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RE: st: RE: Effect size and Power for the difference between means


From   "Steichen, Thomas J." <SteichT@rjrt.com>
To   <statalist@hsphsun2.harvard.edu>
Subject   RE: st: RE: Effect size and Power for the difference between means
Date   Fri, 17 Aug 2007 13:02:34 -0400

Austin,

Yes a typo, I agree... (or maybe just slapping language down 
before thinking it through fully... it could happen).

And I agree the point is to generate invariant-to-scale measures, 
but I'll add: particularly so they may be combined with or 
compared to effect sizes of related studies.

Thanks,
Tom

-----------------------------------
Thomas J. Steichen
steicht@rjrt.com
-----------------------------------
 
-----Original Message-----
From: owner-statalist@hsphsun2.harvard.edu [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of Austin Nichols
Sent: Friday, August 17, 2007 11:53 AM
To: statalist@hsphsun2.harvard.edu
Subject: Re: st: RE: Effect size and Power for the difference between means

Thomas--
I think there is a typo in your message that might lead the poster
astray. You state that "d is then read to indicate that the means of
age1 and age2 differ by d standard deviations" but in the second
paragraph you state that "an effect size is a mean difference divided
by the standard error of that difference" but I think you mean to say
"an effect size is a difference in means divided by a relevant
standard deviation (sometimes the pooled sd of both populations, or
sometimes just one, as in the case where a post-intervention
population's sd is used to define the effect size of the
intervention)."  Note that using estimates of the sd complicates the
formulas somewhat, and that effect sizes may also be measured in other
scales, e.g. log odds.  The point is to compute measures that are
invariant with respect to the scale of measurement in some particular
study, right?  Please correct me if I am wrong...

The original poster does not seem to be setting his comparisons up right:
 sizefx groups age
should instead be
 gen age1=age if groups==1
 gen age2=age if groups==2
 sizefx age1 age2
or somesuch.

On 8/16/07, Steichen, Thomas J. <SteichT@rjrt.com> wrote:
> Diego,
>
> My impression, given what you say in your message, is that you may have a
> misunderstanding of what -sizefx- is intended to compute.
>
> Generally, an effect size is a mean difference divided by the standard error
> of that difference (or, alternatively, is the correlation of two variables
> divided by the standard error of that correlation). This has nothing to do
> with computing sample size, power, etc.
>
> -sizefx age1 age2- merely computes the mean, variance and sample size for
> each variable (age1, age2) then computes the various effect sizes.
>
> For example, Cohen's d is computed as:
>
>  d = abs(m1-m2) / sqrt(((n1*v1)+(n2*v2))/(n1+n2))
>
>  where m1 is the mean, n1 is the sample size and v1 is the variance of age1
>    and m2 is the mean, n2 is the sample size and v2 is the variance of age2
>
> d is then read to indicate that the means of age1 and age2 differ by d
> standard deviations.
>
> Clearly, you do not calculate the variables age1 or age2, you just use them
> in the program.
>
> It is probably fair to note that the typical use of effect sizes is when
> t-values, correlations or the sufficient statistics are all you have (i.e.,
> you do not have raw data). Then you just directly plug in what you have into
> an appropriate formula and spit out the effect size. Because of this, I do
> not see -sizefx- as a particularly useful program.
>
> Tom
>
> -----------------------------------
> Thomas J. Steichen
> steicht@rjrt.com
> -----------------------------------
>
> -----Original Message-----
> From: owner-statalist@hsphsun2.harvard.edu [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of Diego Bellavia
> Sent: Wednesday, August 15, 2007 10:47 AM
> To: STATAlist
> Subject: st: Effect size and Power for the difference between means
>
> Dear Statalisters,
>
> I am sorry for the basic questions, but I have a problem trying to figure out
> how the sizefx command works in STATA 9.2.
>
> 1) Let us say I have two groups  and some outcome variables for which I would
> like to calculate the ES.
> Looking at the help file of sizefx, examples are like
>
> sizefx age1 age2
> sizefx before after (matched design)
>
> The problem is that I do not know how to calculate age1 and age2 (I know this is very very basic,
> please mercy on me).
> Then I tryed something like
>
> sizefx groups age
>
> to see the ES of age in the different groups, and I got something like
>
> Effect Size Measures: Cohen's d and Hedges' g
> -----------------------------------------------------
> Cohen's d statistic (pooled variance) = 2.2798227
> Cohen's d statistic (t-statistic method) = 2.2847456
> Hedges' g statistic = 2.2847456
>
> Effect size correlations: r
> -----------------------------------------------------
> ES correlation (Cohen's d method) r = .75173368
> ES correlation (t-statistic method) r = .75214284
> ES correlation (Hedges' g method) r = .75214284
>
> No problems with the r but regarding the Cohen's d and the Hedge's g 2.27 and 2.28 values
> become 0.227 and 0.228 respectively ?
>
> Another weird thing is that sometimes I have higher ES for variables that are not significantly
> different between the two groups...how is it possibile ?
>
>
> 2) Regarding the sample size calculations for differences between means what command do you reccomend ?
>   I found "sampsi" (t-test) then "fpower" and "simpower" (for ANOVA). Is this a  complete list or do you use something else ?
>    Are there improvements in STATA 10 regarding this ?
>
>
> Thank you in advance for the help
>
> Diego
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