7.3.3. In Real Life
An example of an everyday choice that is affected by our problems with probabilities is thinking about weather forecasts. It can be simultaneously true that the weather forecasts are highly accurate and that you shouldn’t believe them. The following quote is from a great article by Neville Nicholls about errors and biases in our commonsense reasoning and how they affect the way we think about weather prediction:6
The accuracy of the United Kingdom 24-hour rain forecast is 83%. The climatological probability of rain on the hourly timescale appropriate for walks is 0.08 (this is the base rate). Given these values, the probability of rain, given a forecast of rain, is 0.30. The probability of no rain, given a forecast of rain, is 0.70. So, it is more likely that you would enjoy your walk without getting wet, even if the forecast was for rain tomorrow.
It’s a true statement but not easy to understand, because we don’t find probability calculations intuitive. The trick is to avoid them. Often probability statistics can be equally well-expressed using frequencies, and they will be better understood this way. We know the probabilities concerning base rates will be neglected, so you need to be extra careful if the message you are trying to convey relies on this information. It also helps to avoid conditional probabilitiesthings like “the probability of X given Y”and relative risks”your risk of X goes down by Y% if you do Z.” People just don’t find it easy to think about information given in this way.7
7.3.4. End Notes
Or at least it’s commonly attributed to Mark Twain. It’s one of those free-floating quotations.
vos Savant, M. (1997). The Power of Logical Thinking. New York: St Martin’s Press.
Paul Erdos published a colossal number of papers in his lifetime by collaborating with mathematicians around the world. If you published a paper with Erdos, your Erdos number is 1; if you published with someone who published with Erdos, it is 2. The mathematics of these indices of relationship can be quite interesting. See “The Erdos Number Project,” http://www.oakland.edu/enp.
Cosmides, L., & Tooby, J. (1996). Are humans good intuitive statisticians after all? Rethinking some conclusions from the literature on judgment under uncertainty. Cognition, 58(1), 1-73.
Krauss, S., & Wang, X. T. (2003). The psychology of the Monty Hall problem: Discovering psychological mechanisms for solving a tenacious brain teaser. Journal of Experimental Psychology: General, 132(1), 3-22.
Nicholls, N. (1999). Cognitive illusions, heuristics, and climate prediction. Bulletin of the American Meteorological Society, 80(7), 1385-1397 (http://ams.allenpress.com/pdfserv/i1520-0477-080-07-1385.pdf).
Gigerenzer, G., & Edwards, A. (2003). Simple tools for understanding risks: From innumeracy to insight. British Medical Journal, 327, 741-744 (http://bmj.bmjjournals.com/cgi/reprint/327/7417/741). This article is great on ways you can use frequency information as an alternative to help people understand probabilities.
7.3.5. See Also
A detailed discussion of the psychology of the Monty Hall dilemma, but one that doesn’t focus on the base-rate interpretation highlighted here is given by Burns, B. D., & Wieth, M. (in press). The collider principle in causal reasoning: Why the Monty Hall dilemma is so hard. Journal of Experimental Psychology: General. More discussion of the Monty Hall dilemma and a simulation that lets you compare the success of the stick and switch strategies is at http://www.cut-the-knot.org/hall.shtml.
Taken from : Mind Hacks
