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 latest GitHub-version of effectsize:

install.packages("remotes")
remotes::install_github("easystats/effectsize")

Or install the latest stable release from CRAN:

install.packages("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
  • Parameter and Model Standardization
  • ANOVA Effect Sizes
  • Effect Sizes in Bayesian Models
  • For Simple Hypothesis Tests
• Effect Sizes Conversion
  • Between Effect Sizes
  • Effect Size from Test Statistics
• 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        | [-2.18, -0.57]

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 transfom 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.