Dual-energy computed tomography (DECT) is a recent advancement in CT technology, which can potentially reduce artifacts and provide accurate quantitative information for diagnosis. Recently, statistical iterative reconstruction (SIR) methods were introduced to DECT for radiation dose reduction. The statistical noise modeling of measurement data plays an important role in SIR and impacts on the image quality. Contrary to the conventional CT projection data, of which noise is independent from ray to ray, in spectral CT the basis material sinogram data has strong correlations. In order to analyze the image quality improvement by applying correlated noise model, we compare the effects of two different noise models (i.e., correlated noise model and independent model by ignoring correlations) by analyzing the bias and variance trade-off. The results indicate that in the same bias level, the correlated noise modeling results in up to 20.02% noise reduction compared to the independent noise model. In addition, their impacts to different numerical are also evaluated. The results show that using the non-diagonal covariance matrix in SIR is challenging, where some numerical algorithms such as a direct application of separable paraboloidal surrogates (SPS) cannot converge to the correct results.