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This paper revisits the classical Kennicutt method for inferring the stellarinitial mass function (IMF) from the integrated light properties of galaxies.The large size, uniform high quality data set from the Sloan Digital Sky SurveyDR4 is combined with more in depth modeling and quantitative statisticalanalysis to search for systematic IMF variations as a function of galaxyluminosity. Galaxy H alpha equivalent widths are compared to a broadband colorindex to constrain the IMF. This parameter space is useful for breakingdegeneracies which are traditionally problematic. Age and dust corrections arelargely orthogonal to IMF variations. In addition the effects of metallicityand smooth star formation history e-folding times are small compared to IMFvariations. We find that for the sample as a whole the best fitting IMF slopeabove 0.5 M_sun is Gamma = 1.4535 with a negligible random error of +/- 0.0004and a systematic error of +/- 0.1. Galaxies brighter than around M_r,0.1 = -20(including galaxies like the Milky Way which has M_r,0.1 ~ -21) are well fit bya universal Gamma ~ 1.4 IMF, similar to Salpeter, and smooth, exponential starformation histories (SFH). Fainter galaxies prefer steeper IMFs and the qualityof the fits reveal that for these galaxies a universal IMF with smooth SFHs isactually a poor assumption. Several sources of sample bias are ruled out as thecause of these luminosity dependent IMF variations. Analysis of bursting SFHmodels shows that an implausible coordination of burst times is required to fita universal IMF to the M_r,0.1 = -17 galaxies. This leads to the conclusionsthat the IMF in low luminosity galaxies has fewer massive stars, either bysteeper slope or lower upper mass cutoff, and is not universal.

Evidence for a non-universal stellar initial mass function from the integrated properties of SDSS galaxies