Don't stick with concrete numbers. That does not make sense. The interpretation of an effect size always depends on the context of the expreiment, and it always includes a judgement call. These numbers you cite should be taken more as a rough indication of an interpretation of an effect size. It is not relevant if you take 0.24 or .3 as "medium" indicator. The reason for your worries may be that, for instance, 0.28 could be taken as an indication for a either a medium or a small effect, what seems to be contratictionary. This contradiction comes from the fact that you used a strict cut-off value for your interpretation that is not sensibly related to the context of the experiment you try to interpret. You want a precise, definite and clear-cut answer where nothing such exists. 

Btw, this is not much different from using "p

hi,

I agree with Wilhelm that these estimate effect size by Cohen are just estimation. and in text terms, it is divided to small, medium, and large; which reflects the intended approximation for researchers to choose from.

In my practice and this is what i have witnessed in literature that when researcher doubt between small and medium effect size, the decision become conservative by choosing the small ES or a number closer to the small rather than the medium. by this, researcher will avoid Type II error.

Regards

Thankyou both

Dear John, the effect size of a correlation coefficient is best explained by the percentage of common variance it represents.

It is considered that a percentage lower than 5% common variance of no practical importance; This cutoff corresponds to a correlation coefficient of 0.224.

It is considered that from 10% common variance one relationship with presents practical importance; This cutoff corresponds to a correlation coefficient 0.316.

20 to 30% of common variance is considered a relationship with a medium effect, corresponding to a correlation coefficient between 0.447 and 0.548.

From 50% of common variance it is considered a relationship with a strong effect, corresponding to a correlation coefficient 0.707.

From 80% of common variance it is considered a relationship with a very strong effect, corresponding to a correlation coefficient 0.894.

From 90% of common variance it is considered that the relationship is perfect, what corre a correlation coeficeiten 0949 or higher.

The cutoffs for the interpretation of effect size reported in the literature with rounded values of what I mention here.

Hi John,

Pearson correlations are indeed mathematically equivalent to point-biserial correlations. However, a problem could be the base rate sensitivity of point-biserial correlations.

Is the base rate of your dichotomous variable different from 50%?

If so, you might want to consider a different correlation method or adjusting the threshold for regarding your effect size as “small”. Babchishin & Helmus (2015) showed that the higher the deviation from a 50 % base rate, the smaller the observed Pearson’s point-biserial correlation coefficient.

Rice & Harris (2005) provide simple formulas to make adjustments for magnitude of correlations that take into account base rate sensitivity.

Babchishin, K. M., & Helmus, L. M. (2016). The influence of base rates on correlations: An evaluation of proposed alternative effect sizes with real-world data. Behavior research methods, 48(3), 1021-1031.

Rice, M. E., & Harris, G. T. (2005). Comparing effect sizes in follow-up studies: ROC Area, Cohen's d, and r. Law and human behavior, 29(5), 615.

Lisanne

Article Rice ME, Harris GTComparing effect sizes in follow-up studie...

Article The influence of base rates on correlations: An evaluation o...

I agree with lisanne . However I wish to add that the benchmark are merely prescriptive. As an expert in your field the context and your opinion is highly important in deciding whether a particular correlation(effect size) is low, medium or high.

My problem with these tee-shirt sizes applied to correlations (or anything else) is the same as my problem with most cook books when they say "two medium onions". What the heck is a medium onion? How much bigger is it than a small onion?

Why did we bother measuring the correlation in the first place? If a reader cannot interpret the numeric value, calling it "medium" isn't going to help.

Despite the fact that correlations are measured on a continuous scale, researchers often try to make them more interpretable by converting them to what have been called, unkindly, tee-shirt sizes : small, medium and large. They do this referencing the work of Cohen (1992) , who recommended Pearson r values of 0.10, 0.30, and 0.50 to demarcate small, medium, and large effects, respectively. However, recent research has cast doubt on this classification. A major review of studies by Gignac and Szodorai (2020) based on 708 meta-analytically derived correlations, reported that the 25th, 50th, and 75th percentiles corresponded to correlations of 0.11, 0.19, and 0.29, respectively. Fewer than 3% of correlations met Cohen's definition of "large". They suggest that in real life, the terms small, medium and large more closely correspond to correlations of 0.10, 0.20 and 0.30.

Gignac, G., Szodorai, E. (2016). Effect size guidelines for individual differences researchers Personality and Individual Differences 102(Personality and Individual Differences5472013), 74-78. https://dx.doi.org/10.1016/j.paid.2016.06.069

And what is missing is the context. For an ecological field study, an r of 0.1 is rather large, and for a dose-response relationship in a cell-culture experiment an r of 0.9 is rather low. "One size fits it all" is never working.

Absolutely, Jochen Wilhelm .

The key variable is the measurement error, which sets an upper limit on the size of R2.

r is from -1 to +1. 0 is no effect. Towards +1 means positive relation. Towards - 1 means inverse relation. r = 0.1 to 0.5 is weak positive relation. r = 0.5 to 0.75 is moderate positive relation, r = 0.75 to 0.9 is strong relation. r = 0.9 to 1 is very strong relation. However, it also depends on field of studies.

For dose-response studies, below 0.9 is not countable. For co-localization studies, previously mentioned ranged works fine. To establish the relation between two components, previously mentioned ranged works fine. For rare instance, you may make it more liberal.

For biological studies, you may need further studies to prove the relations from functional point of views. If it is functionally works fine, even very weak relation will stand.

It really does depend on the context not some arbitrary handed down rules of thumb.

I am reminded of a famous clinical  trial of the effect of taking aspirin on heart attack - the odds ratio was so dramatic that the trial was stopped and placebo group advised to take aspirin. And yet the odds ratio of a heart attack for placebo compared to taking aspirin was, a rather a lowly 1.83 and the R- squared was a puny 0.0011 (way below your weak effect); yet this was sufficient for action. It is always a judgement call and you have to argue the case and persuade other researchers of the validity of your arguments.

Kelvyn Jones - excellent example! Do you have a reference by any chance?

I think it was the Physicians' Health Study. I will try and track down.

In the mean time ; some food for thought: we have to accept that there are outcomes where chance does genuinely part a large part so we now have evidence that luck plays a bigger part in some cancers than genes and lifestyle;

see

http://www.iflscience.com/health-and-medicine/bad-luck-identified-biggest-cancer-risk

Good Answer Kelvyn Jones

thanks Kelvyn Jones, you just hit the nail on the head.

Excellent answers by all the intervinients. You did shed a great light on the topic. Thank you all