Goodness-of-Fit (GoF) based spectrum sensing of orthogonal frequency-division multiplexing (OFDM) signals is investigated in this paper. To this end, some novel local sensing methods based on Shapiro-Wilk (SW), Shapiro-Francia (SF), and Jarque-Bera (JB) tests are first studied. In essence, a new threshold selection technique is proposed for SF and SW tests. Then, three studied methods are applied to spectrum sensing for the first time and their performance are analyzed. Furthermore, the computational complexity of the above methods is computed and compared to each other. Simulation results demonstrate that the SF detector outperforms other existing GoF-based methods over AWGN channels. Furthermore simulation results demonstrate the superiority of the proposed SF method in additive colored Gaussian noise channels and over fading channel in comparison with the conventional energy detector.