Computes the Cliff's Delta effect size for ordinal variables with the related confidence interval using efficient algorithms.

`cliff.delta(d, ... )`# S3 method for formula
cliff.delta(formula, data=list() ,conf.level=.95,
use.unbiased=TRUE, use.normal=FALSE,
return.dm=FALSE, ...)

# S3 method for default
cliff.delta(d, f, conf.level=.95,
use.unbiased=TRUE, use.normal=FALSE,
return.dm=FALSE, ...)

d

a numeric vector giving either the data values (if `f`

is a factor) or the treatment group values (if `f`

is a numeric vector)

f

either a factor with two levels or a numeric vector of values (see Detials)

conf.level

confidence level of the confidence interval

use.unbiased

a logical indicating whether to compute the delta's variance using the "unbiased" estimate formula or the "consistent" estimate

use.normal

logical indicating whether to use the normal or Student-t distribution for the confidence interval estimation

return.dm

logical indicating whether to return the dominance matrix. **Warning**: the explicit computation of the dominance uses a sub-optimal algorithm both in terms of memory and time

formula

a formula of the form `y ~ f`

, where `y`

is a numeric variable giving the data values and `f`

a factor with two levels giving the corresponding group

data

an optional matrix or data frame containing the variables in the formula `formula`

. By default the variables are taken from `environment(formula)`

.

...

further arguments to be passed to or from methods.

A list of class `effsize`

containing the following components:

the Cliff's delta estimate

the confidence interval of the delta

the estimated variance of the delta

the confidence level used to compute the confidence interval

the dominance matrix used for computation, only if `return.dm`

is TRUE

a qualitative assessment of the magnitude of effect size

the method used for computing the effect size, always `"Cliff's Delta"`

the method used to compute the delta variance estimation, either `"unbiased"`

or `"consistent"`

the distribution used to compute the confidence interval, either `"Normal"`

or `"Student-t"`

The magnitude is assessed using the thresholds provided in (Romano 2006), i.e. |d|<0.147 "negligible", |d|<0.33 "small", |d|<0.474 "medium", otherwise "large"

Uses the original formula reported in (Cliff 1996).

If the dominance matrix is required i.e. `return.dm=TRUE`

) the full matrix is computed thus using the naive algorithm.
Otherwise, if `treatment`

and `control`

are `factor`

s then the optimized linear complexity algorithm is used, otherwise the RLE algorithm (with complexity n log n) is used.

Norman Cliff (1996). Ordinal methods for behavioral data analysis. Routledge.

J. Romano, J. D. Kromrey, J. Coraggio, J. Skowronek, Appropriate statistics for ordinal level data: Should we really be using t-test and cohen's d for evaluating group differences on the NSSE and other surveys?, in: Annual meeting of the Florida Association of Institutional Research, 2006.

K.Y. Hogarty and J.D.Kromrey (1999). Using SAS to Calculate Tests of Cliff's Delta. Proceedings of the Twenty-Foursth Annual SAS User Group International Conference, Miami Beach, Florida, p 238. Available at: http://www2.sas.com/proceedings/sugi24/Posters/p238-24.pdf

```
# NOT RUN {
## Example data from Hogarty and Kromrey (1999)
treatment <- c(10,10,20,20,20,30,30,30,40,50)
control <- c(10,20,30,40,40,50)
res = cliff.delta(treatment,control,return.dm=TRUE)
print(res)
print(res$dm)
# }
```

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