18--20.Project Euclid: euclid.ss/1177012245
- See Comment: William Kruskal. [Quantifying Probabilistic Expressions]: Comment. Statist. Sci., Volume 5, Number 1 (1990), 20--21.Project Euclid: euclid.ss/1177012246
- See Comment: Judith M. Tanur. [Quantifying Probabilistic Expressions]: Comment: On the Possible Dangers of Isolation. Statist. Sci., Volume 5, Number 1 (1990), 21--22.Project Euclid: euclid.ss/1177012247
- See Comment: Thomas S. Wallsten, David V. Budescu. [Quantifying Probabilistic Expressions]: Comment. Statist. Sci., Volume 5, Number 1 (1990), 23--26.Project Euclid: euclid.ss/1177012248
- See Comment: Robert L. Winkler. [Quantifying Probabilistic Expressions]: Comment: Representing and Communicating Uncertainty. Statist. Sci., Volume 5, Number 1 (1990), 26--30.Project Euclid: euclid.ss/1177012249
- See Comment: Charles Wolf. [Quantifying Probabilistic Expressions]: Comment. Statist. Sci., Volume 5, Number 1 (1990), 31--32.Project Euclid: euclid.ss/1177012250
- See Comment: Frederick Mosteller, Cleo Youtz. [Quantifying Probabilistic Expressions]: Rejoinder. Statist. Sci., Volume 5, Number 1 (1990), 32--34.Project Euclid: euclid.ss/1177012251