A method based on matching synthetic and experimental emissivity spectra was applied to spatially resolved measurements of a laser-induced plasma ignited in argon at atmospheric pressure. The experimental emissivity spectra were obtained by Abel inversion of intensity spectra measured from a thin plasma slice perpendicular to the plasma axis. The synthetic spectra were iteratively calculated from an equilibrium model of plasma radiation that included free-free, free-bound, and bound-bound transitions. From both the experimental and synthetic emissivity spectra, spatial and temporal distributions of plasma temperature and number densities of plasma species (atoms, ions, and electrons) were obtained and compared. For the best-fit synthetic spectra, the temperature and number densities were read directly from the model; for experimental spectra, these parameters were obtained by traditional Boltzmann plot and Stark broadening methods. In both cases, the same spectroscopic data were used. Two approaches revealed a close agreement in electron number densities, but differences in plasma excitation temperatures and atom number densities. The trueness of the two methods was tested by the direct Abel transform that reconstructed the original intensity spectra for comparing them to the measured spectra. The comparison yielded a 9 and 13% difference between the reconstructed and experimental spectra for the numerical and traditional methods, respectively. It was thus demonstrated that the spectral fit method is capable of providing more accurate plasma diagnostics than the Boltzmann plot and Stark broadening methods.