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Standardized Effect Size (SES) Calculation

ses_calc.Rd

[Stable]

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").

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)

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").

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")
#>                             estimate   lower.ci   upper.ci conf.level
#> Rank-Biserial Correlation -0.6666667 -0.9023481 -0.1240779       0.95

# Example 2: Using formula notation to calculate WMW odds
data(mtcars)
ses_calc(formula = mpg ~ am, data = mtcars, ses = "odds")
#>          estimate   lower.ci  upper.ci conf.level
#> WMW Odds 0.204878 0.08958479 0.4685507       0.95

# 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"))
#>              estimate  lower.ci  upper.ci conf.level
#> Concordance 0.9909091 0.9641845 0.9977392       0.95