# 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

1 2 |

### 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

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 | ```
## 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)
``` |