Adaptive directional microphone arrays have been widely utilized in hearing aids to help wearers understand speech in noisy environments. However, a practical and objective way of measuring the benefit of this technique is not obvious. One commonly used measure for directional microphone arrays is directivity index (DI), which evaluate the arrays' capability to attenuate a diffuse noise field. However, the DI has rarely been considered for the Adaptive directional microphone arrays because a truly diffuse noise field is required for the measurement. This paper investigates the feasibility of measuring the DI of adaptive directional hearing aids in a diffuse noise field generated by a loudspeaker array playing uncorrelated noise signals simultaneously. The requirement for the degree of diffuseness of the noise field is studied based on numerical simulations for first-order and second-order adaptive microphone arrays. The possibility of measuring the DI in both anechoic and non-anechoic conditions is investigated. The accuracy of the proposed approach is further discussed.