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# stats; dependent proportions; not binary; 4 'groups'

Thu 12 Jul, 2012 10:32 am
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!
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engineer

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Thu 12 Jul, 2012 12:00 pm
@john-330,
Instead of variables called "Looking Up" and "Looking Down" you have one variable called "Looking" with values of "Up" or "Down". Now all of your behavior variables are binary. PC (yes or no), LT (yes or no), L (up or down). Also note that PC and LT might be mutually exclusive, but unless you have a third Looking variable (straight ahead) I don't see how looking is mutually exclusive with the other two.

Finally since all of these are supposed to be mutually exclusive, you could wrap all of these into a single variable called behavior.

B = 1 = PC and looking down
= 2 = LT and looking down
= 3 = Looking UP
= 4 = Just looking Down

And then the ANOVA is extremely straight forward. You can add all the cases here you want.

Interactions are only possible if the variables are not mutually exclusive since they must interact to see any effect.
john-330

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Wed 25 Jul, 2012 03:14 pm
@engineer,
Hi engineer,

Thanks for the response.

Unfortunately, the data are not binary and I do need you to just pretend that they're mutually exclusive (even though yes, I know that they aren't).

Please recall that what I gave before was just an example. The actual data, I assure you, are mutually exclusive and not binary. I need to compare percents.

After posting, I thought of a more lucid and relevant example...

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) Are the percents for the 2004 republican party different from one another? (same for 2011 republican party)

2) Do the percents in each racial category differ from one another across years?

john-330

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Wed 25 Jul, 2012 03:19 pm
@john-330,
Also, sorry for not responding earlier. I posted this query on several sites and was waiting for an e-mail notification that someone replied. I didn't get one, and stupidly didn't think to just check back.

This is still a very important question to me and I really appreciate any effort.

I must not have given a great example the first time around because I got a similar response from a local statistician. Hopefully this new one will make the situation more understandable -- what I need is to be able to compare multiple dependent percents.
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