The anhedral or dihedral of the horizontal tail is usually to correct unwanted pitching moments when the plane is yawed off the heading C/L. This was the case in the older pattern planes that used anhedral in the stab. But, in some cases (including the F-4) it also is a way to get more of the stab in clean air in a high AOA situation when the stab airflow might be blanked by the wing flaps. Most of time though, it's a correction for yaw/pitch coupling.

Paul