I've been thinking a little about how to set up a valid test of the alternate hypotheses. The following came to mind. I would have to give it a lot more thought in regards to its sensitivity, etc. but here goes.
I'll describe this as involving the owner, O, and the dog, D. In each trial the O leaves at time T0, goes to some location at time Ta, at some randomly chosen time, Tl between Ta and Tmax the owner starts home returning at time Tr. For now, lets simplify and assume the place that O goes is always the same and the travel time (Ta - T0) is constant and the same as the the travel time needed to return (Tr - Tl). I'm leaving out details like O being notified when to leave by a text message from someone who has no other connection to any of the other parties except receiving a text message from O when O arrives.
Meanwhile, D is observed and it is recorded whenever they enter or leave the key region. From this can be computed the "median time in the key area" -- the time before which half the time they eventually spend in the key area occurs. Later this is also computed relative to Tl (the time at which O leaves the remote location to return), by simply subtracting Tl from the median time for each trial.
Now over all the trials compute the variance (or standard deviation) for the median times measured from the T0s and the variance (sd) for the median times measured from the Tls. The conventional hypotheses (either the "random activity" hypothesis, or the "anticipation" hypothesis) predicts that the variance computed from the T0s will be less than the variance computed from the Tls. The psi hypotheses (either the "on the way home" or the "getting ready for O to arrive" hypothesis) predict the opposite.
If we also vary the travel time returning, and use both the median time relative to Tl and to Tr, then we can distinguish these two hypotheses from each other as well.
As I said, this needs much more fleshing out and examination before I could actually recommend it, but I thought I would pass it along.  |