### Compute Odds Ratio Examples

Source: https://github.com/easystats/effectsize/blob/main/_autodocs/api-reference/contingency-table-effect-sizes.md

Examples demonstrating how to compute odds ratios from contingency tables, vectors, and chi-squared test objects.

```r
library(effectsize)

# From contingency table
data("RCT_table")
oddsratio(RCT_table)

# Two-sided vs one-sided CI
oddsratio(RCT_table, alternative = "greater")

# Log odds ratio
oddsratio(RCT_table, log = TRUE)

# From vectors
x <- c(a = 8, b = 14)  # group 1: 8 successes, 14 failures
y <- c(a = 11, b = 13) # group 2: 11 successes, 13 failures
table <- rbind(x, y)
oddsratio(table)

# From chi-squared test
chi_test <- chisq.test(RCT_table)
oddsratio(chi_test)
```

--------------------------------

### Install effectsize from CRAN

Source: https://github.com/easystats/effectsize/blob/main/README.md

Run this command to install the stable release of the effectsize package from CRAN.

```r
install.packages("effectsize")
```

--------------------------------

### Install effectsize from R-universe

Source: https://github.com/easystats/effectsize/blob/main/README.md

Install the latest development version of the effectsize package from R-universe.

```r
install.packages("effectsize", repos = "https://easystats.r-universe.dev/")
```

--------------------------------

### Setup Environment for Effect Size Calculations

Source: https://github.com/easystats/effectsize/blob/main/vignettes/from_test_statistics.Rmd

Initializes the knitr environment and loads the effectsize package for subsequent calculations.

```r
library(knitr)
library(effectsize)

knitr::opts_chunk$set(comment = ">")
options(digits = 2)
options(knitr.kable.NA = "")

set.seed(747)

.eval_if_requireNamespace <- function(...) {
  pkgs <- c(...)
  knitr::opts_chunk$get("eval") &&
    all(sapply(pkgs, requireNamespace, quietly = TRUE))
}
```

--------------------------------

### Format Standardized Vectors

Source: https://github.com/easystats/effectsize/blob/main/man/format_standardize.Rd

Examples demonstrating basic usage and customization of the format_standardize function.

```R
format_standardize(c(-1, 0, 1))
```

```R
format_standardize(c(-1, 0, 1, 2), reference = rnorm(1000))
```

```R
format_standardize(c(-1, 0, 1, 2), reference = rnorm(1000), robust = TRUE)
```

```R
format_standardize(standardize(mtcars$wt), digits = 1)
```

```R
format_standardize(standardize(mtcars$wt, robust = TRUE), digits = 1)
```

--------------------------------

### Glass's Delta Usage Examples

Source: https://github.com/easystats/effectsize/blob/main/_autodocs/api-reference/standardized-differences.md

Examples for calculating Glass's delta with independent samples and interpreting the results.

```r
# Two independent samples (required)
glass_delta(mpg ~ am, data = mtcars)

# With alternative CI
glass_delta(mpg ~ am, data = mtcars, alternative = "greater")

# Interpretation
interpret_glass_delta(-1.10, rules = "gignac2016")
```

--------------------------------

### Hedges' g Usage Examples

Source: https://github.com/easystats/effectsize/blob/main/_autodocs/api-reference/standardized-differences.md

Examples for calculating Hedges' g with independent and paired samples, and interpreting the results.

```r
# Two independent samples
hedges_g(mpg ~ am, data = mtcars)

# Paired samples
hedges_g(Pair(extra[group == 1], extra[group == 2]) ~ 1, data = sleep, verbose = FALSE)

# Interpretation
interpret_hedges_g(-1.48, rules = "sawilowsky2009")
```

--------------------------------

### Interpret Odds Ratio Examples

Source: https://github.com/easystats/effectsize/blob/main/man/interpret_oddsratio.Rd

Examples demonstrating the interpretation of single and multiple odds ratio values.

```R
interpret_oddsratio(1)
interpret_oddsratio(c(5, 2))
```

--------------------------------

### Calculate p_superiority examples

Source: https://github.com/easystats/effectsize/blob/main/_autodocs/api-reference/common-language-effect-sizes.md

Demonstrates usage with independent samples, formulas, one-sample comparisons, and paired data.

```r
library(effectsize)

# Two independent samples
p_superiority(mtcars$mpg[mtcars$am == 0], 
              mtcars$mpg[mtcars$am == 1])

# Using formula
p_superiority(mpg ~ am, data = mtcars)

# One sample (vs. reference)
p_superiority(mtcars$wt, mu = 3)

# Paired samples
x <- c(1.83, 0.50, 1.62, 2.48, 1.68, 1.88, 1.55, 3.06, 1.30)
y <- c(0.878, 0.647, 0.598, 2.05, 1.06, 1.29, 1.06, 3.14, 1.29)
p_superiority(x, y, paired = TRUE)
```

--------------------------------

### Interpret ROPE percentages

Source: https://github.com/easystats/effectsize/blob/main/man/interpret_rope.Rd

Examples demonstrating how to interpret ROPE values for standard and full ROPE scenarios.

```R
interpret_rope(0, ci = 0.9)
interpret_rope(c(0.005, 0.99), ci = 1)
```

--------------------------------

### Load Food Classification Data

Source: https://github.com/easystats/effectsize/blob/main/papers/Phi Fei Fo Fum (2023) Mathematics/OLD/paper.Rmd

Loads the example dataset used for demonstrating association coefficients.

```r
data("food_class")
food_class
```

--------------------------------

### Interpret Direction Examples

Source: https://github.com/easystats/effectsize/blob/main/man/interpret_direction.Rd

Demonstrates how to interpret single numeric values and vectors of values using interpret_direction.

```R
interpret_direction(.02)
interpret_direction(c(.5, -.02))
interpret_direction(0)
```

--------------------------------

### Interpret Eta Squared Values

Source: https://github.com/easystats/effectsize/blob/main/man/interpret_omega_squared.Rd

Examples demonstrating how to interpret eta squared values using default and custom rulesets.

```R
interpret_eta_squared(.02)
interpret_eta_squared(c(.5, .02), rules = "cohen1992")
```

--------------------------------

### Manual aggregation for repeated measures

Source: https://github.com/easystats/effectsize/blob/main/man/repeated_measures_d.Rd

Example of manual data aggregation using tapply before passing to the function.

```R
rouder2016_wide <- tapply(rouder2016[["rt"]], rouder2016[1:2], mean)
repeated_measures_d(rouder2016_wide[, 1], rouder2016_wide[, 2])
```

--------------------------------

### Calculate Pooled Indices

Source: https://github.com/easystats/effectsize/blob/main/man/sd_pooled.Rd

Examples demonstrating the use of pooled deviation functions with formula and vector inputs.

```R
sd_pooled(mpg ~ am, data = mtcars)
mad_pooled(mtcars$mpg, factor(mtcars$am))

cov_pooled(mpg + hp + cyl ~ am, data = mtcars)
```

--------------------------------

### Setup knitr options for power analysis

Source: https://github.com/easystats/effectsize/blob/main/vignettes/statistical_power.Rmd

Configures global knitr settings for the vignette, including conditional evaluation based on the availability of the pwr package.

```r
knitr::opts_chunk$set(
  collapse = TRUE,
  comment = "#>",
  warning = FALSE,
  message = FALSE,
  eval = requireNamespace("pwr", quietly = TRUE)
)

options(digits = 4L, knitr.kable.NA = "")

set.seed(123)
```

--------------------------------

### Interpret Bayes Factor values

Source: https://github.com/easystats/effectsize/blob/main/man/interpret_bf.Rd

Examples demonstrating the interpretation of single and multiple Bayes Factor values.

```R
interpret_bf(1)
interpret_bf(c(5, 2, 0.01))
```

--------------------------------

### Compute eta squared from Bayesian model

Source: https://github.com/easystats/effectsize/blob/main/_autodocs/api-reference/anova-effect-sizes.md

Example demonstrating fitting a Bayesian model with rstanarm and calculating the posterior eta squared.

```r
library(rstanarm)
library(bayestestR)

# Fit Bayesian model
fit_bayes <- rstanarm::stan_glm(
  mpg ~ factor(cyl) * wt + qsec,
  data = mtcars, family = gaussian(),
  refresh = 0
)

# Compute eta squared from PPD
es <- eta_squared_posterior(fit_bayes, verbose = FALSE)

# Summarize posterior
bayestestR::describe_posterior(es, test = NULL)
```

--------------------------------

### Interpret Probability of Direction values

Source: https://github.com/easystats/effectsize/blob/main/man/interpret_pd.Rd

Examples demonstrating how to interpret single and multiple probability of direction values using default and custom rule sets.

```R
interpret_pd(.98)
interpret_pd(c(.96, .99), rules = "makowski2019")
```

--------------------------------

### Interpret Correlation Coefficients

Source: https://github.com/easystats/effectsize/blob/main/man/interpret_r.Rd

Examples of interpreting correlation coefficients using default and custom rule sets.

```R
interpret_r(.015)
interpret_r(c(.5, -.02))
interpret_r(.3, rules = "lovakov2021")
```

--------------------------------

### Interpret ICC values

Source: https://github.com/easystats/effectsize/blob/main/man/interpret_icc.Rd

Examples demonstrating how to interpret single and multiple ICC values using the default Koo (2016) rules.

```R
interpret_icc(0.6)
interpret_icc(c(0.4, 0.8))
```

--------------------------------

### Get Standardized Coefficients with `standardize_parameters()`

Source: https://github.com/easystats/effectsize/blob/main/papers/effectsize (2020) JOSS/paper.md

Use `standardize_parameters()` to obtain a table of standardized coefficients from a model. The default standardization method is 'refit'.

```r
model <- lm(mpg ~ cyl * am,
            data = mtcars)

standardize_parameters(model)
#>  Parameter   | Coefficient (std.) |         95% CI
#> -------------------------------------------------
#>  (Intercept) |              -0.10 | [-0.30,  0.11]
#>  cyl         |              -0.74 | [-0.95, -0.53]
#>  am          |               0.17 | [-0.04,  0.39]
#>  cyl:am      |              -0.19 | [-0.41,  0.02]
#> 
#>  # Standardization method: refit
```

--------------------------------

### Handling Helpful Warnings in R

Source: https://github.com/easystats/effectsize/blob/main/_autodocs/errors.md

Examples of common warnings triggered by missing data or incorrect function usage, which can be suppressed using verbose = FALSE.

```r
# Missing values in data
cohens_d(c(1, 2, NA, 4), c(5, NA, 7, 8), verbose = TRUE)
# Warning: Removed X missing values

# Paired samples reminder
cohens_d(x, y, paired = FALSE)
# Note: Consider repeated_measures_d() for more options
```

--------------------------------

### Load required packages

Source: https://github.com/easystats/effectsize/blob/main/vignettes/statistical_power.Rmd

Initialize the environment by loading the pwr and effectsize packages.

```r
library(pwr)
library(effectsize)
```

--------------------------------

### Load effectsize package

Source: https://github.com/easystats/effectsize/blob/main/README.Rmd

Initializes the package and configures options for symbol display.

```R
library(effectsize)
options(es.use_symbols = TRUE) # get nice symbols when printing! (On Windows, requires R >= 4.2.0)
```

--------------------------------

### View Available Rule Sets

Source: https://github.com/easystats/effectsize/blob/main/_autodocs/configuration.md

Access help documentation to list all available rule sets for a specific function.

```r
?interpret_cohens_d  # Lists all available rule sets
```

--------------------------------

### Load effectsize library

Source: https://github.com/easystats/effectsize/blob/main/vignettes/effectsize_API.Rmd

Initializes the package for use in the R session.

```r
library(effectsize)
```

--------------------------------

### Prepare Data and Model

Source: https://github.com/easystats/effectsize/blob/main/vignettes/anovaES.Rmd

Load the dataset and fit a linear model to demonstrate ANOVA-like effect size calculations.

```r
data(obk.long, package = "afex")
# modify the data slightly for the demonstration:
obk.long <- obk.long[1:240 %% 3 == 0, ]
obk.long$id <- seq_len(nrow(obk.long))

m <- lm(value ~ treatment, data = obk.long)

parameters::model_parameters(m)
```

--------------------------------

### Calculate Rank Biserial Correlation

Source: https://github.com/easystats/effectsize/blob/main/man/rank_biserial.Rd

Example usage of rank_biserial with the mtcars dataset.

```R
data(mtcars)
mtcars$am <- factor(mtcars$am)
mtcars$cyl <- factor(mtcars$cyl)
```

--------------------------------

### Load and Display Music_preferences2

Source: https://github.com/easystats/effectsize/blob/main/man/Music_preferences2.Rd

Load the dataset into the R environment and display its contents.

```R
data("Music_preferences2")
Music_preferences2
```

--------------------------------

### Load and display Music_preferences dataset

Source: https://github.com/easystats/effectsize/blob/main/man/Music_preferences.Rd

Load the dataset into the R environment and print the contingency table to the console.

```r
data("Music_preferences")
Music_preferences
```

--------------------------------

### Handling Deprecation Warnings in R

Source: https://github.com/easystats/effectsize/blob/main/_autodocs/errors.md

Example of a deprecation warning indicating that a function is outdated and should be replaced.

```r
# Example (fictitious):
old_function(x)
# Warning: old_function() is deprecated as of effectsize 1.0.0
# Use new_function() instead
```

--------------------------------

### Load and Inspect hardlyworking Dataset

Source: https://github.com/easystats/effectsize/blob/main/man/hardlyworking.Rd

Load the dataset into the R environment and display the first five rows to verify the structure.

```r
data("hardlyworking")
head(hardlyworking, n = 5)
```

--------------------------------

### Load and inspect the preferences2025 dataset

Source: https://github.com/easystats/effectsize/blob/main/man/preferences2025.Rd

Load the dataset into the R environment and display the first five rows.

```r
data("preferences2025")
head(preferences2025, n = 5)
```

--------------------------------

### Standardize Model Parameters

Source: https://github.com/easystats/effectsize/blob/main/vignettes/effectsize.Rmd

Demonstrates standardizing coefficients for linear models using datawizard and parameters packages.

```r
model <- lm(mpg ~ cyl * am,
  data = mtcars
)

datawizard::standardize(model)

parameters::standardize_parameters(model)
```

--------------------------------

### Calculate Fei (פ) Effect Size

Source: https://github.com/easystats/effectsize/blob/main/papers/Phi Fei Fo Fum (2023) Mathematics/OLD/paper.tex

Examples of calculating the Fei effect size for various categorical distributions.

```R
O - c(90, 10)
p_E - c(0.35, 0.65)
fei(O, p = p_E)
```

```R
O - c(10, 20, 80, 5)
p_E - c(.25, .25, .25, .25)
fei(O, p = p_E)
```

```R
O - c(90, 10)
p_E - c(0.5, 0.5)

fei(O, p = p_E)
```

--------------------------------

### Load and Inspect the Screening Test Dataset

Source: https://github.com/easystats/effectsize/blob/main/man/screening_test.Rd

Load the dataset into the R environment and display the first five rows to verify the structure.

```R
data("screening_test")
head(screening_test, n = 5)
```

--------------------------------

### Calculate Cohen's d with mtcars

Source: https://github.com/easystats/effectsize/blob/main/man/cohens_d.Rd

Example demonstrating the preparation of data for effect size calculation using the mtcars dataset.

```R
data(mtcars)
mtcars$am <- factor(mtcars$am)
```

--------------------------------

### Register custom method

Source: https://github.com/easystats/effectsize/blob/main/vignettes/effectsize_API.Rmd

Ensure the custom method is accessible in the global environment.

```r
# This is for: https://github.com/easystats/easystats/issues/348
.anova_es.superMODEL <<- .anova_es.superMODEL
```

--------------------------------

### Interpret Goodness of Fit Indices

Source: https://github.com/easystats/effectsize/blob/main/man/interpret_gfi.Rd

Examples of interpreting various fit indices by passing a vector of values to the respective functions.

```R
interpret_gfi(c(.5, .99))
interpret_agfi(c(.5, .99))
interpret_nfi(c(.5, .99))
interpret_nnfi(c(.5, .99))
interpret_cfi(c(.5, .99))
interpret_rmsea(c(.07, .04))
interpret_srmr(c(.5, .99))
interpret_rfi(c(.5, .99))
interpret_ifi(c(.5, .99))
interpret_pnfi(c(.5, .99))
```

--------------------------------

### Calculate Ratio of Means

Source: https://github.com/easystats/effectsize/blob/main/man/means_ratio.Rd

Basic usage of means_ratio with two numeric vectors, including examples of adjusted and log-transformed outputs.

```R
x <- c(1.83, 0.50, 1.62, 2.48, 1.68, 1.88, 1.55, 3.06, 1.30)
y <- c(0.878, 0.647, 0.598, 2.05, 1.06, 1.29, 1.06, 3.14, 1.29)
means_ratio(x, y)
means_ratio(x, y, adjust = FALSE)

means_ratio(x, y, log = TRUE)
```

--------------------------------

### Package Directory Structure

Source: https://github.com/easystats/effectsize/blob/main/_autodocs/INDEX.md

Visual representation of the R package file hierarchy.

```text
effectsize/
├── R/                              (63 source files)
│   ├── cohens_d.R                 (standardized differences)
│   ├── eta_squared-main.R         (ANOVA effect sizes)
│   ├── xtab_diff.R                (contingency tables: OR, RR, etc.)
│   ├── xtab_corr.R                (contingency tables: Cramér's V, etc.)
│   ├── rank_diff.R                (rank-based effect sizes)
│   ├── convert_*.R                (20+ conversion functions)
│   ├── interpret*.R               (25+ interpretation functions)
│   ├── effectsize.R               (generic function)
│   ├── effectsize.htest.R         (S3 method for htest)
│   ├── effectsize.BFBayesFactor.R (Bayesian support)
│   └── [utilities, printing, formatting files]
├── DESCRIPTION                     (package metadata)
├── NAMESPACE                       (exports: 240+ functions)
└── man/                           (roxygen2 documentation)
```

--------------------------------

### Interpret R-squared values in R

Source: https://github.com/easystats/effectsize/blob/main/man/interpret_r2.Rd

Examples of interpreting single and multiple R-squared values using the default Cohen (1988) rules.

```R
interpret_r2(.02)
interpret_r2(c(.5, .02))
```

--------------------------------

### Interpret p-values with default and custom rules

Source: https://github.com/easystats/effectsize/blob/main/man/interpret_p.Rd

Demonstrates basic usage with default settings and the 'rss' rule set.

```R
interpret_p(c(.5, .02, 0.001))
```

```R
interpret_p(c(.5, .02, 0.001), rules = "rss")
```

--------------------------------

### Loading and Displaying the food_class Dataset

Source: https://github.com/easystats/effectsize/blob/main/man/food_class.Rd

Load the dataset into the R environment and display its contents.

```r
data("food_class")
food_class
#>           Soy Milk Meat
#> Vegan      47    0    0
#> Not-Vegan   0   12   21
```

--------------------------------

### Interpret Cohen's d values

Source: https://github.com/easystats/effectsize/blob/main/man/interpret_cohens_d.Rd

Examples of interpreting single and multiple Cohen's d values using default and custom rule sets.

```R
interpret_cohens_d(.02)
interpret_cohens_d(c(.5, .02))
interpret_cohens_d(.3, rules = "lovakov2021")
```

--------------------------------

### Handle Unsupported Model Classes

Source: https://github.com/easystats/effectsize/blob/main/_autodocs/errors.md

Verify model compatibility using insight::supported_models().

```r
weird_model <- list(coef = 1)
eta_squared(weird_model)
# Error: Model type not supported. See supported_models() for list.
```

--------------------------------

### Compare Fei and Cohen's w

Source: https://github.com/easystats/effectsize/blob/main/papers/Phi Fei Fo Fum (2023) Mathematics/OLD/paper.Rmd

Compares the output of Fei and Cohen's w for a uniform 2-cell distribution.

```R
O <- c(90, 10)
p_E <- c(0.5, 0.5)

fei(O, p = p_E)
cohens_w(O, p = p_E)
```

--------------------------------

### Interpret Pearson's r

Source: https://github.com/easystats/effectsize/blob/main/README.md

Use interpret_r to get a qualitative interpretation of a Pearson's r correlation coefficient based on predefined rules of thumb.

```r
interpret_r(r = 0.3)
```

--------------------------------

### Load effectsize and set options

Source: https://github.com/easystats/effectsize/blob/main/README.md

Load the effectsize package and set an option to display nice symbols when printing results. This requires R version 4.2.0 or later on Windows.

```r
library(effectsize)
options(es.use_symbols = TRUE) # get nice symbols when printing! (On Windows, requires R >= 4.2.0)
```

--------------------------------

### Define and use interpretation rules

Source: https://github.com/easystats/effectsize/blob/main/_autodocs/api-reference/interpretation-functions.md

Demonstrates creating custom rule sets with rules() and applying them to numeric values or data frames using interpret().

```r
library(effectsize)

# Create custom rules
my_rules <- rules(
  c(0.2, 0.5, 0.8),
  labels = c("negligible", "small", "medium", "large"),
  name = "My Effect Size Rules"
)

# Interpret values
interpret(0.3, rules = my_rules)
interpret(c(0.1, 0.35, 0.6, 0.9), rules = my_rules)

# Or using named vector
d_rules <- rules(
  c("small" = 0.2, "medium" = 0.5, "large" = 0.8)
)
interpret(0.4, rules = d_rules)

# With data frame
cohens_d_result <- cohens_d(mpg ~ am, data = mtcars)
interpret(cohens_d_result, rules = "cohen1988")
```

--------------------------------

### Calculate Overlap and U3 for Numeric Vectors

Source: https://github.com/easystats/effectsize/blob/main/man/p_superiority.Rd

Examples of calculating probability of overlap and Cohen's U3 for two numeric vectors, demonstrating how directionality affects the result.

```R
x <- c(1.83, 0.5, 1.62, 2.48, 1.68, 1.88, 1.55, 3.06, 1.3)
y <- c(0.878, 0.647, 0.598, 2.05, 1.06, 1.29, 1.06, 3.14, 1.29)

p_overlap(x, y)
p_overlap(y, x) # direction of effect does not matter

cohens_u3(x, y)
cohens_u3(y, x) # direction of effect does matter
```

--------------------------------

### Calculate Effect Sizes for Grouped Data

Source: https://github.com/easystats/effectsize/blob/main/man/p_superiority.Rd

Examples of calculating Cohen's U2, probability of superiority, and Wilcoxon-Mann-Whitney odds using formula notation with the mtcars dataset.

```R
cohens_u2(mpg ~ am, data = mtcars)

p_superiority(mpg ~ am, data = mtcars, parametric = FALSE)

wmw_odds(mpg ~ am, data = mtcars)
```

--------------------------------

### Handle Incompatible CI and Alternative

Source: https://github.com/easystats/effectsize/blob/main/_autodocs/errors.md

Different alternative hypotheses result in different CI bounds.

```r
# While not strictly wrong, extreme CIs may be generated
cohens_d(x, y, ci = 0.95, alternative = "less")
```

--------------------------------

### Standardize parameters and posteriors in R

Source: https://github.com/easystats/effectsize/blob/main/_autodocs/api-reference/other-effect-sizes.md

Shows how to extract standardized parameters from linear models and standardize Bayesian posterior distributions.

```r
# Standardized parameters from linear model
model <- lm(mpg ~ hp + wt + cyl, data = mtcars)
standardize_parameters(model)

# From Bayesian model
library(rstanarm)
fit_bayes <- stan_glm(mpg ~ hp + wt, data = mtcars, refresh = 0)
standardize_posteriors(fit_bayes)
```

--------------------------------

### Interpret using named rule sets and transformations

Source: https://github.com/easystats/effectsize/blob/main/man/interpret.Rd

Shows how to pass rules directly as named vectors or apply transformations like absolute value during interpretation.

```R
interpret(c(0.35, 0.15), c("small" = 0.2, "large" = 0.4), name = "Cohen's Rules")
interpret(c(0.35, 0.15), rules(c(0.2, 0.4), c("small", "medium", "large")))

bigness <- rules(c(1, 10), c("small", "medium", "big"))
interpret(abs(-5), bigness)
interpret(-5, bigness, transform = abs)
```

--------------------------------

### Print and Format Effect Size Objects

Source: https://github.com/easystats/effectsize/blob/main/_autodocs/types.md

Use print and format methods to display results, optionally including additional metrics like CLES or formatting for markdown.

```r
d <- cohens_d(x, y)
print(d)                          # Default print method
print(d, append_CLES = TRUE)      # Add common language effect sizes

format(d)                         # Format for markdown
```

--------------------------------

### Calculate Partial Eta-Squared from F-statistics

Source: https://github.com/easystats/effectsize/blob/main/vignettes/from_test_statistics.Rmd

Demonstrates fitting an ANOVA model with afex and comparing the results with manual conversion using F_to_eta2.

```r
library(afex)

data(md_12.1)

aov_fit <- aov_car(
  rt ~ angle * noise + Error(id / (angle * noise)),
  data = md_12.1,
  anova_table = list(correction = "none", es = "pes")
)
aov_fit
```

```r
library(effectsize)
options(es.use_symbols = TRUE) # get nice symbols when printing! (On Windows, requires R >= 4.2.0)

F_to_eta2(
  f = c(40.72, 33.77, 45.31),
  df = c(2, 1, 2),
  df_error = c(18, 9, 18)
)
```

--------------------------------

### Compare with Cohen's d for one sample

Source: https://github.com/easystats/effectsize/blob/main/man/repeated_measures_d.Rd

Demonstrates the equivalence between d_z and Cohen's d for one sample of individual differences.

```R
cohens_d(chocolate - poop ~ 1, data = preferences2025)
```

--------------------------------

### Perform Equivalence Testing on Effect Size Tables

Source: https://github.com/easystats/effectsize/blob/main/man/equivalence_test.effectsize_table.Rd

Demonstrates performing equivalence tests on various effect size objects like eta_squared, oddsratio, and Cohen's d, including optional plotting using the see package.

```R
data("hardlyworking")
model <- aov(salary ~ age + factor(n_comps) * cut(seniority, 3), data = hardlyworking)
es <- eta_squared(model, ci = 0.9, alternative = "two.sided")
equivalence_test(es, range = c(0, 0.15)) # TOST

data("RCT_table")
OR <- oddsratio(RCT_table, alternative = "greater")
equivalence_test(OR, range = c(0, 1))

ds <- t_to_d(
  t = c(0.45, -0.65, 7, -2.2, 2.25),
  df_error = c(675, 525, 2000, 900, 1875),
  ci = 0.9, alternative = "two.sided" # TOST
)
# Can also plot
if (require(see)) plot(equivalence_test(ds, range = 0.2))
if (require(see)) plot(equivalence_test(ds, range = 0.2, rule = "cet"))
if (require(see)) plot(equivalence_test(ds, range = 0.2, rule = "bayes"))
```

--------------------------------

### Load Smoking_FASD dataset

Source: https://github.com/easystats/effectsize/blob/main/man/chisq_to_phi.Rd

Load the Smoking_FASD dataset for further analysis.

```R
data("Smoking_FASD")
```

--------------------------------

### Interpret a Structural Equation Model

Source: https://github.com/easystats/effectsize/blob/main/man/interpret_gfi.Rd

Demonstrates how to fit a SEM model using lavaan and interpret the results.

```R
structure <- " ind60 =~ x1 + x2 + x3
               dem60 =~ y1 + y2 + y3
               dem60 ~ ind60 "

model <- lavaan::sem(structure, data = lavaan::PoliticalDemocracy)

interpret(model)
```

--------------------------------

### Configuring Environment Variables

Source: https://github.com/easystats/effectsize/blob/main/_autodocs/configuration.md

Environment variables used by related packages to control parallel processing and warning displays.

```bash
# datawizard settings
DATAWIZARD_PARALLEL=TRUE

# insight settings
INSIGHT_SHOW_WARNINGS=FALSE
```

--------------------------------

### Converting between probability metrics

Source: https://github.com/easystats/effectsize/blob/main/man/oddsratio_to_probs.Rd

Demonstrates the conversion between different effect size metrics and probabilities using baseline risk p0.

```R
p0 <- 0.4
p1 <- 0.7

(OR <- probs_to_odds(p1) / probs_to_odds(p0))
(RR <- p1 / p0)
(ARR <- p1 - p0)
(NNT <- arr_to_nnt(ARR))

riskratio_to_probs(RR, p0 = p0)
oddsratio_to_probs(OR, p0 = p0)

all.equal(nnt_to_probs(NNT, p0 = p0, odds = TRUE),
          probs_to_odds(p1))

arr_to_probs(-ARR, p0 = p1)
nnt_to_probs(-NNT, p0 = p1)
```

--------------------------------

### Load and Display RCT_table

Source: https://github.com/easystats/effectsize/blob/main/man/RCT_table.Rd

Load the dataset into the R environment and display its contents.

```r
data("RCT_table")
RCT_table
```

--------------------------------

### Calculate Cohen's w for Custom Distributions

Source: https://github.com/easystats/effectsize/blob/main/papers/Phi Fei Fo Fum (2023) Mathematics/OLD/paper.Rmd

Demonstrates Cohen's w calculation for non-uniform and multinomial distributions where the value may exceed 1.

```R
O <- c(90, 10)
p_E <- c(0.35, 0.65)
cohens_w(O, p = p_E)


O <- c(10, 20, 80, 5)
p_E <- c(.25, .25, .25, .25)
cohens_w(O, p = p_E)
```

--------------------------------

### Use effectsize_table methods

Source: https://github.com/easystats/effectsize/blob/main/_autodocs/types.md

Demonstrates calculating Cohen's d and applying standard methods like print, interpret, and plot.

```r
library(effectsize)
d <- cohens_d(mpg ~ am, data = mtcars)
class(d)
# [1] "effectsize_difference" "effectsize_table"    "see_effectsize_table" "data.frame"

print(d)
interpret(d)
plot(d)  # with see package
```

--------------------------------

### rules(values, labels = NULL, name = NULL, right = TRUE)

Source: https://github.com/easystats/effectsize/blob/main/man/rules.Rd

Creates a container for interpretation rules of thumb, defining categories based on reference values.

```APIDOC
## rules(values, labels = NULL, name = NULL, right = TRUE)

### Description
Creates a container for interpretation rules of thumb. This object is typically used in conjunction with the interpret function to categorize statistical values.

### Parameters
- **values** (vector) - Required - Vector of reference values (edges defining categories or critical values).
- **labels** (vector) - Optional - Labels associated with each category. If NULL, the function attempts to infer them from the values vector.
- **name** (string) - Optional - A name for the set of rules to be displayed during printing.
- **right** (logical) - Optional - For threshold-type rules, indicates if thresholds are included in the interval to the right (lower values) or left (higher values). Defaults to TRUE.

### Example
```r
rules(c(0.2, 0.5, 0.8), c("small", "medium", "large"))
rules(c("small" = 0.2, "medium" = 0.5), name = "Cohen's Rules")
```
```

--------------------------------

### print.effectsize_table

Source: https://github.com/easystats/effectsize/blob/main/man/print.effectsize_table.Rd

Prints an effectsize_table object to the console.

```APIDOC
## print(x, digits = 2, use_symbols = getOption("es.use_symbols", FALSE), ...)

### Description
Prints the effectsize_table object with specified formatting.

### Parameters
- **x** (effectsize_table) - Required - The object to print.
- **digits** (numeric/string) - Optional - Number of digits for rounding or significant figures.
- **use_symbols** (boolean) - Optional - Whether to use proper symbols instead of transliterated names.
```

--------------------------------

### Load and inspect the rouder2016 dataset

Source: https://github.com/easystats/effectsize/blob/main/man/rouder2016.Rd

Load the dataset into the R environment and display the first 5 rows to verify the structure.

```r
data("rouder2016")
head(rouder2016, n = 5)
```

--------------------------------

### Define a custom model class

Source: https://github.com/easystats/effectsize/blob/main/vignettes/effectsize_API.Rmd

Create a simple linear model and assign it a custom class name.

```r
mod <- lm(mpg ~ factor(cyl) + am, mtcars)

class(mod) <- "superMODEL"
```

--------------------------------

### Compute eta squared for ANOVA models

Source: https://github.com/easystats/effectsize/blob/main/_autodocs/api-reference/anova-effect-sizes.md

Demonstrates calculating partial, non-partial, and generalized eta squared, along with interpretation using Cohen's rules.

```r
library(effectsize)
data(mtcars)
mtcars$am_f <- factor(mtcars$am)
mtcars$cyl_f <- factor(mtcars$cyl)

# Fit ANOVA model
model <- aov(mpg ~ am_f * cyl_f, data = mtcars)

# Partial eta squared (default)
eta2 <- eta_squared(model)
print(eta2)

# Non-partial eta squared
eta_squared(model, partial = FALSE)

# With generalized eta squared
eta_squared(model, generalized = "cyl_f")

# Interpretation
interpret(eta2, rules = "cohen1992")
interpret_eta_squared(0.10, rules = "cohen1992")
```

--------------------------------

### display(x, ...) and standardize_info(model, ...)

Source: https://github.com/easystats/effectsize/blob/main/_autodocs/api-reference/other-effect-sizes.md

Utility functions for formatting results and retrieving standardization information from models.

```APIDOC
## display(x, ...)
## standardize_info(model, ...)

### Description
Utility functions to display effect size results or extract standardization information from statistical models.

### Parameters
- **x / model** (object) - Required - The result object or model to process
- **...** (any) - Optional - Additional arguments

### Return Value
Formatted display or information data frame.
```

--------------------------------

### Setting Reproducible Options

Source: https://github.com/easystats/effectsize/blob/main/_autodocs/configuration.md

Explicitly setting global options to ensure consistent output across environments.

```r
# Set all options explicitly for reproducibility
options(
  es.use_symbols = TRUE,
  datawizard.verbose = FALSE,
  insight.print_name = TRUE
)

# Use standard rule sets, document in methods
d <- cohens_d(x, y, ci = 0.95)
interpret(d, rules = "cohen1988")  # Named rule set in methods section
```

--------------------------------

### Compute Effect Sizes for 2-by-2 Tables

Source: https://github.com/easystats/effectsize/blob/main/man/oddsratio.Rd

Demonstrates calculating odds ratios, risk ratios, Cohen's h, absolute risk reduction, and number needed to treat using a contingency table.

```R
data("RCT_table")
RCT_table # note groups are COLUMNS

oddsratio(RCT_table)
oddsratio(RCT_table, alternative = "greater")

riskratio(RCT_table)

cohens_h(RCT_table)

arr(RCT_table)

nnt(RCT_table)
```

--------------------------------

### Compare with Cohen's d for independent groups

Source: https://github.com/easystats/effectsize/blob/main/man/repeated_measures_d.Rd

Demonstrates the equivalence between d and Cohen's d for two independent groups.

```R
cohens_d(rt ~ cond, data = rouder2016, ci = NULL)
```

--------------------------------

### Standardize GLM Parameters

Source: https://github.com/easystats/effectsize/blob/main/vignettes/effectsize.Rmd

Shows how to produce standardized parameters for generalized linear models with exponentiation.

```r
model <- glm(am ~ cyl + hp,
  family = "binomial",
  data = mtcars
)

parameters::standardize_parameters(model, exponentiate = TRUE)
```

--------------------------------

### Calculate risk ratio with different base-rate

Source: https://github.com/easystats/effectsize/blob/main/vignettes/convert_p_OR_RR.Rmd

Demonstrates how the base-rate risk significantly impacts the calculated risk ratio.

```r
oddsratio_to_riskratio(OR, 0.04)
```

--------------------------------

### Compare Mahalanobis D and Cohen's D

Source: https://github.com/easystats/effectsize/blob/main/man/mahalanobis_d.Rd

Demonstrates that Mahalanobis D reduces to Cohen's D when only a single variate is provided.

```R
mahalanobis_d(hp ~ am, data = mtcars)

cohens_d(hp ~ am, data = mtcars)
```

--------------------------------

### Visualize effect size results

Source: https://github.com/easystats/effectsize/blob/main/_autodocs/README.md

Plot effect size results using the see package.

```r
library(see)
result <- eta_squared(model)
plot(result)
```

--------------------------------

### Interpret VIF values in R

Source: https://github.com/easystats/effectsize/blob/main/man/interpret_vif.Rd

Demonstrates how to pass a vector of VIF values to the interpret_vif function for classification.

```R
interpret_vif(c(1.4, 30.4))
```

--------------------------------

### Optimize Large Datasets

Source: https://github.com/easystats/effectsize/blob/main/_autodocs/configuration.md

Strategies for large datasets including skipping CI, using fast approximations, and data subsetting.

```r
# For very large datasets, consider:
# 1. Compute effect sizes only (skip CI)
result <- cohens_d(x, y, ci = FALSE)

# 2. Use approximation methods where available
result <- F_to_d(f_stat, df, df_error)  # Fast approximation

# 3. Subset data before computation
subset_result <- cohens_d(x[1:10000], y[1:10000])
```

--------------------------------

### Load and inspect Smoking_FASD dataset

Source: https://github.com/easystats/effectsize/blob/main/man/Smoking_FASD.Rd

Use the data function to load the dataset into the R environment and display its contents.

```R
data("Smoking_FASD")
Smoking_FASD
```

--------------------------------

### Standardize Model Parameters with `standardize()`

Source: https://github.com/easystats/effectsize/blob/main/papers/effectsize (2020) JOSS/paper.md

Use `standardize()` to refit a linear model with standardized data, allowing for comparison of coefficients.

```r
model <- lm(mpg ~ cyl * am,
            data = mtcars)

standardize(model)
#> 
#> Call:
#> lm(formula = mpg ~ cyl * am, data = data_std)
#> 
#> Coefficients:
#> (Intercept)          cyl           am       cyl:am 
#>     -0.0977      -0.7426       0.1739      -0.1930
```

--------------------------------

### oddsratio()

Source: https://github.com/easystats/effectsize/blob/main/_autodocs/api-reference/contingency-table-effect-sizes.md

Compute odds ratio for 2×2 contingency tables.

```APIDOC
## oddsratio(x, y = NULL, ci = 0.95, alternative = "two.sided", log = FALSE, ...)

### Description
Compute odds ratio for 2×2 contingency tables. This function accepts contingency tables, data frames, or output from statistical tests like chisq.test() or fisher.test().

### Parameters
- **x** (matrix, data.frame, htest, or crosstab) - Required - A 2×2 contingency table, or output from chisq.test() / fisher.test()
- **y** (numeric or factor) - Optional - Second variable if x is a vector/factor (creates contingency table)
- **ci** (numeric) - Optional - Confidence interval level. Set FALSE or NA to skip CI. Default: 0.95
- **alternative** (character) - Optional - CI direction: "two.sided", "greater", or "less". Default: "two.sided"
- **log** (logical) - Optional - If TRUE, returns log(odds ratio) instead of odds ratio. Default: FALSE
- **...** (any) - Optional - Additional arguments

### Return Value
A data frame with class effectsize_table and see_effectsize_table containing:
- **Odds_ratio or log_Odds_ratio** (numeric) - The odds ratio (or log odds ratio)
- **CI** (numeric) - CI level (if computed)
- **CI_low** (numeric) - Lower CI bound
- **CI_high** (numeric) - Upper CI bound

### Request Example
library(effectsize)
# From contingency table
data("RCT_table")
oddsratio(RCT_table)

# Log odds ratio
oddsratio(RCT_table, log = TRUE)
```

--------------------------------

### Configure pseudo-R² in parameter standardization

Source: https://github.com/easystats/effectsize/blob/main/_autodocs/configuration.md

Toggle the inclusion of pseudo-R² statistics when standardizing model parameters.

```r
# Include pseudo-R² statistics
standardize_parameters(model, include_pseudo_r2 = TRUE)

# Exclude pseudo-R² (faster)
standardize_parameters(model, include_pseudo_r2 = FALSE)
```

--------------------------------

### Configuring confidence intervals

Source: https://github.com/easystats/effectsize/blob/main/_autodocs/README.md

Shows how to adjust or disable confidence intervals using the ci parameter in effect size functions.

```r
# 95% CI (default)
cohens_d(x, y, ci = 0.95)

# 90% CI
cohens_d(x, y, ci = 0.90)

# No CI (faster)
cohens_d(x, y, ci = FALSE)
```

--------------------------------

### print_html.effectsize_table

Source: https://github.com/easystats/effectsize/blob/main/man/print.effectsize_table.Rd

Prints an effectsize_table object in HTML format.

```APIDOC
## print_html(x, digits = 2, use_symbols = getOption("es.use_symbols", FALSE), ...)

### Description
Formats and prints the effectsize_table as an HTML table.

### Parameters
- **x** (effectsize_table) - Required - The object to print.
- **digits** (numeric/string) - Optional - Number of digits for rounding.
- **use_symbols** (boolean) - Optional - Whether to use proper symbols.
```

--------------------------------

### Standardize variables and model coefficients in R

Source: https://github.com/easystats/effectsize/blob/main/_autodocs/api-reference/other-effect-sizes.md

Demonstrates standardizing a data frame and refitting a linear model with standardized predictors.

```r
# Standardize variables
df <- mtcars
df_std <- standardize(df)

# Refit model with standardized predictors
model <- lm(mpg ~ hp + wt, data = mtcars)
model_std <- standardize(model)
coef(model_std)

# Post-hoc standardization of coefficients
model_posthoc <- standardize(model, method = "posthoc")
```

--------------------------------

### print_md.effectsize_table

Source: https://github.com/easystats/effectsize/blob/main/man/print.effectsize_table.Rd

Prints an effectsize_table object in markdown format.

```APIDOC
## print_md(x, digits = 2, use_symbols = getOption("es.use_symbols", FALSE), ...)

### Description
Formats and prints the effectsize_table as a markdown table.

### Parameters
- **x** (effectsize_table) - Required - The object to print.
- **digits** (numeric/string) - Optional - Number of digits for rounding.
- **use_symbols** (boolean) - Optional - Whether to use proper symbols.
```