power.t.test formula

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Hi,

Does anyone of you knows a reference for the formula used in power.t.test
function? And also why it uses the Student's distribution instead of Normal.
(I know both of them can be used but don't see whether choose one or the
other)
It is  a straightforward first-principles calculation. The t
distribution calculation is exact for normally distributed data with the
same unknown variance in both groups. Formulas based on the normal
distribution assumes the variance to be known, which overestimates small n.
O__  ---- Peter Dalgaard             ?ster Farimagsgade 5, Entr.B
  c/ /'_ --- Dept. of Biostatistics     PO Box 2099, 1014 Cph. K
 (*) \(*) -- University of Copenhagen   Denmark      Ph:  (+45) 35327918
~~~~~~~~~~ - (p.dalgaard at biostat.ku.dk)              FAX: (+45) 35327907
Peter Dalgaard:
Does anyone of you knows a reference for the formula used in power.t.test
function? And also why it uses the Student's distribution instead of
Normal. (I know both of them can be used but don't see whether choose one
or the other)
It is  a straightforward first-principles calculation. The t
distribution calculation is exact for normally distributed data with the
same unknown variance in both groups.
I didn?t know about power.t.test. A very nice function, indeed. Is there a 
similar function that handles unequal number of observations for each 
group, and unequal variances?

The help file mislead me into thinking that power.t.test handles unequal 
number of observations, and for example  ?power.t.test(c(10,3),1)? *does* 
give some output (and not a warning or error), just not the output I was 
expecting.

(It gives two power values, one for sample of size 10 (for each group) and 
one for samples of size 3 (for each group), while I was expecting the power 
for a sample size 10 for one group and 3 for the other group).
Karl Ove Hufthammer
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Hello,
Thank you, but can you understand this result? first I calculate the sd
for n = 2 and then n with that sd. It should give me 2 right?

FC = 1.5
alfa = 0.01
power = 0.85
sd1 <-   power.t.test( n = 2, delta = FC, sig.level = alfa,
+                    power = power, type = "two.sample", sd = NULL)$sd
  n1 <- round( power.t.test( n = NULL, delta = FC, sig.level =
alfa,power = power, type = "two.sample", sd = sd1)$n)
Error in uniroot(function(n) eval(p.body) - power, c(2, 1e+07)) :
  f() values at end points not of opposite sign
The error message pretty much says it: uniroot is looking for a root
between 2 and 1e7 and complains that the root is not properly bracketed.
 If the root is supposed to be AT 2, then this easily happens due to
rounding issues. (This could have better error trapping, but you're
really not expected to be planning studies with such low n.)
O__  ---- Peter Dalgaard             ?ster Farimagsgade 5, Entr.B
  c/ /'_ --- Dept. of Biostatistics     PO Box 2099, 1014 Cph. K
 (*) \(*) -- University of Copenhagen   Denmark      Ph:  (+45) 35327918
~~~~~~~~~~ - (p.dalgaard at biostat.ku.dk)              FAX: (+45) 35327907
Look at the pwr package, it has functions for 2 samples of different sizes.

Hope this helps,
Gregory (Greg) L. Snow Ph.D.
Statistical Data Center
Intermountain Healthcare
greg.snow at imail.org
801.408.8111

> -----Original Message-----
> From: r-help-bounces at r-project.org [mailto:r-help-bounces at r-
> project.org] On Behalf Of Karl Ove Hufthammer
> Sent: Friday, April 24, 2009 2:41 AM
> To: r-help at stat.math.ethz.ch
> Subject: Re: [R] power.t.test formula
> 
> Peter Dalgaard:
> 
> >> Does anyone of you knows a reference for the formula used in
> power.t.test
> >> function? And also why it uses the Student's distribution instead of
> >> Normal. (I know both of them can be used but don't see whether
> choose one
> >> or the other)
> >
> > It is  a straightforward first-principles calculation. The t
> > distribution calculation is exact for normally distributed data with
> the
> > same unknown variance in both groups.
> 
> I didn?t know about power.t.test. A very nice function, indeed. Is
> there a
> similar function that handles unequal number of observations for each
> group, and unequal variances?
> 
> The help file mislead me into thinking that power.t.test handles
> unequal
> number of observations, and for example  ?power.t.test(c(10,3),1)?
> *does*
> give some output (and not a warning or error), just not the output I
> was
> expecting.
> 
> (It gives two power values, one for sample of size 10 (for each group)
> and
> one for samples of size 3 (for each group), while I was expecting the
> power
> for a sample size 10 for one group and 3 for the other group).
> 
> --
> Karl Ove Hufthammer
> 
> ______________________________________________
> R-help at r-project.org mailing list
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide http://www.R-project.org/posting-
> guide.html
> and provide commented, minimal, self-contained, reproducible code.
Greg Snow:
Look at the pwr package, it has functions for 2 samples of different
sizes.

Hope this helps,
Great! Thanks.
Karl Ove Hufthammer