effsize (version 0.5.4)

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(treatment, ... )
## S3 method for class 'formula':
cliff.delta(formula, data=list() ,conf.level=.95, 
                                use.unbiased=TRUE, use.normal=FALSE, 
                                return.dm=FALSE, ...)
## S3 method for class 'default':
cliff.delta(treatment, control, conf.level=.95, 
                         use.unbiased=TRUE, use.normal=FALSE, 
                         return.dm=FALSE, ...)

Arguments

treatment

numeric vector or ordered factor of data values for the treatment group (see Details)

control

numeric vector or ordered factor of data values for the control group (see Details)

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:
• estimate
  the Cliff's delta estimate
• conf.int
  the confidence interval of the delta
• var
  the estimated variance of the delta
• conf.level
  the confidence level used to compute the confidence interval
• dm
  the dominance matrix used for computation, only if return.dm is TRUE
• magnitude
  a qualitative assessment of the magnitude of effect size
• method
  the method used for computing the effect size, always "Cliff's Delta"
• variance.estimation
  the method used to compute the delta variance estimation, either "unbiased" or "consistent"
• CI.distribution
  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"

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 factors 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

See Also

cohen.d, print.effsize

Examples

## 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)