R: Power calculations for the mean of a normal distribution...

pwr.norm.test {pwr} | R Documentation

## Power calculations for the mean of a normal distribution (known variance)

### Description

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

### Usage

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

### Arguments

`d` | Effect size d=mu-mu0
`n` | Number of observations
`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

Exactly one of the parameters 'd','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)

### References

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

### Examples

    ## Power at mu=105 for H0:mu=100 vs. H1:mu>100 (sigma=15) 20 obs. (alpha=0.05)
    sigma<-15
    c<-100
    mu<-105
    d<-(mu-c)/sigma
    pwr.norm.test(d=d,n=20,sig.level=0.05,alternative="greater")

    ## Sample size of the test for power=0.80
    pwr.norm.test(d=d,power=0.8,sig.level=0.05,alternative="greater")

    ## Power function of the same test
    mu<-seq(95,125,l=100)
    d<-(mu-c)/sigma
    plot(d,pwr.norm.test(d=d,n=20,sig.level=0.05,alternative="greater")$power,
        type="l",ylim=c(0,1))
    abline(h=0.05)
    abline(h=0.80)

    ## Power function for the two-sided alternative
    plot(d,pwr.norm.test(d=d,n=20,sig.level=0.05,alternative="two.sided")$power,
        type="l",ylim=c(0,1))
    abline(h=0.05)
    abline(h=0.80)

[Package pwr version 1.2-2 Index]