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I have some questions about how to analyze ranked data.

The data looks like this: 4 groups of people with HIV and 16 other groups of people living in the same village were asked to rank 12 challenges for people with HIV according to importance. (f.e. physical health - social acceptance - mental health - ...) How can I know if a certain challenge is perceived differently by people with HIV than by other people?

Another question: All respondents (120) were asked to pick individually from the list of challenges the 5 that were most challenging to themselves. How can I know if people with HIV choose different challenges than other people?

What is the best way to present the findings? Are there any statistical test for it? Kruskal wallis is possible? I've been looking all over the internet but i'm stuck..

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    $\begingroup$ You wish to compare how each of the problems were ranked in terms of difficulty? You realize the main limitation is: if the first group perceives everything as much, much more difficult than the second but the ranking is the same... then you don't have any findings. $\endgroup$
    – AdamO
    Jul 15 '16 at 20:16
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For your second task, you could consider ordination methods, so that you are plotting the location of individuals within a multivariate 'challenge-space'. Distinct clusters for those with and without HIV would seem to support your hypothesis.

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For your first question, convert your choices into numerical data(in order) for each group and then take the absolute difference between each choice from each person in each group. The ones that have the biggest difference could possibly be considered the ones that each group perceives the most different.

Let's say you have two people and each one belongs to a group A and B respectively. Each person has a rank for 12 items, 1-12. For item 1: A chose 1 and B chose 7. If the rest of the items are constant or very close to zero, groups A and B perceived item 1 different since that item has the biggest difference.

You also need to make a judgement call on whether that makes sense. Maybe come up with a subset of ranks that you are certain, each group would think differently about, and do the difference thing and see if it fits your subset.

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Define importance score to be the ranks, it takes value 1 to 12, with 1 being least important and 12 being most important

Pick a factor of interest, for example, health, then collect importance scores from group 1 and group 2, for example:

score_health_1 <- c(1,2,3,2,4,1,2,4,3,1,2,2,3,1)

score_health_2 <- c(3,4,5,5,6,1,2,4,6,5,3,3,2,8,7,4)

Then you can do a wilcox.test(score_health_1, score_health_2) or a t-test. You can do this for each of the 12 factors individually.

If you are interested in multivariate test, for example, heath and social, Then you can use Hottelling t^2 test, which accounts for correlation in multivariate test.

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