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