# What are correlation coefficient strong, moderate and weak ranges of distance and phik correlations?

I'm using python to calculate different types of correlations such as Pearson, Spearman, Kendall, Cramer's v, phik and distance correlations for some data results in my research. I want to know the very strong, strong, moderate and weak ranges for each correlation of these to classify the different correlation results in my research. I got the ranges for Pearson, Spearman, Kendall, Cramer's v, but I can't find the ranges of distance (dcor in python) and phik.

I need the very strong, strong, moderate and weak ranges of distance (dcor in python) and phik correlations.

• Welcome to Cross Validated! The notions of “strong” and “weak” correlations are murky. Why do you need such words when you have the calculated value?
– Dave
Commented Mar 12 at 13:50
• Hi Monica and welcome on this site! I agree with @Dave. Thresholds like that are controversial in the first place, and their relevance is very dependent on the context of your research. There are many questions and answers on this website about this general issue (see stats.stackexchange.com/q/30118/164936, stats.stackexchange.com/q/126463/164936 , or stats.stackexchange.com/q/432661/164936 for some examples). So you should mention why you need this, otherwise I don't think it's possible to give you a good, precise answer, which is relevant to your specific situation. Commented Mar 18 at 8:59
• I'm calculating correlations between different metrics in a quantum circuit and I need to distinguish between metrics that are strongly correlated and other ones that are weakly correlated. @J-J-J Commented Mar 28 at 0:35
• So calculate the correlations. What’s the problem?
– Dave
Commented Mar 28 at 3:12
• You can just say what the correlation values are. The categories are arbitrary for Pearson correlation, anyway.
– Dave
Commented Mar 28 at 14:36

Drawing on the discussion in the comment section, one problem is that existing benchmarks are not necessarily good comparison points for your specific case.

Some often-cited benchmarks for a variety of effect sizes have been designed by Jacob Cohen, from his experience as a researcher in psychology (Cohen, 1988). However, he repeatedly warned against using them without thinking first if they are adequate for your research purpose. Some of the benchmarks you found might come from his work, though other authors provided alternative benchmarks (e.g. Bosco et al., 2015).

So if you're conducting research in a field outside of psychology (in the comment section you mention research relative to a quantum circuit, so I guess physics), it would be definitely a good idea to check if the conventions you plan to use are relevant to your field and research topic.

Some measures of effect size may have no benchmark attached to them, maybe because they are quite new and there is a lack of studies using them so far; or maybe because no one bothered to conduct a literature review to survey the magnitude of these effect sizes observed in their field of study, and then design a convention system from it.

Now, one alternative to using benchmarks is to simply report the values you're observing in your study, as noted by Dave in the comment section, so you'd be leaving the interpretation to the readers. However, you'd be losing one advantage of benchmarks, which is to give some point of comparison. As a remedy, you could include a comparison to values observed in other similar studies in your field, if any.

I guess you've probably already thought of it, but it might be also a good idea to discuss the practical implications of observing such or such value for an effect size, if your study lends itself to this kind of consideration (e.g. with the effect sizes you observed, what kind of benefit-cost ratio can we expect for possible applications of your research?). It would you give some additional basis to say if the effect size is relatively large or small.

Note that interpreting effect sizes and using benchmarks for this purpose is an issue that has been discussed several times on this website. For some hopefully helpful examples, see:

References

Cohen, J. (1988). Statistical Power Analysis for the Behavioral Sciences (2nd edition). Routledge.

Bosco, F. A., Aguinis, H., Singh, K., Field, J. G., & Pierce, C. A. (2015). Correlational effect size benchmarks. Journal of Applied Psychology, 100(2), 431–449. https://doi.org/10.1037/a0038047