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The intensity scintillation index (S4) exhibits a linear frequency dependence derived from a power law phase screen model, with the exponent determined by the phase spectral index (p). However, it is well known that a departure from linearity occurs as S4 increases and saturates under strong scatter conditions. Additionally, statistical errors over a finite time window can also cause the scintillation statistic to deviate from the power law dependence on frequency. This paper presents a parametric analysis on the deviation in the S4 frequency dependence from the power law form. This investigation focuses on the contribution of statistical uncertainty in S4 calculations to the deviation in the frequency dependence according to the selected parameters: S4 and Fresnel frequency (fF). The deviation is determined by comparing p estimates calculated from the power law relationship of S4 at different L‐band frequencies with those inferred from a model‐fitting method using a multi‐frequency global navigation satellite system scintillation data set. The results show the well‐known departure from linearity as S4 increases, and reveal increasing deviations with decreasing fF. The spectral analysis indicates that the variability at the lowest frequencies of intensity spectra contributes to the statistical errors in S4 calculations due to the finite time window, particularly when scintillations are dominated by low‐frequency contributions at low fF. Simulation results of scintillation realizations show much lower deviations with a 30‐min compared to 1‐min window. This suggests a 1‐min window can be too short for reliable S4 calculations due to statistical uncertainty, especially at low fF. Plain Language Summary: The S4 index is a widely used measure to quantify scintillation strength. The relationship between S4 values at different signal frequencies is theoretically expected to follow a linearity. However, this simple relationship is only valid under certain conditions, and the calculation of S4 with a finite time window can introduce uncertainty that causes deviations from the expected frequency dependence. In this study, we analyze the uncertainty in the relationship between S4 values at different frequencies, considering the specific scintillation conditions. Our observations confirm two main findings: (a) a well‐known departure from linearity at high levels of scintillation, and (b) deviations caused by statistical uncertainty due to large‐scale fluctuations over a finite time window for S4 calculations. We validate these findings through simulations that cover a wide range of scintillation scenarios. Key Points: Deviation/departure of S4 frequency dependence from the power law form was parametrically investigated via global navigation satellite system scintillation observationsIn addition to the well‐known departure at high S4, larger deviations in the S4 frequency dependence were observed at lower fFSimulation shows lower deviations with a 30‐min S4 window rather than 1‐min due to statistical uncertainty depending on the window length [ABSTRACT FROM AUTHOR]