COMMUNICATING UNCERTAINTY IN SCIENCE: PART TWO.
David Allison
Dean, Distinguished Professor, and Provost Professor at Indiana University Bloomington
On a recent hike, we came upon this snake which I believed, and later confirmed was a timber rattlesnake. Though not absolutely certain it was a timber rattler while on the hike, I was almost certain. That near certainty kept me at a safe distance. Absolute Certainty? Near Certainty? Are these quantifiable in a way that can be tied to objective information?
An RFA from NIH’s NINDS states “Principles of rigorous research …tend to be encompassed by general topics that include…Understanding and measuring uncertainty”.[1]
How does one do that and what does it mean?
As I wrote previously[2], uncertainty refers to a state of mind. There are situations in which not only does the quantitative relationship between some logical aspect of uncertainty and some degree of uncertainty expressed by a human not scale in the mathematic way one would expect, but may not even be monotonically related. We humans sometimes react to information that by any logical rationale should increase our uncertainty by instead decreasing it, or vice versa. Consider the so-called ‘Linda problem’:
“Tversky and Kahneman (1983) asked participants to solve the following problem.
Linda is 31 years old, single, outspoken, and very bright. She majored in philosophy. As a student, she was deeply concerned with issues of discrimination and social justice, and also participated in anti-nuclear demonstrations. Which is more probable?
Linda is a bank teller.
Linda is a bank teller and is active in the feminist movement.
More than 80 percent of participants chose option 2, regardless of whether they were novice, intermediate or expert statisticians. However, the probability of two events occurring in conjunction is always less than or equal to the probability of either one occurring alone.”[3]
Here, information that mathematically necessitates that one should decrease a probability estimate actually leads people to increase a probability estimate.
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If we equate probability to degree of certainty, this is a situation in which communication of information that should affect certainty in one direction actually affects it in the opposite.
The statistician Dennis Lindley stated “Whatever way uncertainty is approached, probability is the only sound way to think about it.” Yet, he also stated “Uncertainty is a personal matter; it is not the uncertainty but your uncertainty.”
?So, if we are to communicate uncertainty in science, and I believe in principle that we should do so, we need to first find the quantitative indicators of aspects of research, research reporting, or research findings that logically ought to lead to greater degrees of certainty. Yet then, we will need to figure out how we wish to assess whether and deal with the fact that conveying these facts may not actually lead to greater degrees of certainty in the human mind.
?What do you think?
David B. Allison - September 25, 2022
Chairman at Essential Micronutrients Foundation
2 年Important topic. I recommend the book by William Briggs, Uncertainty https://link.springer.com/book/10.1007/978-3-319-39756-6. He explores the philosophical issues behind the statistics. All probability is conditional.
Assistant Professor of Nutrition Science
2 年Interesting thoughts about uncertainty and certainty, but where I really got intrigued was reading about the study asking participants about Linda. What was the information about her being a bank teller supposed to signify? Is there an implicit bias regarding people who are bank tellers or was this a random choice of service positions?