`effect_size_MB.Rd`

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
)
```

- 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

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` |

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

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

```
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
```