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I'm planning on doing quantile regression for estimating pain relief after hip surgery. My aim is to construct for my patients information in this format:

4 out of 5 patients experience with your background experience at least a 50 % decrease in pain intensity one year after surgery

My problem is: Is 80 % perceived as very probable? Is 90 % much better?

What I'm looking for is some kind of reference article on how people perceive percentages to determine a good quantile. I've been looking on Google scholar for something useful but strangely I haven't found anything that I can use. There is plenty of articles on how to communicate risk, a good summary can be found here, but none of them discuss how percentages in this fashion.

I guess what I'm looking for is something like the p-value graph (originally posted in this question) but with "John Doe's" instead of "Scientist's".

Magical p-values

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As mentioned in the comment @Tim, prospect theory proposes that probabilities are perceived in a particular way, such as in this figure:

probability weighting function from Wikipedia

The "weighted probability" could also be called subjective probability or perceived probability.

This function suggests you might be justified to propose three categories of low probability, middle probability, and high probability. While you might not be able to find a paper that provides thresholds for categories of divisions among these, you should be able to find some papers that attempt to parameterize this function, and then just come up with your own thresholds based on that.

As an example, here is a citation for one of the first papers that came up on Google when I used the search string "prospect theory probability weighting function medical risk":

Bleichrodt, H. and Pinto, J. L. 2000. A Parameter-free elicitation of the probability weighting function in medical decision analysis. Management Science 46(11): 1485-1496.

I only briefly looked at this paper, but this along with the search terms given should give you a start into that literature.

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I imagine this would depend on the background of the individual. Someone with a strong statisticsl background would probably have a lower threshold on what is a reasoanbly high percentage than somone who doesn't.

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    $\begingroup$ Yes, you're probably right but I still think there must be some point where people in general start to believe that the chances are pretty good. I'm a little surprised that I can't find any article on this (I guess I don't have the right search terms, but still...) $\endgroup$ – Max Gordon Jun 9 '12 at 12:19
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    $\begingroup$ I think this would be more likely to be found in the psychology literature than the statistics literature. You would think someone has done an experiment on this. If not maybe you could do one of your own. $\endgroup$ – Michael Chernick Jun 9 '12 at 12:39
  • $\begingroup$ That was my original masterplan. But when I started searching at Google scholar was swamped by all articles on patient communication. I figured maybe someone here had heard/knew of a study $\endgroup$ – Max Gordon Jun 9 '12 at 13:32
  • $\begingroup$ You'll want to look into the work of Gerd Gigerenzer--his books and his website connected to the Max Plank Institute in Germany. $\endgroup$ – rolando2 Jun 10 '12 at 3:40

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