Calculates HPS effect size — effect_size

Calculates the HPS effect size estimator based on data from a multiple baseline design, as described in Hedges, Pustejovsky, & Shadish (2013). Note that the data must contain one row per measurement occasion per subject.

effect_size_MB(
  outcome,
  treatment,
  id,
  time,
  data = NULL,
  phi = NULL,
  rho = NULL
)

Arguments

outcome: vector of outcome data or name of variable within data. May not contain any missing values.
treatment: vector of treatment indicators or name of variable within data. Must be the same length as outcome.
id: factor vector indicating unique cases or name of variable within data. Must be the same length as outcome.
time: vector of measurement occasion times or name of variable within data. Must be the same length as outcome.
data: (Optional) dataset to use for analysis. Must be data.frame.
phi: (Optional) value of the auto-correlation nuisance parameter, to be used in calculating the small-sample adjusted effect size
rho: (Optional) value of the intra-class correlation nuisance parameter, to be used in calculating the small-sample adjusted effect size

Value

A list with the following components

`g_dotdot`	total number of non-missing observations
`K`	number of time-by-treatment groups containing at least one observation
`D_bar`	numerator of effect size estimate
`S_sq`	sample variance, pooled across time points and treatment groups
`delta_hat_unadj`	unadjusted effect size estimate
`phi`	corrected estimate of first-order auto-correlation
`sigma_sq_w`	corrected estimate of within-case variance
`rho`	estimated intra-class correlation
`theta`	estimated scalar constant
`nu`	estimated degrees of freedom
`delta_hat`	corrected effect size estimate
`V_delta_hat`	estimated variance of `delta_hat`

Note

If phi or rho is left unspecified (or both), estimates for the nuisance parameters will be calculated.

References

Hedges, L. V., Pustejovsky, J. E., & Shadish, W. R. (2013). A standardized mean difference effect size for multiple baseline designs across individuals. Research Synthesis Methods, 4(4), 324-341. doi:10.1002/jrsm.1086

Examples

data(Saddler)
effect_size_MB(outcome = outcome, treatment = treatment, id = case, 
               time = time, data = subset(Saddler, measure=="writing quality"))
#>                          est    se
#> unadjusted effect size 2.149 0.634
#> adjusted effect size   1.963 0.579
#> degree of freedom      8.918      

data(Laski)
effect_size_MB(outcome = outcome, treatment = treatment, id = case, 
               time = time, data = Laski)
#>                           est    se
#> unadjusted effect size  1.474 0.337
#> adjusted effect size    1.388 0.317
#> degree of freedom      13.100