# Power calculations for t-tests of means (one sample, two samples and paired samples)

### Description

Compute power of tests or determine parameters to obtain target power (similar to power.t.test).

### Usage

1 2 3 |

### Arguments

`n` |
Number of observations (per sample) |

`d` |
Effect size |

`sig.level` |
Significance level (Type I error probability) |

`power` |
Power of test (1 minus Type II error probability) |

`type` |
Type of t test : one- two- or paired-samples |

`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.

### See Also

power.prop.test

### Examples

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 | ```
## One sample (power)
## Exercise 2.5 p. 47 from Cohen (1988)
pwr.t.test(d=0.2,n=60,sig.level=0.10,type="one.sample",alternative="two.sided")
## Paired samples (power)
## Exercise p. 50 from Cohen (1988)
d<-8/(16*sqrt(2*(1-0.6)))
pwr.t.test(d=d,n=40,sig.level=0.05,type="paired",alternative="two.sided")
## Two independent samples (power)
## Exercise 2.1 p. 40 from Cohen (1988)
d<-2/2.8
pwr.t.test(d=d,n=30,sig.level=0.05,type="two.sample",alternative="two.sided")
## Two independent samples (sample size)
## Exercise 2.10 p. 59
pwr.t.test(d=0.3,power=0.75,sig.level=0.05,type="two.sample",alternative="greater")
``` |