This paper presents a method for detecting scene changes in video sequences, in which the $chi^{2}$-test is modified by imposing weights according to NTSC standard. To automatically determine threshold values for scene change detection, the proposed method utilizes the frame differences that are obtained by the weighted $chi^{2}$-test. In the first step, the mean and the standard deviation of the difference values are calculated, and then, we subtract the mean difference value from each difference value. In the next step, the same process is performed on the remained difference values, mean-subtracted frame differences, until the stopping criterion is satisfied. Finally, the threshold value for scene change detection is determined by the proposed automatic threshold estimation algorithm. The proposed method is tested on various video sources and, in the experimental results, it is shown that the proposed method is reliably estimates the thresholds and detects scene changes.