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Interpret Correlation Coefficient

Source: R/interpret_r.R
interpret_r.Rd

Interpret Correlation Coefficient

Usage

interpret_r(r, rules = "funder2019", ...)

interpret_phi(r, rules = "funder2019", ...)

interpret_cramers_v(r, rules = "funder2019", ...)

interpret_rank_biserial(r, rules = "funder2019", ...)

interpret_fei(r, rules = "funder2019", ...)

Arguments

r

Value or vector of correlation coefficient.

rules

Can be "funder2019" (default), "gignac2016", "cohen1988", "evans1996", "lovakov2021" or a custom set of rules().

...

Not directly used.

Details

Since Cohen's w does not have a fixed upper bound, for all by the most simple of cases (2-by-2 or 1-by-2 tables), interpreting Cohen's w as a correlation coefficient is inappropriate (Ben-Shachar, et al., 2024; Cohen, 1988, p. 222). Please us cramers_v() of the like instead.

Note

As \(\phi\) can be larger than 1 - it is recommended to compute and interpret Cramer's V instead.

Rules

Rules apply to positive and negative r alike.

  • Funder & Ozer (2019) ("funder2019"; default)

    • r < 0.05 - Tiny

    • 0.05 <= r < 0.1 - Very small

    • 0.1 <= r < 0.2 - Small

    • 0.2 <= r < 0.3 - Medium

    • 0.3 <= r < 0.4 - Large

    • r >= 0.4 - Very large

  • Gignac & Szodorai (2016) ("gignac2016")

    • r < 0.1 - Very small

    • 0.1 <= r < 0.2 - Small

    • 0.2 <= r < 0.3 - Moderate

    • r >= 0.3 - Large

  • Cohen (1988) ("cohen1988")

    • r < 0.1 - Very small

    • 0.1 <= r < 0.3 - Small

    • 0.3 <= r < 0.5 - Moderate

    • r >= 0.5 - Large

  • Lovakov & Agadullina (2021) ("lovakov2021")

    • r < 0.12 - Very small

    • 0.12 <= r < 0.24 - Small

    • 0.24 <= r < 0.41 - Moderate

    • r >= 0.41 - Large

  • Evans (1996) ("evans1996")

    • r < 0.2 - Very weak

    • 0.2 <= r < 0.4 - Weak

    • 0.4 <= r < 0.6 - Moderate

    • 0.6 <= r < 0.8 - Strong

    • r >= 0.8 - Very strong

References

  • Lovakov, A., & Agadullina, E. R. (2021). Empirically Derived Guidelines for Effect Size Interpretation in Social Psychology. European Journal of Social Psychology.

  • Funder, D. C., & Ozer, D. J. (2019). Evaluating effect size in psychological research: sense and nonsense. Advances in Methods and Practices in Psychological Science.

  • Gignac, G. E., & Szodorai, E. T. (2016). Effect size guidelines for individual differences researchers. Personality and individual differences, 102, 74-78.

  • Cohen, J. (1988). Statistical power analysis for the behavioral sciences (2nd Ed.). New York: Routledge.

  • Evans, J. D. (1996). Straightforward statistics for the behavioral sciences. Thomson Brooks/Cole Publishing Co.

  • Ben-Shachar, M.S., Patil, I., Thériault, R., Wiernik, B.M., Lüdecke, D. (2023). Phi, Fei, Fo, Fum: Effect Sizes for Categorical Data That Use the Chi‑Squared Statistic. Mathematics, 11, 1982. doi:10.3390/math11091982

See also

Page 88 of APA's 6th Edition.

Examples

interpret_r(.015)
#> [1] "tiny"
#> (Rules: funder2019)
#> 
interpret_r(c(.5, -.02))
#> [1] "very large" "tiny"      
#> (Rules: funder2019)
#> 
interpret_r(.3, rules = "lovakov2021")
#> [1] "medium"
#> (Rules: lovakov2021)
#>