Re: Comparing empirical frequency distributions

On 26 Aug 2008 23:11:57 GMT, Niklaus Kuehnis
<kuehnik_0505@xxxxxxxxxxxxxx> wrote:

Thanks, Rich, for your reply.

RichUlrich <rich.ulrich@xxxxxxxxxxx> wrote:
On 26 Aug 2008 10:10:58 GMT, Niklaus Kuehnis
<kuehnik_0505@xxxxxxxxxxxxxx> wrote:

Question 1:
Is there any reasonable way to compare the frequency distributions of
prod1 vs. prod2 regarding all adjectives in a single test?

Q1.
The conventional way would be to score up the polarized adjectives
as a composite, Good vs. Bad, and do a t-test.

I can't do that because I don't have any a-priori knowledge about the
goodness/badness of adjectives. There are also more neutral
adjectives among them.

Your examples were Tasty, Affordable, and Healthy ...
where there is not much question. It seems almost obvious
that Better vs. Worse is the question that has the most
interest to an audience of potential customer-consumers.

For that, you would ignore the neutral ones for the time being.


After that, you could do a Principal Factor Analysis, with varimax
rotation, and identify two or three "factors".

How? After summing up I would have one variable per subject.

Pardon my misleading segue. "After that interesting analysis, or
instead of it, you could start with your 30 items (and do a PF
analysis)." If half the items are good/bad, then Good/Bad, using
the obvious items, will probably be what emerges as the most
interesting component.


Question 2:
I thought of comparing the distributions of prod1 and prod2 using a
chisquare goodness-of-fit test. This test is usually referred to as a
test to compare an empirical to a theoretical distribution. Can I use
it to compare two empirical distributions?

You can compare a single adjective in a 2x2 table, with a
chisquare contingency-table test.

I believe a binomial test would be the best choice.

A binomial test is used to compare to a fixed proportion,
most often, 1/2. There are several ways to describe and compute
the difference between two proportions, including Ray's.

For "sales" applications, it would be enough to simply present
the set of results, using their nominal significance as single tests.
That's also enough, if every single adjective shows a difference.
If this is a study in psychological research, the fact of multiple
testing should be taken into account.

With an N of 200, the "power" of conducting Bonferroni
correction will be small, partly because it is hard to achieve
a really tiny p-value in a 2x2 test with N=200. Conducting an
overall test from the separate chisquared values would be
more powerful, especially if there are actual differences on
most of the adjectives. But combining 30 tests will still be
*far* inferior to conducting a set of 3 or 4 tests based on
components -- both in power, and (IMO) in intelligibility.

--
Rich Ulrich
.

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