Calculates HPS effect size — effect_size

Calculates the HPS effect size estimator based on data from an (AB)^k design, as described in Hedges, Pustejovsky, & Shadish (2012). Note that the data must contain one row per measurement occasion per subject.

effect_size_ABk(
  outcome,
  treatment,
  id,
  phase,
  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.
phase: factor vector indicating unique phases (each containing one contiguous control condition and one contiguous treatment condition) 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

`M_a`	Matrix reporting the total number of time points with data for all ids, by phase and treatment condition
`M_dot`	Total number of time points used to calculate the total variance (the sum of `M_a`)
`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 the effect size

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. (2012). A standardized mean difference effect size for single case designs. Research Synthesis Methods, 3, 224-239. doi:10.1002/jrsm.1052

Examples

data(Lambert)
effect_size_ABk(outcome = outcome, treatment = treatment, id = case, 
                phase = phase, time = time, data = Lambert)
#>                            est    se
#> unadjusted effect size  -1.162 0.123
#> adjusted effect size    -1.157 0.123
#> degree of freedom      160.238      
   
data(Anglesea)
effect_size_ABk(outcome = outcome, treatment = condition, id = case, 
                phase = phase, time = session, data = Anglesea)
#>                          est    se
#> unadjusted effect size 1.793 2.436
#> adjusted effect size   1.150 1.562
#> degree of freedom      2.340