Between-Case Standardized Mean Difference

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.

Value

An object of class sc_bcsmd.

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.

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)
#> Between-Case Standardized Mean Difference
#> 
#> Method: REML
#> Base model
#> 
#>   Effect BC-SMD   se LL-CI95% UL-CI95%
#>  phaseB1   0.85 0.02     0.81     0.89
#>  phaseA2   0.86 0.02     0.82     0.90
#>  phaseB2   1.67 0.02     1.63     1.71
#>   phaseC   2.55 0.02     2.51     2.58
#> 
#> Full plm model
#> 
#>   Effect BC-SMD   se LL-CI95% UL-CI95%
#>  phaseB1   0.87 0.04     0.79     0.95
#>  phaseA2   0.95 0.08     0.79     1.11
#>  phaseB2   1.89 0.13     1.64     2.15
#>   phaseC   2.90 0.18     2.55     3.24

## Specify the model and provide an hplm object:
model <- hplm(study, contrast_level = "preceding", slope = FALSE,  trend = FALSE)
between_smd(model)
#> Between-Case Standardized Mean Difference
#> 
#> Method: REML
#> Provided
#> 
#>   Effect BC-SMD   se LL-CI95% UL-CI95%
#>  phaseB1   0.85 0.02     0.81     0.89
#>  phaseA2   0.01 0.02    -0.03     0.05
#>  phaseB2   0.82 0.02     0.78     0.86
#>   phaseC   0.87 0.02     0.84     0.91

## excluding the residuals gives a more accurate estimation:
between_smd(model, include_residuals = FALSE)
#> Between-Case Standardized Mean Difference
#> 
#> Method: REML
#> Provided
#> 
#>   Effect BC-SMD   se LL-CI95% UL-CI95%
#>  phaseB1   1.02 0.02     0.97     1.07
#>  phaseA2   0.01 0.02    -0.04     0.06
#>  phaseB2   0.98 0.02     0.93     1.02
#>   phaseC   1.05 0.02     1.00     1.09