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While non-proportionality is assumed to degrade scintillator energy resolution, the quantitative relationship between non-proportionality and energy resolution is not well understood. We report on the results of experimental data analysis and Monte Carlo simulation used jointly to study the relationship between scintillator electron response non-proportionality and gamma ray energy resolution. Energy resolution for Compton interactions was compared to energy resolution for photoelectric interactions, to investigate the hypothesis that non-proportionality affects these two types of interactions differently. The difference is thought to be due to low energy quanta such as Auger electrons and fluorescent x-rays produced by photoelectric interactions (which predominantly interact with inner shell electrons) but not by Compton interactions (which predominantly interact with valence electrons). A newly constructed Compton coincidence apparatus (SLYNCI) was used to measure electron response non- proportionality in Nal(Tl) that was excited by Compton-scattered electrons. Measured values for both light output vs. electron energy and energy resolution vs. electron energy were then used to predict gamma ray energy resolution, based on Monte Carlo simulations that mimicked the distribution of energetic electrons emitted following photoelectric absorption of gamma rays in the scintillator. Predicted values were compared to experimental data obtained by exciting the scintillator with isotopic sources. In this manner, the component of gamma ray energy resolution degradation due to non-proportionality was determined, as well as the electron energy resolution component due to electron response counting statistics and other possible limiting factors such as Landau fluctuations in the dE/dx along the electron track.