In statistics, Cramér's V is a measure of association between two nominal variables, giving a value between 0 and 1 (inclusive). It was first proposed by Harald Cramér (1946).
It is actually considered in many papers I came accross that a threshold value of 0.15 (sometimes even 0.1) can be considered as meaningful, hence giving hints of a low association between the variables being tested. Do you have any reference, mathematical foundation or explanation on why this threshold is relevant ?
Regards,
Roland.
Greetings Roland,
first. By convention, the range of V= .1 to .3 is considered as weak effect, then .3 to .5 = middle sized effect, and >.5 = strong. Such conventions are used whenever you have no idea how to interpret the effect size in your particular domain (e.g., saving the live of just one person certainly should be considered as 'important' (and meaningful), while mildly supporting the claim of a theory that nobody cares about might be viewed with more caution). I would argue "meaningfulness" is nothing that a single measure can indicate... And referring to .15 as threshold (and doing so repeatedly) might just reflect a lack of 'reflection' about the topic of effect sizes.
Please consider how to calculate V. It is (roughly said) the sum of (data minus expectation) divided by N (number of cases; plus some details...). So it is proportional to how much variance in the data was unexpected, similar to a percentage of observations that did not fit into your prior beliefs. Are these 'percent' of cases enough to change your mind about the hypothesis? Matter of debate :), or of convention if one does not know how to interpret results :))
Hope this helps, René
As for any measure of association, you need to consider the statistical significance, which can be read from the p-value. If this is below you threshold, you might consider the value of V significant. Then, in addition, you must also consider effect size. A small but statistical significant V might not be relevant, see the René's post.
People often cite Cohen 1988. But I don't think it agrees with the proposed 0.15 cutoff . Cohen, J. 1988. Statistical Power Analysis for the Behavioral Sciences, 2nd Edition. Routledge.
Dear Salvatore,
A lot of people actually cite Cramer's book, first published in 1946, entitled "Mathematical methods of Statistics", Chapter 21.
However, i found few hints inside to understand the 0.15 cutoff.
Hello Roland,
There are guidelines, of course, but these may well be useless for many variable sets or contexts. I don't know of any mathematical reason to suggest that .15 (ir any other value) is magically better as a threshold for a relationship being judged as noteworthy.
Jacob Cohen, in his 1988 text, Statistical power analysis for the behavioral sciences (2nd ed.), proposed these levels for the simpler version of V, the phi coefficient (in which one of the two dimensions has 1 df):
"Small" effect size = phi of .10; "medium" ES = phi of .30; "large" ES = phi of .50.
However, Cohen would be the first to admit that such guidelines may be meaningless in specific data/variable/population contexts; there is no substitute for intimate understanding of these features.
Here's a simple example of how a very low correlation can still be useful: Consider a correlation of .01 between a no-cost, one-question cancer screener and the subsequent occurrence of cancer within a year. Sounds useless, right?
(With these hypothetical values from 100,000 cases: screen+/cancer+ = 6,472; screen+/cancer- = 57,922; screen-/cancer+ = 3,356; screen-/cancer- = 32,250; the chi-square = 10.114, and phi = .01). In this scenario, the one-question screener would potentially save nearly 6,500 lives. So, is it useful?
Good luck with your work.
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