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# Re: st: sampsi and percentages

 From Ricardo Ovaldia To "statalist@hsphsun2.harvard.edu" Subject Re: st: sampsi and percentages Date Tue, 30 Aug 2011 11:39:24 -0700 (PDT)

```Thank you Ronan. My original question was whether it makes sense to compute power and sample size using means in a study similar to the example I gave with the auto data.
You are correct that  ratio can be greater than 1, while a proportion cannot. However in my case the ratio will always be between 0 and 1.

I am wondering wheter powering on the difference of means in such comparisons makes sense.

Ricardo

Ricardo Ovaldia, MS
Statistician
Oklahoma City, OK

----- Original Message -----
From: Ronan Conroy <rconroy@rcsi.ie>
To: "statalist@hsphsun2.harvard.edu" <statalist@hsphsun2.harvard.edu>
Cc:
Sent: Tuesday, August 30, 2011 10:10 AM
Subject: Re: st: sampsi and percentages

On 2011 Lún 30, at 15:45, Ricardo Ovaldia wrote:

>
> Thank you, but these are not proportions. They are intensity measures. You can think of them as ratios of two continous things.
> For example with the auto data, they could be the ratio of car's length  to weight (length / weight) which is always between 0 and 1.
>

> Now less say that you want to compare these ratio between between foreign and domestic cars.
>

I am a little confused. A ratio can be greater than 1, while a proportion cannot.

In your example, however, you are asking if the difference in weight between foreign and domestic cars is explained by the difference in length between them.

. regress weight length foreign

Source |      SS      df      MS              Number of obs =      74
-------------+------------------------------          F(  2,    71) =  316.54
Model |  39647744.7    2  19823872.3          Prob > F      =  0.0000
Residual |  4446433.7    71  62625.8268          R-squared    =  0.8992
Total |  44094178.4    73  604029.841          Root MSE      =  250.25

------------------------------------------------------------------------------
weight |      Coef.  Std. Err.      t    P>|t|    [95% Conf. Interval]
-------------+----------------------------------------------------------------
length |  31.44455  1.601234    19.64  0.000    28.25178    34.63732
foreign |  -133.6775  77.47615    -1.73  0.089    -288.1605    20.80555
_cons |  -2850.25  315.9691    -9.02  0.000    -3480.274  -2220.225
------------------------------------------------------------------------------

Length is a significant determinant of weight, and adjusted for this there is no significant difference between domestic and foreign cars (the effect size is interesting, but the standard error is very large).

Is this analogous to what you had in mind?

Ronán Conroy
rconroy@rcsi.ie
Associate Professor
Division of Population Health Sciences
Royal College of Surgeons in Ireland
Beaux Lane House
Dublin 2

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