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effectsize 
Size does matter
The goal of this package is to provide utilities to work with indices of effect size and standardized parameters, allowing computation and conversion of indices such as Cohen’s d, r, odds-ratios, etc.
Installation
Run the following to install the stable release of effectsize from CRAN:
install.packages("effectsize")
Or this one to install the latest development version:
install.packages("remotes")
remotes::install_github("easystats/effectsize")
Documentation
Click on the buttons above to access the package documentation and the easystats blog, and check-out these vignettes:
- Data Standardization
- Effect Sizes
- Effect Sizes Conversion
- Automated Interpretation of Indices of Effect Size
Features
This package is focused on indices of effect size. Check out the package
website for a full list of features and functions provided by
effectsize.
library(effectsize)
Effect Size Computation
Standardized Differences (Cohen’s d, Hedges’ g, Glass’ delta)
The package provides functions to compute indices of effect size.
cohens_d(mpg ~ am, data = mtcars)
## Cohen's d | 95% CI
## --------------------------
## -1.48 | [-2.27, -0.67]
##
## - Estimated using pooled SD.
hedges_g(mpg ~ am, data = mtcars)
## Hedges' g | 95% CI
## --------------------------
## -1.44 | [-2.21, -0.65]
##
## - Estimated using pooled SD.
## - Bias corrected using Hedges and Olkin's method.
glass_delta(mpg ~ am, data = mtcars)
## Glass' delta | 95% CI
## -----------------------------
## -1.17 | [-2.01, -0.66]
effectsize also provides effect sizes for contingency tables, rank
tests, and more…
ANOVAs (Eta2, Omega2, …)
model <- aov(mpg ~ factor(gear), data = mtcars)
eta_squared(model)
## Parameter | Eta2 | 90% CI
## ----------------------------------
## factor(gear) | 0.43 | [0.18, 0.59]
omega_squared(model)
## Parameter | Omega2 | 90% CI
## ------------------------------------
## factor(gear) | 0.38 | [0.14, 0.55]
epsilon_squared(model)
## Parameter | Epsilon2 | 90% CI
## --------------------------------------
## factor(gear) | 0.39 | [0.14, 0.56]
And more…
Regression Models (Standardized Parameters)
Importantly, effectsize also provides advanced
methods
to compute standardized parameters for regression models.
m <- lm(rating ~ complaints + privileges + advance, data = attitude)
standardize_parameters(m)
## # Standardization method: refit
##
## Parameter | Coefficient (std.) | 95% CI
## ------------------------------------------------
## (Intercept) | -9.57e-16 | [-0.22, 0.22]
## complaints | 0.85 | [ 0.58, 1.13]
## privileges | -0.04 | [-0.33, 0.24]
## advance | -0.02 | [-0.26, 0.22]
Also, models can be re-fit with standardized data:
standardize(m)
##
## Call:
## lm(formula = rating ~ complaints + privileges + advance, data = data_std)
##
## Coefficients:
## (Intercept) complaints privileges advance
## -9.57e-16 8.55e-01 -4.35e-02 -2.19e-02
Effect Size Conversion
The package also provides ways of converting between different effect sizes.
convert_d_to_r(d = 1)
## [1] 0.447
And for recovering effect sizes from test statistics.
F_to_d(15, df = 1, df_error = 60)
## d | 95% CI
## -------------------
## 1.00 | [0.46, 1.53]
F_to_r(15, df = 1, df_error = 60)
## r | 95% CI
## -------------------
## 0.45 | [0.22, 0.61]
F_to_eta2(15, df = 1, df_error = 60)
## Eta2 (partial) | 90% CI
## -----------------------------
## 0.20 | [0.07, 0.34]
Effect Size Interpretation
The package allows for an automated interpretation of different indices.
interpret_r(r = 0.3)
## [1] "large"
## (Rules: funder2019)
Different sets of “rules of thumb” are implemented (guidelines are detailed here) and can be easily changed.
interpret_d(d = 0.45, rules = "cohen1988")
## [1] "small"
## (Rules: cohen1988)
interpret_d(d = 0.45, rules = "gignac2016")
## [1] "moderate"
## (Rules: gignac2016)
Utilities
Data Standardization, Normalization, Scaling, and Rank-Transforming
Many indices of effect size stem out, or are related, to
standardization.
Thus, it is expected that effectsize provides functions to standardize
data.
A standardization sets the mean and SD to 0 and 1:
library(parameters) # for describe_distribution
df <- standardize(attitude)
describe_distribution(df$rating)
## Mean | SD | IQR | Range | Skewness | Kurtosis | n | n_Missing
## ----------------------------------------------------------------------------
## -5.46e-16 | 1 | 1.29 | [-2.02, 1.67] | -0.40 | -0.49 | 30 | 0
Alternatively, normalization is similar to standardization in that it is a linear translation of the parameter space (i.e., it does not change the shape of the data distribution). However, it puts the values within a 0 - 1 range, which can be useful in cases where you want to compare or visualise data on the same scale.
df <- normalize(attitude)
describe_distribution(df$rating)
## Mean | SD | IQR | Range | Skewness | Kurtosis | n | n_Missing
## ------------------------------------------------------------------------
## 0.55 | 0.27 | 0.35 | [0.00, 1.00] | -0.40 | -0.49 | 30 | 0
This is a special case of a rescaling function, which can be used to rescale the data to an arbitrary new scale. Let’s change all numeric variables to “percentages”:
df <- change_scale(attitude, to = c(0, 100))
describe_distribution(df$rating)
## Mean | SD | IQR | Range | Skewness | Kurtosis | n | n_Missing
## -----------------------------------------------------------------------------
## 54.74 | 27.05 | 35.00 | [0.00, 100.00] | -0.40 | -0.49 | 30 | 0
For some robust statistics, one might also want to transform the numeric
values into ranks, which can be performed using the ranktransform()
function.
ranktransform(c(1, 3, -2, 6, 6, 0.5))
## [1] 3.0 4.0 1.0 5.5 5.5 2.0
or signed-ranks:
ranktransform(c(1, 3, -2, 6, 6, 0.5), sign = TRUE)
## [1] 2.0 4.0 -3.0 5.5 5.5 1.0
Citation
In order to cite this package, please use the following citation:
- Ben-Shachar M, Lüdecke D, Makowski D (2020). effectsize: Estimation of Effect Size Indices and Standardized Parameters. Journal of Open Source Software, 5(56), 2815. doi: 10.21105/joss.02815
Corresponding BibTeX entry:
@Article{,
title = {{e}ffectsize: Estimation of Effect Size Indices and Standardized Parameters},
author = {Mattan S. Ben-Shachar and Daniel Lüdecke and Dominique Makowski},
year = {2020},
journal = {Journal of Open Source Software},
volume = {5},
number = {56},
pages = {2815},
publisher = {The Open Journal},
doi = {10.21105/joss.02815},
url = {https://doi.org/10.21105/joss.02815}
}
Contributing and Support
If you have any questions regarding the the functionality of the package, you may either contact us via email or also file an issue. Anyone wishing to contribute to the package by adding functions, features, or in another way, please follow this guide and our code of conduct.