We use Raman microscopic images with high spatial and spectral resolution to investigate differences between human follicular thyroid (Nthy-ori 3-1) and follicular thyroid carcinoma (FTC-133) cells, a well-differentiated thyroid cancer. Through comparison to classification of single-cell Raman spectra, the importance of subcellular information in the Raman images is emphasized. Subcellular information is extracted through a coarse-graining of the spectra at high spatial resolution (∼1.7 μm2), producing a set of characteristic spectral groups representing locations having similar biochemical compositions. We develop a cell classifier based on the frequencies at which the characteristic spectra appear within each of the single cells. Using this classifier, we obtain a more accurate (89.8%) distinction of FTC-133 and Nthy-ori 3-1, in comparison to single-cell spectra (77.6%). We also infer which subcellular components are important to cellular distinction; we find that cancerous FTC-133 cells contain increased populations of lipid-containing components and decreased populations of cytochrome-containing components relative to Nthy-ori 3-1, and that the regions containing these contributions are largely outside the cell nuclei. In addition to increased classification accuracy, this approach provides rich subcellular information about biochemical differences and cellular locations associated with the distinction of the normal and cancerous follicular thyroid cells.