between_smd: Between-Case Standardized Mean Difference

In scan: Single-Case Data Analyses for Single and Multiple Baseline Designs

Between-Case Standardized Mean Difference

Description

Calculates a standardized mean difference from a multilevel model as described in Pustejovsky et al. (2014)

Usage

between_smd(
  data,
  method = c("REML", "MCMCglmm"),
  ci = 0.95,
  include_residuals = TRUE,
  ...
)

## S3 method for class 'sc_bcsmd'
print(x, digits = 2, ...)

## S3 method for class 'sc_bcsmd'
export(
  object,
  caption = NA,
  footnote = NA,
  filename = NA,
  digits = 2,
  round = 2,
  ...
)

Arguments

data	Either an scdf or an object returned from the hplm() or bplm() function.
method	Either "REML" or "⁠MCMglmm"⁠. This indicated which statistical method is applied to calculate the model.
ci	A numeric between 0 and 1 setting the width of the confidence interval (when method is REML) or the credible interval (when method is MCMCglmm). The default is 0.95 for a 95-percent interval.
include_residuals	Logical. See details.
...	Further arguments passed to the hplm() or bplm()function.
x	An object returned by baseline_smd().
digits	The minimum number of significant digits to be use. If set to "auto" (default), values are predefined.
object	An scdf or an object exported from a scan function.
caption	Character string with table caption. If left NA (default) a caption will be created based on the exported object.
footnote	Character string with table footnote. If left NA (default) a footnote will be created based on the exported object.
filename	String containing the file name. If a filename is given the output will be written to that file.
round	Integer passed to the digits argument used to round values.

Details

The BC-SMD is calculate as ⁠BC-SMD = Phase difference / sqrt(residual + random_intercept)⁠. This is most closely related to Cohen's d. If you want to have the most exact estimation based on the between case variance, you have to exclude the residual variance by setting the argument include_residuals = FALSE you get ⁠BC-SMD = Phase difference / sqrt(random_intercept)⁠. The 'base' model only includes the phase level as a predictor like originally proposed by Hedges et al. Whereas the 'Full plm' model includes the trend and the phase slope as additional predictors.

Value

An object of class sc_bcsmd.

Functions

• print(sc_bcsmd): Print results

• export(sc_bcsmd): export results

References

Pustejovsky, J. E., Hedges, L. V., & Shadish, W. R. (2014). Design-Comparable Effect Sizes in Multiple Baseline Designs: A General Modeling Framework. Journal of Educational and Behavioral Statistics, 39(5), 368–393. https://doi.org/10.3102/1076998614547577

Examples

## Create a example scdf:
des <- design(
  n = 150,
  phase_design = list(A1 = 10, B1 = 10, A2 = 10, B2 = 10, C = 10),
  level = list(B1 = 1, A2 = 0, B2 = 1, C = 1),
  rtt = 0.7,
  random_start_value = TRUE
)
study <- random_scdf(des)

## Standard BC-SMD return:
between_smd(study)

## Specify the model and provide an hplm object:
model <- hplm(study, contrast_level = "preceding", slope = FALSE,  trend = FALSE)
between_smd(model)

## excluding the residuals gives a more accurate estimation:
between_smd(model, include_residuals = FALSE)

scan documentation built on Sept. 11, 2025, 5:12 p.m.