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

Stan Brown wrote:
Greetings. I'm embarrassed to ask this, but I'm more embarrassed at not knowing the answer:

Survey taken: 1366 mailed out

Responses received: 380
119 "yes"
29 neutral
232 "no"

In case you're wondering, it was about a proposed sewer system in my town, where people currently have septic and density is low. The estimated cost is about $150 a month per household in taxes, plus monthly sewer fees, plus $3-5K to connect. No wonder the people are opposed, and no wonder the response rate was so high.

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?

If you used the usual z-test for comparing two independent proportions, 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. Nor is it clear to me how you'd come up with a null hypothesis that specifies different proportions for the 3 categories. So a simple comparison of Yes and No may well be the appropriate thing to do here (plus reporting the number & percentage of Neutrals).

If you were looking for associations between Yes/No/Neutral and some other categorical variable (with chi-square test of association), then it would be a different story. Assuming the expected counts were high enough, you could include the Neutral category; and you could decompose the overall chi-square into orthogonal components to address more specific questions.

--
Bruce Weaver
bweaver@xxxxxxxxxxxx
www.angelfire.com/wv/bwhomedir
.

Relevant Pages

  • Re: Binomial dta: how to handle dont-cares?
    ... If you used the usual z-test for comparing two independent proportions, ... And of course, chi-square GOF tests can ... the number & percentage of Neutrals). ... If you were looking for associations between Yes/No/Neutral and some ...
    (sci.stat.edu)
  • Re: Binomial dta: how to handle dont-cares?
    ... On a null hypothesis of "opinion is evenly divided" I get a tiny p- ... surveys, when you have don't-care responses, how are they best ... with the survey at the bottom to be mailed in. ... neutrals as though they had not responded? ...
    (sci.stat.edu)
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