effsize (version 0.6.4)

# cliff.delta: Cliff's Delta effect size for ordinal variables

## Description

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

## Usage

```cliff.delta(d, ... )
"cliff.delta"(formula, data=list() ,conf.level=.95,  use.unbiased=TRUE, use.normal=FALSE,  return.dm=FALSE, ...)
"cliff.delta"(d, f, conf.level=.95,  use.unbiased=TRUE, use.normal=FALSE,  return.dm=FALSE, ...)```

## Arguments

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.

## Value

A list of class `effsize` containing the following components: containing the following components: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"`

## Details

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.

## References

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

`cohen.d`, `print.effsize`

## Examples

Run this code
``````## 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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