R: Power calculations for correlation test

pwr.r.test {pwr} | R Documentation

## Power calculations for correlation test

### Description

Compute power of test or determine parameters to obtain target power (same as power.anova.test).

### Usage

    pwr.r.test(n = NULL, r = NULL, sig.level = 0.05, power = NULL,
        alternative = c("two.sided", "less","greater"))

### Arguments

`n` | Number of observations
`r` | Linear correlation coefficient
`sig.level` | Significance level (Type I error probability)
`power` | Power of test (1 minus Type II error probability)
`alternative` | a character string specifying the alternative hypothesis, must be one of "two.sided" (default), "greater" or "less"

### Details

These calculations use the Z' transformation of correlation coefficient : Z'=arctanh(r)+r/(2*(n-1)) and a bias correction is applied. Note that contrary to Cohen (1988) p.546, where zp' = arctanh(rp) + rp/(2*(n-1)) and zc' = arctanh(rc) + rc/(2*(n-1)), we only use here zp' = arctanh(rp) + rp/(2*(n-1)) and zc' = arctanh(rc).

Exactly one of the parameters 'r','n','power' and 'sig.level' must be passed as NULL, and that parameter is determined from the others. Notice that the last one has non-NULL default so NULL must be explicitly passed if you want to compute it.

### Value

Object of class '"power.htest"', a list of the arguments (including the computed one) augmented with 'method' and 'note' elements.

### Note

'uniroot' is used to solve power equation for unknowns, so you may see errors from it, notably about inability to bracket the root when invalid arguments are given.

### Author(s)

Stephane Champely <champely@univ-lyon1.fr> but this is a mere copy of Peter Dalgaard work (power.t.test). The modified bias correction is contributed by Jeffrey Gill.

### References

Cohen, J. (1988). Statistical power analysis for the behavioral sciences (2nd ed.). Hillsdale,NJ: Lawrence Erlbaum.

### Examples

    ## Exercise 3.1 p. 96 from Cohen (1988)
    pwr.r.test(r=0.3,n=50,sig.level=0.05,alternative="two.sided")
    pwr.r.test(r=0.3,n=50,sig.level=0.05,alternative="greater")

    ## Exercise 3.4 p. 208
    pwr.r.test(r=0.3,power=0.80,sig.level=0.05,alternative="two.sided")
    pwr.r.test(r=0.5,power=0.80,sig.level=0.05,alternative="two.sided")
    pwr.r.test(r=0.1,power=0.80,sig.level=0.05,alternative="two.sided")

[Package pwr version 1.2-2 Index]