## Need help with CHI square tests based on likert responses

Hi peeps, thanks for making such a helpful site - I'm hoping you can help me with my honors year thesis and teach me a thing or two on the way

Without bogging down in details or confusing the issue, I'm basically comparing participants and their friends. A simplification of the study is to say that there are three items which the participants rate on a 7 point likert scale, and they also rate the items for their friends. The purpose of this is to see if participants and their friends share similar interests, or at least see how much participants believe their friends share similar interests.

i.e "I like apples!" - rate 1-7 where 1 means strongly disagree, and 7 means strongly agree. Do this for yourself (how much agree you like apples) and for three friends (how much they each like apples).

Then the same sort of question is asked for bananas, and cherries so, the results for each participant should look something like this:

Apples - Participant (7), Friend 1 (7), Friend 2 (3), Friend 3 (5)
Bananas - Participant (3), Friend 1 (4), Friend 2 (3), Friend 3 (3)
Cherries - Participant (6), Friend 1 (5), Friend 2 (7), Friend 3 (6)

So the data above tells us a couple of things:

1. The participant is an Apples 'man' (it's their preference) as are the participants 1st and 3rd friend, whereas the 2nd friend is into cherries.
2. 75% of people like apples the most and 25% of people like cherries the most.

Now bare with me on this because I'm not too sure, but the first test I'm looking at doing is a Chi square goodness of fit test. I have 3 categories of fruit and I can categorise responses based onto based on highest preference. Lets say I have 99 participants reporting on 297 friends - all things being equal, I can expect the following results:

Preference A - 33 participants, and 33 of each type of friend (1st/2nd/3rd)
Preference B - 33 participants, and 33 of each type of friend (1st/2nd/3rd)
Preference C - 33 participants, and 33 of each type of friend (1st/2nd/3rd)

If however all 3 participants report the same, so it seems like Apples are the bomb, Cherries are ok, and no one likes bananas, and the observed data doesnt match the expected data, then it could be significant.

So if you're still with me and still interested, I've got some questions

1) What sort of combinations should I be looking at here? It seems doable to look at each participant preference type, compared to a mixed combination of friends (i.e. Type A with friends type ABC, AAA, AAB, AAC, etc.) but not specific combinations (i.e. Type A with AAB, ABA, BAA) unless it's restricted to 2 friends (Type A with AB, BA, etc.)

2) Lets say previous studies have been done and they found 50% of people prefer Apples, 30% prefer Bananas, and 20% prefer Cherries. Should I be expecting the same in my Chi test? Should I run two tests, one expecting 33% of each category, and one expecting a 50/30/20 mix?

3) What happens when participants report a 7 for both Apples and Cherries - how do I categorise them? Make a new category perhaps? Lets say that 30% of responses are hard to categorise because of participants doubling up in their preferences - what then?

4) Lets say some participants rate Apples and Bananas as 1 (strongly disagree) and Cherries as 2 (disagree) - is it right to categorise them as Cherry people?

The good thing is that at least I can run some ANOVA (I think) based on the likert responses (without categorising them) however that's probably best to make another thread on. Thanks in advance for anyone who wants to help, and even for those who didn't think "too not, not gunna read it"

with regards,
Richard