Detrended fluctuation analysis was applied to the magnetic storm index SYM-H for the epoch 1981--2002. The objective was to determine the characteristic fractal statistical differences, if any, between a quiet and active magnetosphere. The entire data set comprises over 11 million points that include numerous intervals that can be classified as quiet or active. For quiet intervals we required Kp ≤ 1 for 10,000 consecutive minutes. Similarly, to qualify as an active interval required Kp ≥ 4 for 10,000 consecutive minutes. All active intervals included magnetic storms. Detrended fluctuation analysis was applied to each of these intervals to obtain local scaling exponents. A clear difference in statistical behavior during quiet and active intervals is implied through analysis of the scaling exponents for the quiet and active intervals; active intervals generally have larger values of scaling exponents. This implies that although SYM-H appears monofractal on shorter timescales, it is more properly described as a multifractional Brownian motion. An overall trend toward higher scaling exponents was also discovered for increasing magnetospheric activity, possibly implying an increase in organization with magnetospheric activity. The overall distribution of the scaling exponents for active intervals was Gaussian. For quiet intervals, however, it was bi-Gaussian, perhaps indicative of different internal (magnetospheric) and external (solar wind) nonlinear forcings.