R help - Dec 2017 - delta and sd parameters for power.t.test

What is the rationale behind having both the delta and sd parameters for
the power.t.test function? For the relevant noncentrality parameter, we
only need the ratio delta/sd. If my effect size is given as Cohen's d,
then I only got that ratio and not sd.

As far as I see, in such a case, I can specify delta=d and leave sd at
its default value 1. Is this correct or am I missing something?

Thanks.
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> On Dec 14, 2017, at 2:26 PM, Lasse Kliemann <lasse at
lassekliemann.de> wrote:
> 
> What is the rationale behind having both the delta and sd parameters for
> the power.t.test function?
One is the standard deviation of the hypothesized data (or pooled sd in the case
of two sample) under the "alternative" and one is the mean of that
data (or equivalently the differences if this is a two-sample test).
> For the relevant noncentrality parameter, we
> only need the ratio delta/sd. If my effect size is given as Cohen's d,
> then I only got that ratio and not sd.
> 
If the data has been "standardized", then Cohen's d could be given
to the function as the value for delta since the sd default is 1.

> As far as I see, in such a case, I can specify delta=d and leave sd at
> its default value 1. Is this correct or am I missing something?
> 
Actually it sounds as though we are missing something. The power.t.test function
makes no mention of Cohen's d or effect size. Is this question in response
to a homework assignment about which we have not been informed?

Further questions should have some actual R code to make this an on-topic
discussion for Rhelp.

> Thanks.
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David Winsemius
Alameda, CA, USA

'Any technology distinguishable from magic is insufficiently advanced.' 
-Gehm's Corollary to Clarke's Third Law

Lasse Kliemann <lasse at lassekliemann.de> writes:
> What is the rationale behind having both the delta and sd parameters for
> the power.t.test function? For the relevant noncentrality parameter, we
> only need the ratio delta/sd. If my effect size is given as Cohen's d,
> then I only got that ratio and not sd.
>
> As far as I see, in such a case, I can specify delta=d and leave sd at
> its default value 1.
Looking at the code in src/library/stats/R/power.R has clarified this
for me. The only spots were a given value of sd is actually used is (1)
in the computation of the ncp, where we have sqrt(n/tsample) * delta/sd,
so only the ratio delta/sd counts; (2) when delta is to be computed,
then sd is used for the interval given to uniroot, namely sd * c(1e-7,
1e+7), which I guess is a heuristic to cover all the plausible
values. So, yes, Cohen's d can be passed as delta=d when sd=1 is
maintained. Maybe a comment on this in the documentation would be
helpful. (For example, the pwr package
https://CRAN.R-project.org/package=pwr already mentions Cohen's d, but
that package is non-standard and unfortunately not even contained in the
Debian repositories. So it can make sense to stick with the standard
power.t.test as far as possible.)
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