Sorry to have taken so long to send a summary to the list......here's my
original query followed by the responses received, which were quite varied
ranging from very simple to more complicated solutions! Thanks to all
those who responded.
Original query:
Hi,
I'm not sure if the answer to this is obvious and I just can't see it but
I'd appreciate some opinions on the best way to approach the following
data....
There are two products, A and B, one panel of subjects receives A and a
second panel receives B. The data is a kind of preference data where each
subject is offered a number of pieces of the product and the number they
accept is the measure recorded.
The complicating factor is that each individual is offered a different
number of pieces (ranging from 1 to 10) depending on who carried out the
test (this wasn't an intentional part of the design but it's market
research data and the instructions weren't followed correctly by
everyone!). The data can't be treated as proportions as if only 5 pieces
were offered the possibilities for proportion accepted is limited. It
feels like there should be a very simple way to do this but I just can't
see it!
Any suggestions or pointers would be much appreciated!
Responses as follows......
Rather than proportions, it seems more appropriate to model the frequency
as
the DV using a Poisson distribution. In that case you could include an
offset to account for the different number of opportunities to respond.
Paul R. Swank, Ph.D.
Professor, Developmental Pediatrics
Medical School
UT Health Science Center at Houston
---------------------------
Joy,
The following table may summarise the data well.
Group Number accepted Number offered Proportion accepted
A 3 9 0.333
. And so on
.
B
.
.
Now we can simply do a two sample t-test to assess for a difference
between
the two groups if the data are normally distributed or a Mann-Whitney U
test
if otherwise.
Best wishes
Ian
---------------------------------
Hi! Me again!
Knowing your background, I'd first ask, are these "subjects" humans
or animals? If the latter, then the number of pieces accepted should
probably be regarded as censored at the maximum number offered. If
adult humans in a sophisticated society, then it is likely that many
of them won't want to be seen to take all that is offered. But the
actual number taken still seems more relevant than the proportion, so
I'd still analyse assuming censoring at the maximum. (Young
children, dements etc. may behave like animals - anorexics may not
respond at all!) I would in any case check that the distribution of
number of pieces offered was similar for both products - if it is,
that is mildly reassuring, but if not, it's rather unreassuring.
Also - a rather obvious point - are all the pieces of (more or less)
constant size, both by appearance and by satiety produced, both
within and more importantly between the two product groups? If
product A comes in bigger hunks than B, it may be better to analyse
number of hunks taken multiplied by some measure of typical hunk
size.
Hope this helps.
Robert G. Newcombe, PhD, CStat, Hon MFPHM
-------------------------
Dear Joy,
as far as I understand you want to estimate the proportion p(A) or p(B)
that product A or B is accepted, respectively. This could be
done is as follows: Person i may have been offered product X (A,B) n_i(X)
times, and may have accepted f_i(X) times. Then the proportion
p(X) that product X is accepted can be estimated from
p(X) = sum(i) f_i(X) / sum(i) n_i(X).
Is that what you wanted to know?
Yours sicerely,
Volker
-------------------------
I suspect you'll get more sophisticated answers than this one! But here
goes.....
Rather than modelling the proportion of pieces accepted by any person
given
the product, you could model the probability of each individual piece
being
accepted given the product incorporating the person as a random effect.
That presupposes various things, in particular that all the pieces for a
given product have an identical prob of being accepted which may be close
to
the truth or may be complete nonsense! You could allow for that by
factoring
in which piece of the product is being threatened with rejection, if you
have that level of information.
Whenever I attempt to answer a question I always seem to misunderstand the
question! Apologies if I've done so again.
Neil Walker
Westminster PCT
------------------------------
I assume that the "product" is a food (biscuit, sweet...)
& the "pieces" are the number of biscuits or sweets, bits of fruit etc.
offered or accepted. In other words, they are essentially similar.
You may be able to treat it as binomial, with a varying exposure (n),
the number of pieces offered. A GLM-type model will handle this.
There may be some saturation effect (most people accept 1 or
2 sweets, however many are offered; no-one can eat 10).
You can look for this by adding n as a predictor, as well as a parameter.
------------------------------------------
How about a logistic regression model with terms for product and n=the
number of pieces offered.
You should probably use an over-dispersed model, and test for
interactions.
Best wishes
Tim Auton
---------------------------
Joy
Why can't you analyse these as treat the data as proportions? This is
precisely what they seem to be! I would expect to analyse the results with
logistic regression -- though this is not the common type of logistic
regression used for binary data, but the type appropriate for grouped
observations which uses the binomial distribution with n=1 up to 10
according to how many pieces of product were ofered to an individual.
Peter Lane
Research Statistics Unit, GlaxoSmithKline
--------------------------------
Joy
I think the way to do this would be to model the number accepted against
the number offered (maybe a power, using Poisson regression) and then
ask if there was a significant difference between the groups (or if
separating the groups gave a significantly better fit)
Try it and see.
Phil
--------------------------------
Thanks again for all your help,
JOY
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