Re: Changes in Two Proportions
RichUlrich
>Let's say the Group A sample starts at 10%, and the Group B sample
>starts at 15%. If each group improves by an absolute 5%, then they
>went to 15% and 20%, respectively.
This is the additive model, achieved by ANOVA.
>
>Or I could look at it on a relative basis, where Group A increased by
>a relative 50% and Group B by a relative 33%.
Relative Risk is a usually a bad basis of modeling, compared
to looking at Odds Ratios -- They will not differ much for
low fractions. But if you reverse your labels, your two changes
are "90% to 85%" and "85% to 80%". Those are not at all the same
in description as your first use of Relative Risk, but the Odds
Ratio approach is invariant to the direction.
You can get this explicitly with log-linear or logistic models.
>
>Or I could extrapolate to the overall populations and look at the
>simple numerical increases, except that Group A is much smaller than
>Group B.
>
>I can't quite figure out what is a truly fair pre-post comparison.
>
>I can't use simple population numbers, because the population sizes
>are too different.
>
>I can't use percentages, because the 100% upper bound constrains the
>population starting at the higher percentage. For example, a student
>who always scores 95% on a test is less able to improve than a student
>who scores 70% on a test.
>
>How to frame this for meaningful comparison?
The logistic approach is also competitive with the Probit
approach. Probits assume that the underlying distributions --
the generating system that leads to these results --
are Normal, instead of logistic. And there are other
possibilities. I remember a brief discussion of this sort
of issue in DJ Finney's book on Bioassay. The right test
is the one that reflects or preserves the generating
mechanism for the fractions.
In short, there is no analysis that is automatically right.
Usually, the choice does not matter for the tests that
are on hand, because they will all give the same results,
especially when the fractions are in the middle (say,
between 0.20 and 0.80). Especially for extremes, you
may need to argue that one Model is more appropriate
than the others, or else give the reader the choice of
analyses and interpretations.
One area that a modeling debate was active, when I took
health courses in the 1970s, was in the interpretation of the
effects of low levels of radiation. The arguments were both
medical and statistical, with practical applications for power
plants or for nuclear emergencies.
Are there the same Expected Deaths when you expose 100
people to 10 REM versus 10 people to 100 REM? More? Less?
(Further, is "deaths" the only outcome that matters?)
--
Rich Ulrich
Bruce Weaver
> Thanks,
>
> These are not matched pairs. This is data from two separate years of a
> large national survey.
>
> I have seen a substantial change for a particular measure. Now I'm
> teasing out which sub-populations changed the most.
>
> And looking for the clearest way to portray it in a table.
> Note: The author of this message requested that it not be
> archived. This message will be removed from Groups in
> 6 days (Jul 30, 12:16 am).
If I may be so bold, why do you ask that your posts not be archived by
Google Groups? Doing so can make it unnecessarily difficult for
someone to follow the thread in future.
--
Bruce Weaver
bwe...@lakeheadu.ca
www.angelfire.com/wv/bwhomedir
"When all else fails, RTFM."
RichUlrich
On Tue, 22 Jul 2008 21:16:08 -0700, ra...@home.NOT wrote:
>Thanks,
>
>These are not matched pairs. This is data from two separate years of a
>large national survey.
>
>I have seen a substantial change for a particular measure. Now I'm
>teasing out which sub-populations changed the most.
>
>And looking for the clearest way to portray it in a table.
>
I hope that is just a volunteering of extra information; I hope
that you do not mistake my advice as applying only to matched pairs.
So, if your fractions are all in the mid-range, .2 to .8, you can
settle for the simple, additive model. When some the fractions are
small, the multiplicative description is probably better. If some
fractions are high, then you do need to either use Odds Ratios
or consider the relative sizes of (1-P).
By the way, I see in my "header-view" that Bruce is listed as posting
from Google as his "institution". That may account for why he sees
the no-archive message that does not appear in the post as it came
to me.
--
Rich Ulrich
Bruce Weaver
> I don't know what Bruce is talking about, but I don't think anything I
> wrote here needs to be passed on to future generations.
>
> Roy - Carpe Noctem
It appears that Roy is posting via www.giganews.com, not Google. It
must have no archiving as the default setting. The irony is that if
someone quotes when responding, it'll most likely get archived
anyway. ;-)
RichUlrich
>On Wed, 23 Jul 2008 16:36:14 -0400, RichUlrich
><rich....@comcast.net> wrote:
>
>>[rayo, top-posting in response to my Reply ...]
>>
>>On Tue, 22 Jul 2008 21:16:08 -0700, ra...@home.NOT wrote:
>>
[snip]
>Rich,
>
>I woke up this morning and got it. So .. I instruct my SAS geek to do
>proc surveyfreq on two indepedent national surveys, with the variable
>of interest being, say, "did X in past year" and split by gender.
>
>I end up with 4 percentages, each with a variance. So I'm thinking the
>odd ratio entails a simple pooled variance calculation using all four
>variances and the combined sum of all the sample n's (unweighted).
>
>Does that seem right to you?
>
No, not at all. Odds ratios uses ODDS - not variances.
If the odds against Horse1 are 10 to 1, and the Odds against
Horse 2 are 5 to 1, the Odds, those two Odds are 10.0 and 5.0,
and the Odds ratio is 2.0. Or, in the opposite direction, the ratio
is 5/10 or .5 -- An Odds Ratio of 2.0 can be equivalent to 0.5, but
merely expressed in the opposite direction. With that tiiny warning,
the OR is robust against the choice of the direction (i.e., using P or
using (1-P)), as compared to the Relative Risk which is resembles for
small proportions.
Given a single Proportion for something being true, that P can be
stated as the Odds, Odds = P/(1-P). Then you compare to
Odds descriptively as an Odds Ratio, Odds1/Odds2. The Log
of the OR is what is frequently used in analyses.
If all your proportions are small, you might be happier dealing
with the Relative Risk for your comparisons.
[snip, some]
>
>In any case, you have been among the angels of the internet, and I am
>very grateful for what you do.
Thanks.
--
Rich Ulrich
Stan Devia
> Let's say the Group A sample starts at 10%, and the Group B sample
> starts at 15%. If each group improves by an absolute 5%, then they
> went to 15% and 20%, respectively.
>
> a relative 50% and Group B by a relative 33%.
>
> simple numerical increases, except that Group A is much smaller than
> Group B.
>
> I can't quite figure out what is a truly fair pre-post comparison.
>
> I can't use simple population numbers, because the population sizes
> are too different.
>
> I can't use percentages, because the 100% upper bound constrains the
> population starting at the higher percentage. For example, a student
> who always scores 95% on a test is less able to improve than a student
> who scores 70% on a test.
>
> How to frame this for meaningful comparison?
>
Are you able to standardize the rates (either using the direct or
indirect method)? This may allow for a fairer comparison between the
population groups
http://www.avon.nhs.uk/phnet/PHinfo/understanding.htm#Standardised