The metrics used in statistics (indices of fit, model performance, or
parameter estimates) can be very abstract. A long experience is required
to intuitively ** feel** the meaning of their
values. In order to facilitate the understanding of the results they are
facing, many scientists use (often implicitly) some set of

One of the most famous interpretation grids was proposed by
**Cohen (1988)** for a series of widely used indices, such
as the correlation **r** (*r* = .20, small;
*r* = .40, moderate and *r* = .60, large) or the
**standardized difference** (*Cohen’s d*). However,
there is now a clear evidence that Cohen’s guidelines (which he himself
later disavowed; Funder, 2019) are much too stringent and not
particularly meaningful taken out of context (Funder and Ozer 2019). This led to the
emergence of a literature discussing and creating new sets of rules of
thumb.

Although **everybody** agrees on the fact that effect
size interpretation in a study should be justified with a rationale (and
depend on the context, the field, the literature, the hypothesis, etc.),
these pre-baked rules can nevertheless be useful to give a rough idea or
frame of reference to understand scientific results.

The package ** effectsize** catalogs such
sets of rules of thumb for a variety of indices in a flexible and
explicit fashion, helping you understand and report your results in a
scientific yet meaningful way. Again, readers should keep in mind that
these thresholds, as ubiquitous as they may be,

Moreover, some authors suggest the counter-intuitive idea that
*very large effects*, especially in the context of psychological
research, is likely to be a “gross overestimate that will rarely be
found in a large sample or in a replication” (Funder and Ozer 2019). They suggest that
smaller effect size are worth taking seriously (as they can be
potentially consequential), as well as more believable.

There can be used to interpret not only Pearson’s correlation
coefficient, but also Spearman’s, \(\phi\) (phi), Cramer’s *V* and
Tschuprow’s *T*. Although Cohen’s *w* and Pearson’s
*C* are *not* a correlation coefficients, they are often
also interpreted as such.

`interpret_r(x, rules = "funder2019")`

**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’s rules of thumb are actually one of few interpretation grid justified and based on actual data, in this case on the distribution of effect magnitudes in the literature.

`interpret_r(x, rules = "gignac2016")`

**r < 0.1**- Very small**0.1 <= r < 0.2**- Small**0.2 <= r < 0.3**- Moderate**r >= 0.3**- Large

`interpret_r(x, rules = "cohen1988")`

**r < 0.1**- Very small**0.1 <= r < 0.3**- Small**0.3 <= r < 0.5**- Moderate**r >= 0.5**- Large

`interpret_r(x, rules = "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

`interpret_r(x, rules = "lovakov2021")`

**r < 0.12**- Very small**0.12 <= r < 0.24**- Small**0.24 <= r < 0.41**- Moderate**r >= 0.41**- Large

The standardized difference can be obtained through the standardization of linear model’s parameters or data, in which they can be used as indices of effect size.

`interpret_cohens_d(x, rules = "cohen1988")`

**d < 0.2**- Very small**0.2 <= d < 0.5**- Small**0.5 <= d < 0.8**- Medium**d >= 0.8**- Large

`interpret_cohens_d(x, rules = "sawilowsky2009")`

**d < 0.1**- Tiny**0.1 <= d < 0.2**- Very small**0.2 <= d < 0.5**- Small**0.5 <= d < 0.8**- Medium**0.8 <= d < 1.2**- Large**1.2 <= d < 2**- Very large**d >= 2**- Huge

Gignac’s rules of thumb are actually one of few interpretation grid
justified and based on actual data, in this case on the distribution of
effect magnitudes in the literature. These is in fact the same grid used
for *r*, based on the conversion of *r* to *d*:

`interpret_cohens_d(x, rules = "gignac2016")`

**d < 0.2**- Very small**0.2 <= d < 0.41**- Small**0.41 <= d < 0.63**- Moderate**d >= 0.63**- Large

`interpret_cohens_d(x, rules = "lovakov2021")`

**r < 0.15**- Very small**0.15 <= r < 0.36**- Small**0.36 <= r < 0.65**- Moderate**r >= 0.65**- Large

Odds ratio, and *log* odds ratio, are often found in
epidemiological studies. However, they are also the parameters of
** logistic** regressions, where they can be used
as indices of effect size. Note that the (log) odds ratio from logistic
regression coefficients are

Keep in mind that these apply to Odds *ratios*, so Odds ratio
of 10 is as extreme as a Odds ratio of 0.1 (1/10).

`interpret_oddsratio(x, rules = "chen2010")`

**OR < 1.68**- Very small**1.68 <= OR < 3.47**- Small**3.47 <= OR < 6.71**- Medium**OR >= 6.71**- Large

`interpret_oddsratio(x, rules = "cohen1988")`

**OR < 1.44**- Very small**1.44 <= OR < 2.48**- Small**2.48 <= OR < 4.27**- Medium**OR >= 4.27**- Large

This converts (log) odds ratio to standardized difference *d*
using the following formula (J. Cohen 1988;
Sánchez-Meca, Marı́n-Martı́nez, and Chacón-Moscoso 2003):

\[ d = log(OR) \times \frac{\sqrt{3}}{\pi} \]

`interpret_r2(x, rules = "cohen1988")`

**R2 < 0.02**- Very weak**0.02 <= R2 < 0.13**- Weak**0.13 <= R2 < 0.26**- Moderate**R2 >= 0.26**- Substantial

`interpret_r2(x, rules = "falk1992")`

**R2 < 0.1**- Negligible**R2 >= 0.1**- Adequate

`interpret_r2(x, rules = "chin1998")`

**R2 < 0.19**- Very weak**0.19 <= R2 < 0.33**- Weak**0.33 <= R2 < 0.67**- Moderate**R2 >= 0.67**- Substantial

`interpret_r2(x, rules = "hair2011")`

**R2 < 0.25**- Very weak**0.25 <= R2 < 0.50**- Weak**0.50 <= R2 < 0.75**- Moderate**R2 >= 0.75**- Substantial

The Omega squared is a measure of effect size used in ANOVAs. It is an estimate of how much variance in the response variables are accounted for by the explanatory variables. Omega squared is widely viewed as a lesser biased alternative to eta-squared, especially when sample sizes are small.

`interpret_omega_squared(x, rules = "field2013")`

**ES < 0.01**- Very small**0.01 <= ES < 0.06**- Small**0.16 <= ES < 0.14**- Medium**ES >= 0.14**- Large

These are applicable to one-way ANOVAs, or to *partial* Eta /
Omega / Epsilon Squared in a multi-way ANOVA.

`interpret_omega_squared(x, rules = "cohen1992")`

**ES < 0.02**- Very small**0.02 <= ES < 0.13**- Small**0.13 <= ES < 0.26**- Medium**ES >= 0.26**- Large

The interpretation of Kendall’s coefficient of concordance
(*w*) is a measure of effect size used in non-parametric ANOVAs
(the Friedman rank sum test). It is an estimate of agreement among
multiple raters.

`interpret_omega_squared(w, rules = "landis1977")`

**0.00 <= w < 0.20**- Slight agreement**0.20 <= w < 0.40**- Fair agreement**0.40 <= w < 0.60**- Moderate agreement**0.60 <= w < 0.80**- Substantial agreement**w >= 0.80**- Almost perfect agreement

Cohen’s *g* is a measure of effect size used for McNemar’s
test of agreement in selection - when repeating a multiple chose
selection, is the percent of matches (first response is equal to the
second response) different than 50%?

`interpret_cohens_g(x, rules = "cohen1988")`

**d < 0.05**- Very small**0.05 <= d < 0.15**- Small**0.15 <= d < 0.25**- Medium**d >= 0.25**- Large

`effectsize`

also offers functions for interpreting other
statistical indices:

`interpret_gfi()`

,`interpret_agfi()`

,`interpret_nfi()`

,`interpret_nnfi()`

,`interpret_cfi()`

,`interpret_rmsea()`

,`interpret_srmr()`

,`interpret_rfi()`

,`interpret_ifi()`

, and`interpret_pnfi()`

for interpretation CFA / SEM goodness of fit.`interpret_p()`

for interpretation of*p*-values.`interpret_direction()`

for interpretation of direction.`interpret_bf()`

for interpretation of Bayes factors.`interpret_rope()`

for interpretation of Bayesian ROPE tests.`interpret_ess()`

and`interpret_rhat()`

for interpretation of Bayesian diagnostic indices.

Chen, Henian, Patricia Cohen, and Sophie Chen. 2010. “How Big Is a
Big Odds Ratio? Interpreting the Magnitudes of Odds Ratios in
Epidemiological Studies.” *Communications in
Statistics—Simulation and Computation* 39 (4): 860–64.

Chin, Wynne W et al. 1998. “The Partial Least Squares Approach to
Structural Equation Modeling.” *Modern Methods for Business
Research* 295 (2): 295–336.

Cohen, J. 1988. *Statistical Power Analysis for the Behavioral
Sciences, 2nd Ed.* New York: Routledge.

Cohen, Jacob. 1992. “A Power Primer.” *Psychological
Bulletin* 112 (1): 155.

Evans, James D. 1996. *Straightforward Statistics for the Behavioral
Sciences.* Thomson Brooks/Cole Publishing Co.

Falk, R Frank, and Nancy B Miller. 1992. *A Primer for Soft
Modeling.* University of Akron Press.

Field, Andy. 2013. *Discovering Statistics Using IBM SPSS
Statistics*. sage.

Funder, David C, and Daniel J Ozer. 2019. “Evaluating Effect Size
in Psychological Research: Sense and Nonsense.” *Advances in
Methods and Practices in Psychological Science*, 2515245919847202.

Gignac, Gilles E, and Eva T Szodorai. 2016. “Effect Size
Guidelines for Individual Differences Researchers.”
*Personality and Individual Differences* 102: 74–78.

Hair, Joe F, Christian M Ringle, and Marko Sarstedt. 2011.
“PLS-SEM: Indeed a Silver Bullet.” *Journal of Marketing
Theory and Practice* 19 (2): 139–52.

Landis, J Richard, and Gary G Koch. 1977. “The Measurement of
Observer Agreement for Categorical Data.” *Biometrics*,
159–74.

Lovakov, Andrey, and Elena R Agadullina. 2021. “Empirically
Derived Guidelines for Effect Size Interpretation in Social
Psychology.” *European Journal of Social Psychology*.

Sánchez-Meca, Julio, Fulgencio Marı́n-Martı́nez, and Salvador
Chacón-Moscoso. 2003. “Effect-Size Indices for Dichotomized
Outcomes in Meta-Analysis.” *Psychological Methods* 8 (4):
448.

Sawilowsky, Shlomo S. 2009. “New Effect Size Rules of
Thumb.”