  We probe the scale dependence of the primordial spectrum in the light of the
three-year WMAP (WMAP3) alone and WMAP3 in combination with the other
cosmological observations such as galaxy clustering and Type Ia Supernova
(SNIa). We pay particular attention to the combination with the Lyman $\alpha$
(Ly$\alpha$) forest. Different from the first-year WMAP (WMAP1), WMAP3's
preference on the running of the scalar spectral index on the large scales is
now fairly independent of the low CMB multipoles $\ell$. A combination with the
galaxy power spectrum from the Sloan Digital Sky Survey (SDSS) prefers a
negative running to larger than 2$\sigma$, regardless the presence of low
$\ell$ CMB ($2\le \ell \le 23$) or not. On the other hand if we focus on the
Power Law $\Lambda$CDM cosmology with only six parameters (matter density
$\Omega_m h^2$, baryon density $\Omega_b h^2$, Hubble Constant $H_0$, optical
depth $\tau$, the spectral index, $n_s$, and the amplitude, $A_s$, of the
scalar perturbation spectrum) when we drop the low $\ell$ CMB contributions
WMAP3 is consistent with the Harrison-Zel'dovich-Peebles scale-invariant
spectrum ($n_s=1$ and no tensor contributions) at $\sim 1\sigma$. When assuming
a simple power law primordial spectral index or a constant running, in case one
drops the low $\ell$ contributions ($2\le \ell \le 23$) WMAP3 is consistent
with the other observations better, such as the inferred value of $\sigma_8$.
We also find, using a spectral shape with a minimal extension of the running
spectral index model, LUQAS$+$ CROFT Ly$\alpha$ and SDSS Ly$\alpha$ exhibit
somewhat different preference on the spectral shape.
