Description Usage Arguments Details Value Author(s) References See Also Examples

These functions use some conversion to and from the *t* distribution to provide the Cohen's *d* distribution. There are four versions that act similar to the standard distribution functions (the `d.`

, `p.`

, `q.`

, and `r.`

functions, and their longer aliases `.Cohensd`

), three convenience functions (`pdExtreme`

, `pdMild`

, and `pdInterval`

), a function to compute the confidence interval for a Cohen's *d* estimate `cohensdCI`

, and a function to compute the sample size required to obtain a confidence interval around a Cohen's *d* estimate with a specified accuracy (`pwr.cohensdCI`

and its alias `pwr.confIntd`

).

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 | ```
dd(x, df=NULL, populationD = 0,
n=NULL, n1=NULL, n2=NULL,
silent=FALSE)
pd(q, df, populationD = 0, lower.tail = TRUE)
qd(p, df, populationD = 0, lower.tail = TRUE)
rd(n, df, populationD = 0)
dCohensd(x, df=NULL, populationD = 0,
n=NULL, n1=NULL, n2=NULL,
silent=FALSE)
pCohensd(q, df, populationD = 0, lower.tail = TRUE)
qCohensd(p, df, populationD = 0, lower.tail = TRUE)
rCohensd(n, df, populationD = 0)
pdExtreme(d, n, populationD=0)
pdMild(d, n, populationD=0)
pdInterval(ds, n, populationD=0)
cohensdCI(d, n, conf.level = .95, plot=FALSE, silent=TRUE)
confIntD(d, n, conf.level = .95, plot=FALSE, silent=TRUE)
pwr.cohensdCI(d, w = 0.1, conf.level = 0.95,
extensive = FALSE, silent = TRUE)
pwr.confIntd(d, w = 0.1, conf.level = 0.95,
extensive = FALSE, silent = TRUE)
``` |

`x, q, d` |
Vector of quantiles, or, in other words, the value(s) of Cohen's |

`ds` |
A vector with two Cohen's |

`p` |
Vector of probabilites ( |

`df, n1, n2` |
Degrees of freedom or sample sizes for each group ( |

`n` |
Total |

`populationD` |
The value of Cohen's |

`lower.tail` |
logical; if TRUE (default), probabilities are the likelihood of finding a Cohen's |

`conf.level` |
The level of confidence of the confidence interval. |

`plot` |
Whether to show a plot of the sampling distribution of Cohen's |

`w` |
The desired 'half-width' or margin of error of the confidence interval. |

`extensive` |
Whether to only return the required sample size, or more extensive results. |

`silent` |
Whether to provide |

The functions use `convert.d.to.t`

and `convert.t.to.d`

to provide the Cohen's *d* distribution.

More details about `cohensdCI`

and `pwr.cohensdCI`

are provided
in Peters & Crutzen (2017).

`dCohensd`

(or `dd`

) gives the density, `pCohensd`

(or `pd`

) gives the distribution function, `qCohensd`

(or `qd`

) gives the quantile function, and `rCohensd`

(or `rd`

) generates random deviates.

`pdExtreme`

returns the probability (or probabilities) of finding a Cohen's *d* equal to or more extreme than the specified value(s).

`pdMild`

returns the probability (or probabilities) of finding a Cohen's *d* equal to or *less* extreme than the specified value(s).

`pdInterval`

returns the probability of finding a Cohen's *d* that lies in between the two specified values of Cohen's *d*.

`cohensdCI`

provides the confidence interval(s) for a given Cohen's *d* value.

`pwr.cohensdCI`

provides the sample size required to obtain a confidence interval for Cohen's *d* with a desired width.

Gjalt-Jorn Peters

Maintainer: Gjalt-Jorn Peters <gjalt-jorn@userfriendlyscience.com>

Peters, G. J. Y. & Crutzen, R. (2017) Knowing exactly how effective an intervention, treatment, or manipulation is and ensuring that a study replicates: accuracy in parameter estimation as a partial solution to the replication crisis. http://dx.doi.org/

Maxwell, S. E., Kelley, K., & Rausch, J. R. (2008). Sample size planning for statistical power and accuracy in parameter estimation. Annual Review of Psychology, 59, 537-63. https://doi.org/10.1146/annurev.psych.59.103006.093735

Cumming, G. (2013). The New Statistics: Why and How. Psychological Science, (November). https://doi.org/10.1177/0956797613504966

`convert.d.to.t`

, `convert.t.to.d`

, `dt`

, `pt`

, `qt`

, `rt`

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 | ```
### Confidence interval for Cohen's d of .5
### from a sample of 200 participants, also
### showing this visually: this clearly shows
### how wildly our Cohen's d value can vary
### from sample to sample.
cohensdCI(.5, n=200, plot=TRUE);
### How many participants would we need if we
### would want a more accurate estimate, say
### with a maximum confidence interval width
### of .2?
pwr.cohensdCI(.5, w=.1);
### Show that 'sampling distribution':
cohensdCI(.5,
n=pwr.cohensdCI(.5, w=.1),
plot=TRUE);
### Generate 10 random Cohen's d values
rCohensd(10, 20, populationD = .5);
### Probability of findings a Cohen's d smaller than
### .5 if it's 0 in the population (i.e. under the
### null hypothesis)
pCohensd(.5, 64);
### Probability of findings a Cohen's d larger than
### .5 if it's 0 in the population (i.e. under the
### null hypothesis)
1 - pCohensd(.5, 64);
### Probability of findings a Cohen's d more extreme
### than .5 if it's 0 in the population (i.e. under
### the null hypothesis)
pdExtreme(.5, 64);
### Probability of findings a Cohen's d more extreme
### than .5 if it's 0.2 in the population.
pdExtreme(.5, 64, populationD = .2);
``` |

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