In this paper we describe a nonparametric Wilcoxon test and a parametric Z test based on statistical hypothesis testing for the detection of edges. We use the threshold determined by specifying significance level $alpha$, while Bovik, Huang and Munson[4] consider the range of possible values of test statistics for the threshold. From the experimental results of edge detection, the Z method performs sensitively to the noisy image, while the Wilcoxon method is robust over both noisy nd noise-free images. Comparison with our statistical tests and Sobel operator shows that our tests perform more effectively in both noisy and noise-free images.