ses_calc: Standardized Effect Size (SES) Calculation

In Lakens/TOSTER: Two One-Sided Tests (TOST) Equivalence Testing

Standardized Effect Size (SES) Calculation

Description

Calculates non-SMD standardized effect sizes for group comparisons. This function focuses on rank-based and probability-based effect size measures, which are especially useful for non-parametric analyses and when data do not meet normality assumptions.

Usage

ses_calc(x, ..., paired = FALSE, ses = "rb", alpha = 0.05)

## Default S3 method:
ses_calc(
  x,
  y = NULL,
  paired = FALSE,
  ses = c("rb", "odds", "logodds", "cstat"),
  alpha = 0.05,
  mu = 0,
  ...
)

## S3 method for class 'formula'
ses_calc(formula, data, subset, na.action, ...)

Arguments

x	a (non-empty) numeric vector of data values.
...	further arguments to be passed to or from methods.
paired	a logical indicating whether you want a paired t-test.
ses	a character string specifying the effect size measure to calculate: - "rb": rank-biserial correlation (default) - "odds": Wilcoxon-Mann-Whitney odds - "logodds": Wilcoxon-Mann-Whitney log-odds - "cstat": concordance statistic (C-statistic, equivalent to the area under the ROC curve)
alpha	alpha level for confidence interval calculation (default = 0.05).
y	an optional (non-empty) numeric vector of data values.
mu	number indicating the value around which asymmetry (for one-sample or paired samples) or shift (for independent samples) is to be estimated (default = 0).
formula	a formula of the form lhs ~ rhs where lhs is a numeric variable giving the data values and rhs either 1 for a one-sample or paired test or a factor with two levels giving the corresponding groups. If lhs is of class "Pair" and rhs is 1, a paired test is done.
data	an optional matrix or data frame (or similar: see model.frame) containing the variables in the formula formula. By default the variables are taken from environment(formula).
subset	an optional vector specifying a subset of observations to be used.
na.action	a function which indicates what should happen when the data contain NAs. Defaults to getOption("na.action").

Details

This function calculates standardized effect sizes that are not standardized mean differences (SMDs). These effect sizes are particularly useful for non-parametric analyses or when data violate assumptions of normality.

The available effect size measures are:

• Rank-biserial correlation ("rb"): A correlation coefficient based on ranks, ranging from -1 to 1. It can be interpreted as the difference between the proportion of favorable pairs and the proportion of unfavorable pairs. For independent samples, this is equivalent to Cliff's delta.

• Wilcoxon-Mann-Whitney odds ("odds"): The ratio of the probability that a randomly selected observation from group 1 exceeds a randomly selected observation from group 2, to the probability of the reverse. Values range from 0 to infinity, with 1 indicating no effect.

• Wilcoxon-Mann-Whitney log-odds ("logodds"): The natural logarithm of the WMW odds. This transforms the odds scale to range from negative infinity to positive infinity, with 0 indicating no effect.

• Concordance statistic ("cstat"): The probability that a randomly selected observation from group 1 exceeds a randomly selected observation from group 2. Also known as the common language effect size or the area under the ROC curve. Values range from 0 to 1, with 0.5 indicating no effect.

The function supports three study designs:

• One-sample design: Compares a single sample to a specified value

• Two-sample independent design: Compares two independent groups

• Paired samples design: Compares paired observations

For detailed information on calculation methods, see vignette("robustTOST").

Value

A data frame containing the following information:

• estimate: The effect size estimate

• lower.ci: Lower bound of the confidence interval

• upper.ci: Upper bound of the confidence interval

• conf.level: Confidence level (1-alpha)

Purpose

Use this function when:

• You want to report non-parametric effect size measures

• You need to quantify the magnitude of differences using ranks or probabilities

• Your outcome variable is ordinal

• You want to complement results from Wilcoxon-Mann-Whitney type test

See Also

Other effect sizes: boot_ses_calc(), boot_smd_calc(), smd_calc()

Examples

# Example 1: Independent groups comparison (rank-biserial correlation)
set.seed(123)
group1 <- c(1.2, 2.3, 3.1, 4.6, 5.2, 6.7)
group2 <- c(3.5, 4.8, 5.6, 6.9, 7.2, 8.5)
ses_calc(x = group1, y = group2, ses = "rb")

# Example 2: Using formula notation to calculate WMW odds
data(mtcars)
ses_calc(formula = mpg ~ am, data = mtcars, ses = "odds")

# Example 3: Paired samples with concordance statistic
data(sleep)
with(sleep, ses_calc(x = extra[group == 1],
                     y = extra[group == 2],
                     paired = TRUE,
                     ses = "cstat"))

Lakens/TOSTER documentation built on June 9, 2025, 8:57 p.m.