I am designing a study in which I plan to have everyday people predict the results of an experimental study, and I am wondering whether we know if everyday people are better able to comprehend ratios or percentages. If I want participants to estimate the difference between Condition A and Condition B, would they have an easier time reporting the percentage difference between the groups (e.g., Condition B was 0.1% higher, 10% higher, 10,000% higher than Condition A) or reporting the ratio between the groups (e.g., Condition B was 1.001, 1.1, 100 times higher than Condition A). Does anyone know of any research comparing how intuitive ratios are for people relative to percentages?
I don’t know of any studies on this subject.
But wanted to offer something because you’re local.
Based on my experience :
1)__ Neither are intuitive.
2)__ The smaller the representative parts the less intuitive the meaning of either.
3)__ The change in number of students participating in a conversation among themselves** is good barometer of how intuitive the ideas are. **(with a teacher this number tends to be much lower)
I found this. Maybe It can help:
https://news.ycombinator.com/item?id=9895929
Christian’s link offers an interesting idea, that is, ask the question differently. For example, I get different search answers for “odds ratios instead of percentage probabilities”. - And an entirely different response if I search scholar.google.com. asking “using ratios instead of percentage”.
Surely, for ordinary people, proportions are easier to understand, especially if they refer to 1/4, 1/2 and 3/4; which has some limits in terms of precision. If you need more precision than that, you can use percentile.
Thanks all! I wonder if percentages are easier for small differences (e.g., 1% higher vs. 1.01 times higher) and ratios are easier for large differences (e.g., 100 times higher vs. 10,000% higher)? I am hoping to give them a very large range of examples to minimize anchoring them in a particular range, which might just mean it is going to be challenging either way. I appreciate all the helpful info!
These aren't directly answering, but might be useful.
David Hand (great writer on stats) has a book on these rare things: The improbability principle. This blog might also be useful (http://understandinguncertainty.org/blog). Spiegelhalter does a lot on conveying numbers to people. I'm not at the office, but I'll check in some of the books of his I have when I next am. He was best known for DIC and BUGS, but now at least among the public on risk and understanding COVID data. Or being the Loop World Champion or being on WipeOut (youtu.be/906b2wrz49k).
He stresses it is better to say 1 out of 100 than either 1% or .01.
There is additional difficulty when using proportions or percentages: confusion about the reference.
X changes by 20% is different to X changes to 20%. If Y is 100% more than X it is 200% of X, but if Y is 100% of X, it equals X.
Cory Clark …its not the details in these inks that I found relevant.
Its that we continue to question if we understand this. And, first link** has the questionnaire !
1)__ 2004 article, “Doctors' confusion over ratios and percentages in drug solutions: the case for standard labelling”. **It includes their online questionnaire with results. See this link…
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC1079557/
2)__ An article in Physiological Zoology; The Misuse of Ratios, Indices, and Percentages in Ecophysiological Research by Gary Packard, and Thomas Boardman. - An abstract with available PDF
https://www.journals.uchicago.edu/doi/abs/10.1086/physzool.61.1.301637303)
3)__ Journal of Regulatory Economics; The Design of Regulations Expressed as Ratios or Percentage Quotas By Ross McKitrick. An abstract, but you should be able to get full access using your Penn log-in.
https://link.springer.com/article/10.1023/A:1011163207557
4)__ Journal of Sports Medicine; .... “The Use of Ratios and Percentage Changes in Sports Medicine: Time for a Rethink?” by Georg Thieme Verlag
https://www.thieme-connect.com/products/ejournals/abstract/10.1055/s-0032-1316355
Jochen Wilhelm brings up a good point and it reminds me of the confusing explanations I have heard wrt relative risk. Also, since I mentioned Spiegelhalter, I thought I should also add Gigerenzer (his group: https://www.hardingcenter.de/en) who also has done a lot on using different formats to express things like proportions e.g.,
@article{GigerenzerHoffrage1995,
author = {Gigerenzer, Gerd and Hoffrage, Ulrich},
year = {1995},
title = {How to improve {B}ayesian reasoning without instruction: Frequency formats},
journal = {Psychological Review},
volume = {102},
pages = {684--704},
doi = {10.1037/0033-295X.102.4.684},
}
I realize that my comment to this thread is not exactly what you are looking for, but it might expand your awareness of the range that proportional relationships can express. Here is a paper using the language of cognitive linguistics to examine poetic metaphors in mathematical visual poetry. This example uses the proportional relationships found in similar triangles as the substrate or 'source domain' for metaphorical expressions. http://www.kazmaslanka.com/ACVOPM.pdf
I hope you find it interesting in your quest.
I would second our colleague who mentions the work of Gerd Gigerenzer.
Gigerenzer has performed research comparing participants ability to work with probabilities versus relative (natural) frequencies....seems that this research would be relevant to your proposed line of research.
I've pasted links to a sample of the studies:
Article Using natural frequencies to improve diagnostic inferences
Article Using natural frequencies to improve diagnostic inferences
Article Natural Frequencies Do Foster Public Understanding of Medica...
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