Any statisticians, methodologists out there?

Let's say I elicit some data. I ask people: "List, in order of importance, the top 5 characteristics that you associate with the "ideal mother". Half of these people are English speaking Hispanics and the other half are Spanish speaking recent immigrants.

Could I run a correlation on the ranked data between the groups of respondents and then use the correlation values as datapoints for MDS where the distance between points represents the similarity or dissimilarity between respondents? Would this illustrate concensus if I see Spanishn and English speakers in the same cluster with one of the words/concepts?

I talked to a consensus analysis specialist today, and he said I needed data that I could lay out on a number line. Would ranked data do? The ranks would mean 1= "a characteristic most like the ideal mom" and range to 10="least". It is a relative scale, just to see the differences between groups of respondents.

Of course I couldn't decide which concept = #1 until I saw what was the top concept ranked #1 most often by the respndents (degree of concensus?). That's simple counting. But it's the difference between the groups I'm interested. That's simple contingency tables. What the client wants is a graphical representation of points on a graph that shows how the Spanish speaking versus English speaking rank the attributes of an ideal mother. (or other concept, this is just an example).

Ideas?

You know, now that I think about it, this client is trying to substitute their interpretive frame for analysis-- and that's why they want to set it up within a matrix of "archetypes" in a quadrant space. Must talk them out of this.

Q: Why use a statistical elephant gun (MDS) when a simple contingency table will do?

A: Because the non-statistical client wants to see a pretty picture.

I'm going to babble about this until I figure it out...

Could I come up with a formula that pulls the less acculturated to the left side of a quadrant grid, and the more acculturated to the right side of the grid, and then a y axis with the consensus of "ideal mother" at the top and descending into less important attributes of motherhood.
The scales don't have to be numerical, just rank ordered, postioning respondents relative to each other.

That would position respondents in a pretty picture for the client.

Now have to think about how they can compare their positioning statements to this (frankly stupid) "mother archetype" scale.

Idea: Ask the respondents to list the top five things that come to mind for each statement and see if they can be coded into mother attributes? Or other attributes? So what are the opposite of mother attributes, in the bottom quadrants? Anything mentioned that is outside of the category?

9 out of 10 dentists still call him Arnold Swastikanegger.

Can you represent that in a quadrant space plz?

Through writing all this crap out, I have come to realize I need to empahsize that I am looking for a way to show patterns in quali data along 2 dimensions, not looking for statistical tests, significance etc.

This babbling has been impt. Can I sleep now?

jesus, I thought all the stats I've been forced to take would make me some kind of expert but I don't know what you're talking about (also i durnk.

it'a all non-parametric stuff, using categorical or ranked data, kind of rare outside of anthropology and cognitive science. i'm trying to apply the principles to a market research/advertising problem

the cheap tautological way to do this it seems from an amateurish pt of view (hey give the client what they want) is to compute the average list for each group, then map each response on their degree of similarity to the average list, with 100% to each list being opposing dimensions in twospace. you could translate this to quadspace representations too -- but it'll be just as flawed.

if you had the data the way the dude advised you with "forced choice" you could probably do at least slightly better, but still eh.

you could also use a self organizing network and throw all respondents into a big pile and let them sort themselves out then color then black & white or whatever and let there be visual patterns of association apparent. that's actually probably as honest a visual picture as you'll get.

alternately, if you weren't doing 1st vs. 2nd gen, but a more complex thing, you could make one axis length of time in country and the other axis closeness of fit to a single ideal set and look for convergence/divergence. that would actually be informative, too!

The basic idea of MDS--multiudimensional scaling, is that you run a correlation on respondent's rankings or categorical responses. The respondents who ranked an item similarly are then depicted as datapoints that are close together. Respondents who ranked oppositely will be far away from each other on the graph, which looks like a scatterplot. There is not an x and y scale, it is only a representation of the distance between people's shared rankings (that's why it's sometimes called consensus analysis). In theory, you can see if non-English speakers think similarly about something than English speakers, for example, very quicky--do they cluster together.

That said, I like your last idea. I was toying with the "ideal" idea. I would need the respondents to tell me what the ideal is, though, I can't assume it, and ideal might vary by acculturation. How would you look for convergence/divergence exactly with this kind of data?

I'm grappling with how to apply this to a particular problem and I figure if I babble long enough I'll figure it out.

Sterling I think you're onto something. One of the things they are doing is trying to test a positioning statement. They should be able to give me a list of "ideal" associations to compare the responses to.

I've got 4 acculturation categories that range from unacculturated to partially acculturated. I can collapse that into two categories if I need to. Hmmmmm

Sterling, you're right, they are getting a scatterplot at first, like it or not. It's the only way to see the patterns in the data. Acculturated respondents can be squares and unacculturated can be circles or whatever. That will give them an idea of how these groups see the ideal mother.

Then, with the positioning statements I could have the respondents list the first five things that come to mind when they hear the positioning statement, (a natural ranking) and compare that to the ideal derived from the first data set.