This paper presents a change detection algorithm based on Shannon entropy and the Rayleigh distribution for both single-look and multi-look SAR images. While hypothesis testing has been widely used in SAR change detection, few studies have applied this approach to both types of data. To address this, we propose a method that utilizes Shannon entropy to detect changes between two samples. The performance of the algorithm was evaluated through Monte Carlo simulations using synthetic SAR data and further validated on real-world datasets, including single-look images from the CARABAS II dataset and multi-look data from the UAVSAR radar. The results demonstrate that the proposed method is effective in detecting changes. This paper highlights the versatility of the approach, which is capable of handling both single-look and multi-look SAR data, and reinforces the way for future research into alternative entropy measures and probability distributions in change detection tasks.