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

This is a trinomial, not a binomial. There is a formal and accurate
way to treat those data. I'll do that tomorrow morning and will post
the solution here. This turns into a graphic... a confidence
envelope. I'll post the appropriate numbers and will explain how to
draw the graphic since that's not feasible using this form of
communication. OMU

On Feb 6, 7:55 am, Bruce Weaver <bwea...@xxxxxxxxxxxx> wrote:
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
bwea...@xxxxxxxxxxxxxxxxxxxxxxxxxxxxx/wv/bwhomedir- Hide quoted text -

- Show quoted text -


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Relevant Pages

  • Re: Binomial dta: how to handle dont-cares?
    ... In case you're wondering, it was about a proposed sewer system in my town, where people currently have septic and density is low. ... In yes/no surveys, when you have don't-care responses, how are they best treated? ... squaring your z gives the test statistic for a chi-square goodness of fit test with 2 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). ...
    (sci.stat.edu)
  • Re: Significance testing of Dependent proportions
    ... wanted to do significance testing of Independent proportions ( ... >Are you asking how to partition the overall chi-square into orthogonal components? ...
    (sci.stat.consult)