In this paper we present an analysis of ionospheric scintillation data that shows that the underlying statistical structure of the signal can be accurately modeled by the additive complex Gaussian perturbation predicted by the Born approximation in conjunction with an application of the central limit theorem. By making use of this fact it is possible to estimate the in-phase, phase quadrature, and cophased scattered power by curve fitting to measured intensity histograms. By using this procedure we have found that typically more than 80% of the scattered power is in phase quadrature with the undeviated signal component. Thus the signal is modeled by a Gaussian but highly non-Rician process. From simultaneous UHF and VHF data we deduce only a weak dependence of this statistical structure on changes in the Fresnel radius. Moreover, we have found that the signal variance has a nonquadratic wavelength dependence. We have hypothesized that this latter effect is a subtle manifestation of locally homogeneous irregularity structures, a mathematical model proposed by Kolmogorov in his early studies of incompressible fluid turbulence.