Re: Binomial dta: how to handle don't-cares?
- From: Stan Brown <the_stan_brown@xxxxxxxxxxx>
- Date: Thu, 8 Feb 2007 07:08:48 -0500
Tue, 06 Feb 2007 23:41:48 -0500 from Richard Ulrich
<Rich.Ulrich@xxxxxxxxxxx>:
On Mon, 5 Feb 2007 16:52:33 -0500, Stan Brown
<the_stan_brown@xxxxxxxxxxx> wrote:
Survey taken: 1366 mailed out (proposed sewer system)
Responses received: 380
119 "yes"
29 neutral
232 "no"
On a null hypothesis of "opinion is evenly divided" I get a tiny p-
value no matter whether I count "yes" as 119 out of 380 or 119 out of
380-29 = 351. But I wonder what is the right thing to do. In yes/no
surveys, when you have don't-care responses, how are they best
treated?
Okay, there is a preference for No, regardless of what
you do with "neutral." The presentation is more a matter
of politics and of sense, than of statistics.
Who has been campaigning how strongly, for what?
There hasn't been much of a campaign. The town board has been
debating this off and on since before I bought my house last summer.
I think developers probably want it so they can build with higher
density; much of the town is rural and the rest is low-density
suburban. We're 10-20 minutes outside of Ithaca.
- Is this a 'random' sample, or was there any chance that
one side is using the survey as a tool?
There's a chance, but AFAIK a copy was sent to every homeowner in the
proposed district. Reading my copy, I couldn't tell whether the town
supervisor, who prepared it, was hoping for yeses or noes.
It was a one-page summary, including state grant figures and cost
figures, with the survey at the bottom to be mailed in. (No stamp was
provided, making the response rate even more amazing.)
Was this question the whole content of the survey?
Yes,
"My opinion:
"___ I support the proposal
"___ I am neutral toward the proposal
"___ I oppose the proposal."
Definitely, state the full results - all three categories.
Right. I guess I should have made it clear, I have no connection with
this other than as a homeowner who stands to see a $100-a-month rise
in my tax bill *and* the privilege of making expensive connections
and then paying additional user fees.
The ethics of survey-reporting says that you must be explicit
about the context, the content, the questions, etc.
I agree with you that of course the full numbers should be prevented;
my question was about proper drawing of conclusions.
It seems obvious that opinion is quite strongly "no", but I'm looking
at how to frame a proper hypothesis test and p-value.
Alternatively, maybe I should make it a 95% confidence interval. Do I
calculate a binomial CI from a sample size of 380-29, excluding the
neutrals as though they had not responded? Or does the three-way
nature of the question mean that I can't analyze it in a binomial
manner and have to do some sort of Chi-squared?
--
Stan Brown, Oak Road Systems, Tompkins County, New York, USA
http://OakRoadSystems.com/
.
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