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?

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...@lakeheadu.cawww.angelfire.com/wv/bwhomedir- Hide quoted text -

- Show quoted text -

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?

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?

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,

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.

On Mon, 5 Feb 2007 16:52:33 -0500, Stan Brown
the_stan_brown@fastmail.fm> 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?

- Is this a 'random' sample, or was there any chance that
one side is using the survey as a tool?

Was this question the whole content of the survey?

Definitely, state the full results - all three categories.

The ethics of survey-reporting says that you must be explicit
about the context, the content, the questions, etc.

Tue, 06 Feb 2007 23:41:48 -0500 from Richard Ulrich
Rich.Ulr...@comcast.net>:





On Mon, 5 Feb 2007 16:52:33 -0500, Stan Brown
the_stan_br...@fastmail.fm> 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/- Hide quoted text -

- Show quoted text -

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?

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?

Regardless of what your null hypothesis is - focus on your research
question. What are you trying to find out, in plain language. That
will dictate how you handle your data. You could compare proportions
or do other tests but as was previously stated, a simple listing of
percentages may be all you need.

Although your response rate was decent as far as surveys go, it was
still substantially below 50%. You must factor in the possibility
that those were opposed were more likely to respond than those who did
not.

On 7 Feb, 07:14, "mcap" <mca...@hotmail.com> wrote:

Although your response rate was decent as far as surveys go, it was
still substantially below 50%. You must factor in the possibility
that those were opposed were more likely to respond than those who did
not.

Why? This would only be true if it could be established that the
survey originated from the "Yes" camp. If the reverse were true, then
those desiring the scheme would feel greater necessity to reply.

On 14 Feb, 16:21, "illywhacker" <illywac...@gmail.com> wrote:


On Feb 10, 11:50 am, "John M." <john_howard_mor...@hotmail.co.uk
wrote:
If the goal is to infer
frequencies of opinions in the population from a self-selecting sample
such as this survey generates, then one has to model the influence
that opinion has on probability to respond, even if the model chosen
is that it has no influence.

I think I see your point here. The desired model would have to be
created by surveying responsiveness conditional on the level of
opinion, wouldn't it?

Being an amateur in Ststs, I wouln't propose anything. I'd leave it to
a pro.

Several people have given good advice including "the numbers are what
they are and should be reported as such". This is politics more than

8 Feb 2007 09:09:28 -0800 from Old Mac User
chendrixst...@yahoo.com>:

Can someone suggest good search terms, or a good print reference, on
analyzing yes/no/don't-care responses? I tried "trinomial", but as
you might expect I was overwhelmed with the polynomial type.

Can someone suggest good search terms, or a good print reference, on
analyzing yes/no/don't-care responses? I tried "trinomial", but as
you might expect I was overwhelmed with the polynomial type.