On the basis of a new finding reported in previous studies that the structural formation in the induction period of crystallization involves a kind of phase separation of spinodal decomposition due to the orientation fluctuations of polymer segments, we have investigated the structural change of poly(ethylene terephthalate) (PET) from a structure size point of view using a small angle X-ray scattering (SAXS) technique when it was crystallized at 80 or 5 degrees C above the glass transition temperature, T-g, from a melt-quenched glass. A spatial density correlation analysis of the SAXS intensities reveals that the size of the dense domains caused by the density fluctuations in the induction period is fairly large compared with the lamellar thickness after crystallization, indicating that these dense domains are not the embryos predicted by the classical nucleation theory. Thus, the crystal nuclei are not formed until the dense domains grow to a certain critical size, 85 Angstrom in this case. The critical size of crystal nuclei appearing in the dense domains just after the induction period is also determined to be 14 Angstrom.