Estimation of the direction-of-arrival (DoA) of a speaker in a room is important in many audio signal processing applications. Environments with reverberation that masks the DoA information are particularly challenging. Recently, a DoA estimation method that is robust to reverberation has been developed. This method identifies time-frequency bins dominated by the contribution from the direct path, which carries the correct DoA information. However, its implementation is computationally demanding as it requires frequency smoothing to overcome the effect of coherent early reflections and matrix decomposition to apply the direct-path dominance (DPD) test. In this work, a novel computationally-efficient alternative to the DPD test is proposed, based on the directivity measure for sensor arrays, which requires neither frequency smoothing nor matrix decomposition, and which has been reformulated for sound field directivity with spherical microphone arrays. The paper presents the proposed method and a comparison to previous methods under a range of reverberation and noise conditions. Result demonstrate that the proposed method shows comparable performance to the original method in terms of robustness to reverberation and noise, and is about four times more computationally efficient for the given experiment.