Re: Binomial dta: how to handle don't-cares?

Tue, 06 Feb 2007 07:55:31 -0500 from Bruce Weaver
<bweaver@xxxxxxxxxxxx>:
On Mon, 5 Feb 2007 16:52:33 -0500, Stan Brown
Survey taken: 1366 mailed out (proposed sewer system)
Responses received: 380
119 "yes"
29 neutral
232 "no"

If you used the usual z-test for comparing two independent proportions,

I'm sorry, I don't understand. Which two independent proportions do I
have here? Unless I'm missing something, the yeses, noes, and
neutrals are mutually dependent.

squaring your z gives the test statistic for a chi-square goodness of
fit test with 2 categories. And of course, chi-square GOF tests can
have more than two categories (df = # of categories minus 1). But I
seriously doubt you are interested in testing the null hypothesis that
Yes, No, and Neutral are all equally likely in the population.

And you are right to doubt that! :-)

I should make it clear that I had no part in the planning of this
survey. I'm a homeowner in the proposed district, and I filled out an
mailed in my survey, but have no other association. I'm trying to
interpret the results that were published.

(I can't imagine why anyone, let alone 29 persons, would take the
trouble to address and stamp an envelope to mail in a survey saying
"I don't care," but they did.)

The practical question is whether the sewer should be built, and that
in turn should depend on whether a majority are in favor. Ideally,
I'd like to show that there's no need to waste more town resources on
further planning, since it's virtually certain a majority of the town
is opposed. Can I do that, from the available data?

I suppose one null could be "p >= .5, 50% or more are in favor."

Using that null, I could compute p' three different ways:

** 119/(380-29), counting neutrals as non-respondents
** 119/380, counting neutrals as "no"
** (119+29)/380, counting neutrals as "yes"

The second and third seem clearly wrong to me, and I really wonder
about even the first.

The percentages are pretty compelling: 31% in favor, 8% neutral, 61%
opposed, n = 380. But surely there's something useful I can say about
the feelings of the population?

--
Stan Brown, Oak Road Systems, Tompkins County, New York, USA
http://OakRoadSystems.com/
.

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