  We study a combined sample of 264 star-forming, 51 composite, and 73 active
galaxies using optical spectra from SDSS and mid-infrared (mid-IR) spectra from
the Spitzer Infrared Spectrograph. We examine optical and mid-IR spectroscopic
diagnostics that probe the amount of star formation and relative energetic
contributions from star formation and an active galactic nucleus (AGN). Overall
we find good agreement between optical and mid-IR diagnostics.
Misclassifications of galaxies based on the SDSS spectra are rare despite the
presence of dust obscuration. The luminosity of the [NeII] 12.8 \mu m
emission-line is well correlated with the star formation rate (SFR) measured
from the SDSS spectra, and this holds for the star forming, composite, and
AGN-dominated systems. AGN show a clear excess of [NeIII] 15.6 \mu m emission
relative to star forming and composite systems. We find good qualitative
agreement between various parameters that probe the relative contributions of
the AGN and star formation, including: the mid-IR spectral slope, the ratio of
the [NeV] 14.3 \mu m to [NeII] \mu m 12.8 fluxes, the equivalent widths of the
7.7, 11.3, and 17 $\mu m$ PAH features, and the optical "D" parameter which
measures the distance a source lies from the locus of star forming galaxies in
the optical BPT emission-line diagnostic diagram. We also consider the behavior
of the three individual PAH features by examining how their flux ratios depend
upon the degree of AGN-dominance. We find that the PAH 11.3 \mu m feature is
significantly suppressed in the most AGN-dominated systems.
