Calculates the Tau-U index with baseline trend correction
(Parker, Vannest, Davis, & Sauber 2011).

```
Tau_U(
A_data,
B_data,
condition,
outcome,
baseline_phase = NULL,
intervention_phase = NULL,
improvement = "increase"
)
```

## Arguments

- A_data
vector of numeric data for A phase, sorted in order of session
number. Missing values are dropped.

- B_data
vector of numeric data for B phase. Missing values are dropped.

- condition
vector identifying the treatment condition for each
observation in the series.

- outcome
vector of outcome data for the entire series.

- baseline_phase
character string specifying which value of
`condition`

corresponds to the baseline phase. Defaults to first
observed value of `condition`

.

- intervention_phase
character string specifying which value of
`condition`

corresponds to the intervention phase. Defaults to second
unique value of `condition`

.

- improvement
character string indicating direction of improvement.
Default is "increase".

## Details

Tau-U is an elaboration of the `Tau`

that includes a
correction for baseline trend. It is calculated as Kendall's S statistic
for the comparison between the phase B data and the phase A data, plus
Kendall's S statistic for the A phase observations, scaled by the product
of the number of observations in each phase.

Note that `A_data`

must be ordered by session number.

## References

Parker, R. I., Vannest, K. J., Davis, J. L., & Sauber, S. B.
(2011). Combining nonoverlap and trend for single-case research: Tau-U.
*Behavior Therapy, 42*(2), 284--299.
doi:doi:10.1016/j.beth.2010.08.006

## Examples

```
A <- c(20, 20, 26, 25, 22, 23)
B <- c(28, 25, 24, 27, 30, 30, 29)
Tau_U(A_data = A, B_data = B)
#> ES Est
#> 1 Tau-U 0.7380952
```