Independence of observation in 2-way ANOVA

#1
Hi,
I'm a grad student in behavioural neuroscience.

I am looking at individual difference in anxiety in animals.

There are two groups of animals: one anxious and the other non-anxious.
I present then with a potential threat and see if their anxiety levels are reflected on their behaviour.

In the test paradigm, I place a threatening object in front of a cage for a certain time.
The cage is divided into 4 sections: Front, Middle, Back and Furthest back.
I measure proportions of time spent at each location.
For instance, a particular animal spent 20% Front, 40% Middle, 30% Back and 10% Furthest back.

Thus, independent variable is the group; anxious and non-anxious.
Dependent variable is the proportion of time spent at each location.

In order to see if there is any difference between the groups, I am doing a t-test for each location.

But, would it be possible to do a 2-way ANOVA with independent variables: Group (Anxious, Non-anxious) and Location (Front, Middle) and dependent variable: proportion of time spent at each location?

Since the locations are not independent from each other, will this violate the independence of observation?

Thank you,
 

trinker

ggplot2orBust
#2
This may not answer the question you ask but...

When you say:

But, would it be possible to do a 2-way ANOVA with independent variables: Group (Anxious, Non-anxious) and Location (Front, Middle) and dependent variable: proportion of time spent at each location?

It indicates to me that you are trying to put your DV (location) in as a DV and an IV. It doesn't sit right with me. Unless you put the threat in at the front or back of the cage but you didn't indicate that the threat itself changed locations. I actually would recomend a 1 way MANOVA here because you have 4 DV measures: % Front, % Middle, % Back and % Furthest back

that you could use with the anxiety level (IV). I'd then follow up (if there's sig) with univariate (1 way anovas) of each IV group with just one DV measure. Hopefully this helps though I didn't answer your question. I think your design determines different testing than you're using.