`effect_size_ABk.Rd`

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
)
```

- 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

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 |

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

```
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
```