# cower

`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.

## General purpose

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.

## Types of power analysis

• "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

## Installation

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")

``````

## "A priori" power analysis

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).

## "Post-hoc" power analysis

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
``````

## Questions and suggestions

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.