Nominal data analysis?

#1
Hello all, I am having a bit of trouble with analysing my dissertaion.

It involves recording the behaviour of shore crabs at regular intervals. The data collected is nominal, as the behaviour is put into distinct catagories (such as 'locomotory activity'/'stationary'/'Aggressive interaction'). The behaviour of two crabs in a tank is scan sampled every 20 seconds for the duration of the 7 day experiment leading to an exact number of samples per crab per per 24 hour period (4320).

The lighting in the tank switches between on and off every 12 hours.

I am attepmting to determine if activity levels and aggression peak at certain times of the day.
So far I have been able to use fishers exact test to detemine a significant difference between activity levels of the 'day' and 'night' phases of the experiment, but analysing differences by hour is not avaliable as Minitab allows for only 2x2 contingency tables.

I cannot use Chi squared test because Minitab returns saying 'Multiple cells have expected values of less than one, Chi squared approximation probably invalid'

Are there any other tests for non-randomly collected nominal data that I should be considering?


...I would also like to divide the total number of aggressive interactions per hour by the of overall activity (locomotory activity + aggressive interactions) per hour to see if aggression increases RELATIVE to overall activity at certain times of the day. (Which would allow to rule out an increase of aggression as a side effect to increased overall activty level).
Would I be able to use the figures in an anova? (All the figures obtained would be bewteen 0 and 1)

E.g
18:00-19:00
Number of aggressinve interactions recorded: 12
Number locomotory activy recorded: 37

12/ (12+37)= 0.244

19:00-20:00
Aggressive interactions recorded: 6
Locomotory activity recorded: 1

6/ (6+1) =0.857



I have 30,240 samples per crab, but not much of an idea how to analyse it. Any help will be much appreciated.
 
#2
The activity levels may be nominal, but time of day is not. You probably don't want to do a test that doesn't know that 01:00 is closer to 02:00 than to 14:00. To account for this, you will need to fit to a model.

For example, if you think there is a 24-hour cycle, I would fit to a sinusoidal variation model. You might take as an Ansatz that the probability of being in an agressive state is A + B sin(2 pi t / 24 hr + C) and do a ML-fit for A, B, and C. Eventually, you might also want to take into account that each crab may have a different base level of agressivity A.