# [R] Power Analysis

David Cross d.cross at tcu.edu
Tue Apr 19 00:23:05 CEST 2011

```It seems to me, with deltas this large (relative to the SD), that a significance test is a moot point!

David Cross
d.cross at tcu.edu
www.davidcross.us

On Apr 18, 2011, at 5:14 PM, Albyn Jones wrote:

> First, note that you are doing two separate power calculations,
> one with n=2 and sd = 1.19, the other with n=3 and sd = 4.35.
> I will assume this was on purpose.  Now...
>
>> power.t.test(n = 2, delta = 13.5, sd = 1.19, sig.level = 0.05)
>
>     Two-sample t test power calculation
>
>              n = 2
>          delta = 13.5
>             sd = 1.19
>      sig.level = 0.05
>          power = 0.9982097
>    alternative = two.sided
>
> Now, with n=2, the power is already .99.  With n=1, there are zero df.
> So, what n corresponds to a power of .8?
>
>> power.t.test(n = 1.6305, delta = 13.5, sd = 1.19, sig.level = 0.05)
>
>     Two-sample t test power calculation
>
>              n = 1.6305
>          delta = 13.5
>             sd = 1.19
>      sig.level = 0.05
>          power = 0.8003734
>    alternative = two.sided
>
> It looks like 1.63 subjects will do the job :-)
>
> Finally, look at the power.t.test function, there is a line that explains
>
> else if (is.null(n))
>        n <- uniroot(function(n) eval(p.body) - power, c(2, 1e+07))\$root
>
> power.t.test() is making the sensible assumption that we only care about
> sample sizes of at least n = 2....
>
> albyn
>
> On Mon, Apr 18, 2011 at 02:31:19PM -0700, Schatzi wrote:
>> I am trying to do a power analysis to get the number of replicas per
>> treatment.
>>
>> If I try to get the power it works just fine:
>> setn=c(2,3)
>> sdx=c(1.19,4.35)
>> power.t.test(n = setn, delta = 13.5, sd = sdx, sig.level = 0.05,power =
>> NULL)
>>
>> If I go the other way to obtain the "n" I have problems.
>> sdx=c(1.19,4.35)
>> pow=c(.8,.8)
>> power.t.test(n = NULL, delta = 13.5, sd = sdx, sig.level = 0.05, power =
>> 0.8)
>>
>> Is there any way to do this? Thank you.
>>
>> --
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>>
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>> and provide commented, minimal, self-contained, reproducible code.
>>
>
> --
> Albyn Jones
> Reed College
> jones at reed.edu
>
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