We introduce the cross-match test - an exact, distribution free, high-dimensional hypothesis test as an intrinsic evaluation metric for word embeddings. We show that cross-match is an effective means of measuring the distributional similarity between different vector representations and of evaluating the statistical significance of different vector embedding models. Additionally, we find that cross-match can be used to provide a quantitative measure of linguistic similarity for selecting bridge languages for machine translation. We demonstrate that the results of the hypothesis test align with our expectations and note that the framework of two sample hypothesis testing is not limited to word embeddings and can be extended to all vector representations.