Noises can highly influence the performance of segmentation and edge detection process. Traditional edge detection methods are very vulnerable to noise. Statistical models, which are based on t-test, Wilcoxon test, and rank-order test, are suggested for noisy images in the literature. In this paper, we suggest a framework based on rank-order test and k-means clustering, which increases the efficiency of the rank-order test. The performance of the proposed statistical framework was tested on corrupted images with different noise variance. Experimental results show that proposed edge detection framework is more robust to different noise variance than well-known conventional and statistical methods.