[R] Formula of power.t.test

[Uwe Ligges]

Xiaorong Chen wrote:

> Dear Sir or Madam,
> 
> What is the formula for power.t.test(delta=delta, sd=segma, sig.level=0.05, 
> power=0.8, type="one.sample", alternative="one.sided")$n?

See the code of power.t.test by just typing the name of that function 
into the console:

   power.t.test

and you'll easily see that the code collapses in your case to:

   tsample <- 1
   tside <- 1
   p.body <- quote({
     nu <- (n - 1) * tsample
     pt(qt(sig.level/tside, nu, lower = FALSE),
       nu, ncp = sqrt(n/tsample) * delta/sd, lower = FALSE)
   })
   n <- uniroot(function(n) eval(p.body) - power, c(2, 1e+07))$root


Uwe Ligges


> Thank you very much for the help!
> 
> Best,
> 
> Xiaorong
> 
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