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# RE: st: sampsi and percentages

 From "MacLennan, Graeme" <[email protected]> To "'[email protected]'" <[email protected]> Subject RE: st: sampsi and percentages Date Wed, 31 Aug 2011 09:14:45 +0100

```There is indeed, see:

Roula Tsonaka, Dimitris Rizopoulos and Emmanuel Lesaffre. Power and sample size calculations for discrete bounded outcome scores. Statist. Med. 2006; 25:4241-4252
DOI: 10.1002/sim.2679

Graeme.

-----Original Message-----
From: [email protected] [mailto:[email protected]] On Behalf Of Nick Cox
Sent: 31 August 2011 09:05
To: [email protected]
Subject: Re: st: sampsi and percentages

A beta distribution seems a natural candidate. There may well be published work on power for betas.

Nick

On Tue, Aug 30, 2011 at 8:08 PM, Nick Cox <[email protected]> wrote:
> Sure. I was partly in jest, but as a scientist I never feel
> constrained by the particular units in which data arrive, especially
> if they are not even metric units, let alone natural. Your example
> remains units-dependent in that numerator and denominator have quite
> different units. Not important unless this is also true of your real
> example.
>
> The best way forward for you is likely to be not looking for a canned
> approach but simulating datasets of different sizes under plausible
> generating processes and seeing what is or is not detectable.
>
> Nick
>
> On Tue, Aug 30, 2011 at 7:33 PM, Ricardo Ovaldia <[email protected]> wrote:
>>
>> Thank you Nick. I was specificaly talking about how lenght and weight are recorded in the auto data.
>>
>>  gen r= length / weight
>> . sum r
>>     Variable |       Obs        Mean    Std. Dev.       Min
>> Max
>> -------------+-------------------------------------------------------
>> -------------+-
>>            r |        74    .0647308    .0102566   .0475524
>> .0872222
>>
>> The ratio is less that one in all observations!
>> So the statement was not incorrect.
>>
>> Regarding your second point: Yes it behaves as a proportion but I cannot use a sample size calculation for proportion to power this study because there is not a true denominator.
>> Which brings me back to my original issue of how to power this study.
>>
>> Ricardo.
>>
>> Ricardo Ovaldia, MS
>> Statistician
>> Oklahoma City, OK
>>
>>
>> ----- Original Message -----
>> From: Nick Cox <[email protected]>
>> To: [email protected]
>> Cc:
>> Sent: Tuesday, August 30, 2011 10:02 AM
>> Subject: Re: st: sampsi and percentages
>>
>> Two points:
>>
>> 1. In terms of your example, length/weight is not always < 1. The
>> value of that ratio is crucially dependent on some choice of units of
>> measurement. Suppose I measure my (wife's) car's length in
>> centimetres and its weight (mass) in tonnes, for example.
>> You can call this pedantry but I react to incorrect statements!
>>
>> 2. More importantly, if something is bounded by (0,1) -- can we take
>> that pair of () literally as implying 0 < data < 1? -- then it will
>> behave like a proportion regardless of how the calculation was done.
>> For example, an average very near 0 can only be achieved if all
>> values are near 0 and so the variance will be very small, and
>> similarly for an average near 1. However, that may not help much.
>>
>> Nick
>>
>> On Tue, Aug 30, 2011 at 3:45 PM, Ricardo Ovaldia <[email protected]> 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.
>>>
>>> Ricardo
>>>
>>> Ricardo Ovaldia, MS
>>> Statistician
>>> Oklahoma City, OK
>>>
>>>
>>> ----- Original Message -----
>>> From: "Ariel Linden, DrPH" <[email protected]>
>>> To: [email protected]
>>> Cc:
>>> Sent: Tuesday, August 30, 2011 7:51 AM
>>> Subject: re: st: sampsi and percentages
>>>
>>> Ricardo,
>>>
>>> I may be mistaken here, but it seems you have two proportions (if
>>> it's bounded between 0,1 then you have a numerator and a denominator
>>> for each group).
>>>
>>> If that is truly the case, you can use sampsi for proportions:
>>>
>>> . sampsi 0.25 0.4
>>>
>>> Estimated sample size for two-sample comparison of proportions
>>>
>>> Test Ho: p1 = p2, where p1 is the proportion in population 1
>>>                     and p2 is the proportion in population 2
>>> Assumptions:
>>>
>>>         alpha =  0.0500  (two-sided)
>>>         power =  0.9000
>>>             p1 =  0.2500
>>>             p2 =  0.4000
>>>         n2/n1 =  1.00
>>>
>>> Estimated required sample sizes:
>>>
>>>             n1 =      216
>>>             n2 =      216
>>>
>>> I hope this helps
>>>
>>> Ariel
>>>
>>> Date: Mon, 29 Aug 2011 11:40:33 -0700 (PDT)
>>> From: Ricardo Ovaldia <[email protected]>
>>> Subject: st: sampsi and percentages
>>>
>>>
>>>
>>> I need to compute sample size and power for a study comparing two
>>> group on a measurement bounded by (0,1), (a measure of intensity).
>>> I was thinking about using -sampsi- to power on the difference of means.
>>> However, this seems strange to me, is there another way to power
>>> such comparison?
>>>
>

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