need stats help with dependent proportions; 4 groups; not binary

I have some dependent, nested proportions that I need to compare and I have no idea how to do it. Here's a fictional, analogous example.

I gave 6 people a test and recorded their behavior with a video camera as they took it. Each person got some of the questions wrong (wrong answer = WA) and some of the questions right (right answer = RA). While the people were answering each of these questions, they were also engaging in other behaviors, including pencil chewing (PC), leg tapping (LT), looking up (LU), and looking down (LD). I realize that these aren't actually mutually exclusive, but please just pretend they are for the sake of the example.

Once I had all the data, I figured out which questions the participants got right and which questions the participants got wrong. Then I assessed what percentage of time spent answering each question was devoted to engaging in the above four behaviors.

Here is some example means, coded as indicated in the text above:
WA-PC: 40%
WA-LT: 30%
WA-LU: 20%
WA-LD: 10%

RA-PC: 35%
RA-LT: 40%
RA-LU: 10%
RA-LD: 15%

Here is an interpretation of one of these values to clarify what's meant...
"WA-PC=40%" means that, "while the participant was answering questions that were subsequently marked as 'wrong answers,' 40% of their time was spent chewing on a pencil."

So the questions that I want to ask are basically what would be assessed with a repeated measures ANOVA:
1) Does the percentages of time spent engaging in any one behavior differ from the percentages of time engaging in any of the other behaviors? (i.e., is there a main effect of behavior)

2) Do the percentages of time spent in any single behavior differ between the right-answer and wrong-answer groups? (i.e., is there a main effect for 'group'?)

and

3) Is there an interaction?

So, why can't I just do a repeated measures ANOVA? Because all the values are interdependent proportions. For any participant to spend more time looking up, he will necessarily be spending less time looking down. (Yes, you could imagine that maybe if he looks up, that extra percentage comes from a different behavior, but we can't guarantee that).

How do I analyze this data to look for significant differences? Thanks!

attempt #2

For the sake of trying this again, imagine instead that I'm trying to compare the percents of the 2004 republican party that are each of four races, and then to compare those percents against the values for the 2010 republican party.

I.e.... (fictitious data)

2004 republican party = 55% white, 5% black, 20% asian, 20% hispanic/latino.

2011 republican party = 45% white, 8% black, 17% asian, 30% hispanic/latino.

Questions:
1) Is 55% different from 5% different from 20% different from 20%?

2) Do these values differ as compared to the percents from 2011?

Please help!!!

JeffM said:

Yes, 55 is different from 5.

Yes, both 55 and 5 are different from 20.

No, 20 is not different from 20.

Possibly those questions were not your intended questions. I suggest that if my answers do not address your intended questions, whatever those may happen to be, that you start a new thread with questions that are both meaningful and non-trivial.

Click to expand...

While I appreciate the sarcastic and unhelpful response (why did you even take the time to write it?), the questions remain unanswered. I'm asking about statistically significant differences -- the key words being "statistically significant." (Hence why I began the thread with I "need stats help.") By saying they're different, you've made no attempt to account for variance or sample size. You've actually done no statistical comparison at all.

Aside from that, what I provided was just hypothetical numbers to illustrate the problem. The real numbers are much closer. I suppose I could have said "Is 49% different from 50%?," but, by your logic, they're different because they're not the same number and that's the end of the story.

Again, I need a way to statistically compare these values -- something along the lines of a McNemar test, but for scalar data and >2 groups.

In sum Jeff -- in response to your cheeky suggestion, I'll advise that you put away the keyboard, pick up an intro to stats book, and take note that saying "meaningful and non-trivial" is redundant.

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If anyone actually knows how to statistically compare dependent proportions with >2 groups, please post.