# R: Power

## General reference

• Cohen, J. (1992). A Power Primer, Psychological Bulletin, 1 155--159. [1] (http://resolver.scholarsportal.info.ezproxy.library.yorku.ca/resolve/00332909/v112i0001/155_app&form=pdf&file=file.pdf)

## Power graph for one-way Anova

```   dex <- expand.grid( within.var = 1, groups = 3, between.var = seq(.2,1,.05), power = c(.7,.8,.85,.9,.95))

n <- numeric(0)
for ( i in 1:nrow(dex)) {
ni <- do.call("power.anova.test", dex[i,])\$n
}

dex\$n <- n
td( new = T)
td( col = c('black','blue','red','green'))
xyplot( n ~ between.var, dex, groups = power, type = 'l',  lwd = 1.5,
auto.key = list(title= "Power",columns= 2,lines = T, points = F),
xlab = "Between variance / Within variance",
ylab = "n within each group",
panel = function(x,y,...) {
panel.xyplot(x,y,...)
panel.abline(v=seq(.2,1,.1),col='grey')
panel.abline(h=seq(2,40,2),col='grey')
})
```

## R example for power calculation

```
>
> grpmeans <- c( 5, 6, 7)
> wvar <- 1
>
> # The argument which is NULL will be calculated:
>
> power.anova.test(
+       groups = length(grpmeans) ,
+       n = NULL ,
+       between.var = var(grpmeans),
+       within.var = wvar,
+       sig.level = .05,
+       power = .9)

Balanced one-way analysis of variance power calculation

groups = 3
n = 7.431865
between.var = 1
within.var = 1
sig.level = 0.05
power = 0.9

The following funtions computes the power of a design to test a specified linear hypothesis.

power.glh <- function( means, n , within.var, sig.level = 0.9) {

}
NOTE: n is number in each group

>
```

## Power

```power.fisher.test(statmod)
Power of Fisher's Exact Test for Comparing
Proportions

```
```power.anova.test(stats)    Power calculations for balanced one-way analysis of
variance tests
power.prop.test(stats)     Power calculations two sample test for proportions
power.t.test(stats)        Power calculations for one and two sample t tests
print.power.htest(stats)   Print method for power calculation object
```

```asypow.power(asypow)       Asymptotic Power
pbsize(gap)                Power for population-based association design
pow_int(gsl)               Power functions
bpower(Hmisc)              Power and Sample Size for Two-Sample Binomial Test
ciapower(Hmisc)            Power of Interaction Test for Exponential Survival
cpower(Hmisc)              Power of Cox/log-rank Two-Sample Test
gbayes(Hmisc)              Gaussian Bayesian Posterior and Predictive
Distributions
popower(Hmisc)             Power and Sample Size for Ordinal Response
samplesize.bin(Hmisc)      Sample Size for 2-sample Binomial
spower(Hmisc)              Simulate Power of 2-Sample Test for Survival under
Complex Conditions
power.bc(qtlDesign)        Power calculations for Backcross
power.f2(qtlDesign)        Power calculations for F2 intercross
```