Hi ...I posed the above question to Mr. Google and Mr. Bing and ChatGPT 3.5. They all gave me results with bogus links, i.e. links where you can't verify the answers they gave you. It would be great if these OR interpretations could be linked to effect sizes (e.g. Cohen's d).
Help anyone?
Thanks!
Jacob Cohen (1988) gives interpretations for Cohen's h, which is related to odds ratio in some applications. This might be what you want.
There's no meaningful way to convert odds ratio to Cohen's d. They measure different things.
Of course, the interpretations for effect size statistics proposed by Cohen are just his suggestions. There's nothing inherently meaningful about calling a certain effect size "large". Cohen makes that clear. But it is useful to have these kinds of benchmarks.
The odds ratio is an "effect-size". The purpose of "effect-sizes" is to somehow infer meaning on the context. Falling back to small, medium, large beats the purpose of an "effect-size". If the odds ratio is 4/1 that I loose 1 hair on my head today is not that large. But losing at strip poker on the arctic, so I need to sleep outside with multiple polar bears makes me think twice about my life choices.
Sal Mangiafico Cohen' dump thumb rule
Sal's advice to use Cohen's rule of thumb for subdivisions for proportions is certainly well-dressed for a publication with Cohen's h. 😊
The distribution density function of the odds ratios is skewed and platycurian. Cut-offs for small/medium/large boundaries would have to be found using logarithmic transformation and approximation with the Stirling formula. I would therefore strongly suspect such limits to be in a gradation of dimensions. I.e. limits would be doubling, quadrupling. Depending on the underlying scaling, a tenfold or a hundredfold increase could also be considered. The former scaling is closer to everyday clinical practice, in which a doubling of rare events should be understood as a warning of a change. For normal distributions that are not to be expected for odds ratios, standard deviations are suitable for small/medium/large classification. However, we know that the density function of the odds ratios diverge. - So I can't recommend the dumb rule of thumb.😁
A switch has three positions -1/0/1, but with what force was it activated? Switch is in regular switching position = lightly pressed. Switch is in normal switching position, but visibly deformed = medium pressure, switch has jumped out of its socket = strong pressure. 😂 The cut-off for the three strength levels is probably x pond, 10x pond and 100x pond.
David Musoke's clever question Division of the odds ratio
The odds ratio (OR) is a symmetrical measure used in cross-sectional studies. If risks are classified as small/large/medium, odds ratios must be differentiated into small/balanced/large, depending on whether there is an odds ratio OR < 1, OR = 1, OR > 1.
Generative artificial intelligence does not find any sources, because references to numerous lexical sources are only made available in a paid premium version. However, generative artificial intelligence also does not understand the mathematical problems behind the odds ratios. Forums for classification and solutions are ideal here.That's why we meet here in a [email protected]
Free sources are:
https://flexikon.doccheck.com/de/Odds_Ratio
Paid book:
Bortz, J., Lienert,, G.A.: Concise statistics for clinical research. Guide to Nonparametric Analysis of Small Samples. Springer Verlag Berlin 2003.
Forums:
http://www.statistics-forum.de/mittelwert-standarddeviation-f6/wie-berechner-man-mittelwerte-von-odds-ratios-t12159.html
https://de.sci.mathematik.narkive.com/KYCiOYhH/varianz-der-odds-ratio
Recursive reference:
https://www.researchgate.net/topics (;-)
Wim Kaijser many thanks for your great and very "graphic" example, hahah, I am thinking about incorporating this into my lecture. Nice! My wife and I had a laugh!
Yeah, what I always think about with the arbitrariness of effect size interpretations is election results in the U.S. A 55% / 45% result is considered large in some U.S. elections, but is smaller than small in standard effect size interpretations. A 60% / 40% split --- "a 20-point margin" --- is considered a blow out, but it's still smaller than "small" effect size in Cohen's interpretations.
David Musoke ,
This site has effect size interpretations, mostly from Cohen. I don't understand where they are getting the interpretations for odds ratio. https://imaging.mrc-cbu.cam.ac.uk/statswiki/FAQ/effectSize
Here, I have interpretations of the odds ratio, based on Cohen's interpretations for Cohen's h. I guess, specifically for 2 x 2 tables. https://rcompanion.org/handbook/H_10.html .
I remember that I have read it in a reference but I don't remember which reference and the exact values!. In general, Odds ratio of 1.1-1.5 is weak, 1.5-3 medium, more than 3 is strong. Also 0.7-0.9 is weak, 0.4-0.7 is moderate, and less than 0.4 is strong. These are estimates and I recommend mentioning the exact value of odds ratio.
Hi all...Very many good, informative, and funny answers. Thank you all for your contributions. I feel in good company now knowing that the question I posed has no easy answers and depends a lot on the context and environment one is working in. One man's good 4:1 ratio and another one's nightmare ratio.
David Musoke ,
Cohen's d is included here: https://imaging.mrc-cbu.cam.ac.uk/statswiki/FAQ/effectSize
On my site, the link was only to effect size statistics for nominal variables. Cohen's d is listed here: https://rcompanion.org/handbook/I_03.html , and then on the pages for paired-samples and one-sample t-tests.
You are so correct. Thank you for pointing out my mistake, @Sal Mangiafico.
No mistake. Your question is very interesting because it shows the line of sight of a technician looking at a switch.
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