A detailed study has been undertaken of the efficiency of reinforcement in nanocomposites consisting of single-walled carbon nanotubes (SWNTs) in poly(vinyl alcohol) (PVA). Nanocomposite fibers have been prepared by electrospinning and their behavior has been compared with nanocomposite films of the same composition. Stress transfer from the polymer matrix to the nanotubes has been followed from stress-induced Raman band shifts, which are shown to be controlled by both geometric factors such as the angles between the nanotube axis, the stressing direction and the direction of laser polarization, and by finite length effects and bundling. A theory has been developed that takes into account all of these factors and enables the behavior of the different forms of nanocomposite, both fibers and films, to be compared in different polarization configurations. The effective modulus of the SWNTs has been found to be in the range 530-700 GPa which, while being impressive, is lower than the generally accepted value of around 1000 GPa as a result of factors such as finite length effects and nanotube bundling. This value of effective modulus has, however, been shown to be consistent with the contribution of nanotubes to the 20% increase in Young's modulus found for the nanocomposite films with a loading of only 0.2% of SWNTs. Hence a self-consistent method has been developed which enables the efficiency of reinforcement by nanotubes, and potentially other high-aspect-ratio nanoparticles, to be evaluated from stress-induced Raman bands shifts in nanocomposites independent of the specimen geometry and laser polarization configuration.