scan (version 0.66.0)

between_smd: 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 sc_bcsmd
print(x, digits = 2, ...)
# S3 method for sc_bcsmd
export(
  object,
  caption = NA,
  footnote = NA,
  filename = NA,
  digits = 2,
  round = 2,
  ...
)

Value

An object of class sc_bcsmd.

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.

Functions

• print(sc_bcsmd): Print results

• export(sc_bcsmd): export results

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.

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)