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

 From Diego Bellavia To statalist@hsphsun2.harvard.edu Subject Re: st: RE: Effect size and Power for the difference between means Date Fri, 17 Aug 2007 20:23:54 +0000 (GMT)

```Tom,

Thank you for the  clear and thorough explanation on effect size.
I agree with all you sayd and now I understand that my question was
a non sense.
But, I do not understand why ES is not useful for sample size
determination in power analysis ? As you pointed out, in its very basic
formulation, ES reports the number of SDs (d) the outcome variable is increased (o decreased) in the
treatment group compared to the control group.
Therefore, knowing ES  you have an immediate estimation of the impact the specific treatment
has in your study population, and being a ratio of

delta (m1 - m2) / pooled SD (outcome variable)

you take in account variability of the outcome variable a the same time.

All the commands I reviewed in STATA to compute sample size (given power)
or power (when sample size is already known) use the difference in the means (m1 - m2)
and standard deviation of the two groups (sampsi command) or directly the ES (fpower).

However you prefer to put the things, separating the difference of the means in the two groups
and the SD of the outcome variable or putting them together in a ratio (that is ES),
ES remains a critical measure to get sample size (or power) in a power analysis.

Thank you

Diego

----- Messaggio originale -----
Da: "Steichen, Thomas J." <SteichT@rjrt.com>
A: statalist@hsphsun2.harvard.edu
Inviato: Giovedě 16 agosto 2007, 17:32:53
Oggetto: st: RE: Effect size and Power for the difference between means

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,
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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