[IIAOPSW]

>How do you account for confounding variables? For example, unseen or alternative methods of communication e.g. body language like bobbing, or clicking their beaks? Or even the tonality of the squawking? Whistling?

All perfectly acceptable. The relevant feature is merely the ability for the birds to put arbitrary signals in some communications channel, without those symbols having any a priori semantics. We would certainly know if they were winning more often than they should. It might take a while to figure out what non-squawk method they were using, but it wouldn't go over our heads.