cliff.delta {effsize} | R Documentation |

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

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

`formula` |
a formula of the form |

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

`...` |
further arguments to be passed to or from methods. |

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.

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 |

`magnitude` |
a qualitative assessment of the magnitude of effect size |

`method` |
the method used for computing the effect size, always |

`variance.estimation` |
the method used to compute the delta variance estimation, either |

`CI.distribution` |
the distribution used to compute the confidence interval, either |

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"`

Marco Torchiano http://softeng.polito.it/torchiano/

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: https://support.sas.com/resources/papers/proceedings/proceedings/sugi24/Posters/p238-24.pdf

```
## 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)
```

[Package *effsize* version 0.8.1 Index]