`cower`

is an R-package to conduct power analyses on the comparison of
correlation coefficients. Currently, power analyses for the comparisons
of independent correlations -- as tested via Fisher's z-test -- are
available. Results have been tested against G-Power 3.1.

Studies that compare independent correlation coefficients require very
large sample sizes to obtain reasonable power (e.g.: *r* = 0.5 versus
*r* = 0.4 requires 787 participants per group for a power of .80 in a
one-sided test). Therefore, it is often preferable to consider a
comparison of dependent correlations if that is feasible. However, this
is not always possible; it then crucial to know the power to detect a
hypothesized difference in independent correlations. `cower`

is used to
conduct such power analyses.

- "Post-hoc" power analysis - determine the power for two given correlation coefficients and given sample size
- "A priori" power analysis - specify a desired power and two correlation coefficients to determine the required sample size

As `cower`

is not available from CRAN, you can install it directly from
this GitHub repository. To do so, you need the `devtools`

package. Then
run the following commands:

```
library("devtools") # if not available, run: install.packages("devtools")
install_github("m-Py/cower")
# load the package via
library("cower")
```

To compute the number of participants needed to obtain a certain power,
we can use the function `power.indep.cor`

. We specify two hypothesized
population correlation coefficients and the desired power:

```
power.indep.cor(r1 = 0.4, r2 = 0.3, power = .8)
$r1
[1] 0.4
$r2
[1] 0.3
$q
[1] 0.1141293
$n1
[1] 1209
$n2
[1] 1209
$power
[1] 0.8002746
$sig.level
[1] 0.05
$hypothesis
[1] "two.sided"
```

By default, the power for a two-sided test is computed, and an alpha
level of .05 is adapted. The alpha-level can be changed using the
parameter `sig.level`

and the sidedness can be changed using the
parameter `alternative`

(for a one-sided test, set `alternative`

to
"less" or "greater", depending on whether r1 is smaller or greater than
r2).

To determine the achieved power for the comparisons of two given
population correlation coefficients and sample size, we can use
`power.indep.cor`

the following way. Here we do not specify the
parameter `power`

(which is to be computed), but instead specify two
sample sizes `n1`

and `n2`

.

```
power.indep.cor(r1 = 0.4, r2 = 0.3, n1 = 450, n2 = 350)
$r1
[1] 0.4
$r2
[1] 0.3
$q
[1] 0.1141293
$n1
[1] 450
$n2
[1] 350
$power
[1] 0.3576306
$sig.level
[1] 0.05
$hypothesis
[1] "two.sided"
```

Again, we could also adjust the alpha-level and the sidedness of the hypothesis test.

For more information, load the package and open the help page by running:

```
library("cower")
?power.indep.cor
```

If you have any questions or suggestions (which are greatly appreciated), just open an issue at GitHub or contact me via email.

m-Py/cower documentation built on July 8, 2018, 3:17 p.m.

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