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As I was studying Cramers-V I saw two different Youtube videos authoritatively hand down 2 different sets of thresholds for strengths of measures of association.

The first video said that 0-.29 was weak, 0.3-.6 was moderate, and .6-1 was strong.

The second video said 0 was none, <.3 was weak, and .3-1 was strong.

Could anyone answer which one is more conventional, if not more downright correct?

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    $\begingroup$ Convention varies between fields, a strong relationship in (say) economics might be a weak relationship in (say) physics. There's no objective way of deciding what is 'correct'. $\endgroup$ Mar 6, 2018 at 20:49

2 Answers 2

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I'd suggest stay away from those cookie cutter rules, as they don't take the variables into context.

Some fields of study look at variables that are a lot more correlated (e.g. physics, some medical or biological studies, etc.) and for those researchers your first criterion would make more sense. While researchers from other fields that tend to more less correlated data (e.g. behavioral science) may favor the second scheme.

A better approach perhaps is to survey some literature that examines variables to yours and get a sense of the ranges, and how the authors interpret the strength.

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What to take from these inconsistent thresholds is that you should use your own judgement and knowledge of your specific research question to decide how strong or important a given Cramér's V is. See also Practical significance, especially with percents: "standard" measure and threshold and Practical significance and effect size for a discussion on why standard thresholds for effect sizes are problematic in general, not just for Cramér's V.

Similarly to the two videos you mention, you can find various thresholds in scientific publications, that are relevant to their own research questions. Here is a non-exhaustive list of some publications using very different thresholds, to show how useless it can be to use someone else's standards without exercising your own judgement:

  • Chanvril-Ligneel and Le Hay (2014) define an "important Cramér's V" as $V > 0.15$.

  • Dai et al. (2021) use the following thresholds for Cramér's V:

    weak: >0.05; moderate: >0.10; strong: >0.15; and very strong: >0.25.

  • Kakudji et al. (2020):

    A Cramér's V ≥ 0.1 was deemed as a weak association, Cramér's V ≥ 0.3 was seen as a moderate association and Cramér's V ≥ 0.5 regarded as a large effect/association

  • Lee (2016) uses the following thresholds:

    • $ V < 0.1$: negligible
    • $ 0.1< V <0.2$: weak
    • $ 0.2 < V <0.4$: moderate
    • $ 0.4 < V < 0.6$: relatively strong
    • $ 0.6 < V < 0.8$: strong
    • $V > 0.8$: very strong
  • Le Quéau et al. (2017) use the following thresholds:

    • $V < 0.1$: very weak,
    • $0.1 \le V < 0.2$: weak,
    • $0.2 \le V < 0.3$: medium,
    • $V \ge 0.3$: strong.
  • Another method is to convert $V$ to Cohen's $\omega$ (omega), and then interpret the result according to Jacob Cohen's guidelines (Cohen, 1988). (Incidentally, in his book Cohen tends to advise against using these thresholds, and rather suggests them as a kind of last resort).


References

  • Chanvril-Ligneel, F., & Hay, V. L. (2014). Méthodes Statistiques pour les Sciences Sociales. ELLIPSES.
  • Cohen, J. (1988). Statistical Power Analysis for the Behavioral Sciences (2nd edition). Routledge.
  • Dai, J., Teng, L., Zhao, L., & Zou, H. (2021). The combined analgesic effect of pregabalin and morphine in the treatment of pancreatic cancer pain, a retrospective study. Cancer Medicine, 10(5), 1738–1744. https://doi.org/10.1002/cam4.3779
  • Kakudji, B. K., Mwila, P. K., Burger, J. R., & Plessis, J. M. D. (2020). Epidemiological, clinical and diagnostic profile of breast cancer patients treated at Potchefstroom regional hospital, South Africa, 2012-2018: An open-cohort study. Pan African Medical Journal, 36(1), Article 1. https://www.ajol.info/index.php/pamj/article/view/210808
  • Lee, D. K. (2016). Alternatives to P value: Confidence interval and effect size. Korean Journal of Anesthesiology, 69(6), 555–562. https://doi.org/10.4097/kjae.2016.69.6.555
  • Le Quéau, P., Labarthe F., & Zerbib, O. (2017). Analyse de données quantitatives en sciences humaines et sociales [Mooc]. France Université Numérique. https://www.fun-mooc.fr/fr/cours/analyse-de-donnees-quantitatives-en-sciences-humaines-et-sociales-adshs/
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