Context: Zoology undergrad dissertation. The format of my results will be % time individual birds spent doing certain activities (and possibly number of times an activity such as pecking was performed). There is no external way to tell whether the individual bird is male or female, so my hypothesis is that males and females will have different activity budgets. Neither myself and my dissertation supervisor know what statistical test to perform - what test can be used for this?
You could try clustering the behaviour patterns in an unsupervised way using e.g. UMAP (available in several softwares: python had umap-learn, R has a package accessing the python package - watch e.g. this YouTube video for a nice explanation or the article for more details) or t-SNE. You can then see whether you get two clusters that are sized in about the right ratio for the ZZ vs. ZW chromosome ratio, characterize what the clusters are like and then speculate whether they might be clusters by ZZ vs. ZW.
Can you get a feather or other DNA sample in some way? Getting a read on that on a at least a few individuals that way would help a lot to see whether that matches up with the theory. I believe DNA tests on feathers are pretty cheap nowadays.