The exchange bias anisotropy field in CoFe/IrMn ferromagnetic/antiferromagnetic bilayers has been investigated by two different experimental probes. One was the traditional hysteresis loop shift technique and the other was a recently developed technique which monitors small reversible rotations of the magnetization with the anisotropic magnetoresistance (AMR). All the samples show approximately twice the exchange bias anisotropy field measured with the AMR technique compared to that measured with the traditional hysteresis loop method. Based on similar experiments in other materials, there is a portion of the exchange bias uniaxial anisotropy which rotates in a hysteresis loop measurement. It is surmised it is this energy which the hysteresis loop technique neglects and that the AMR technique is a better measure of the exchange bias anisotropy energy.