The Dielectric Laser Acceleration group at SLAC uses micro-fabricated dielectric grating structures and conventional infrared lasers to accelerator electrons. These structures have been estimated to produce an accelerating gradient up to 2 orders of magnitude greater than that produced by conventional RF accelerators. The success of the experiment depends on both the laser damage threshold of the structure and the timing overlap of femtosecond duration laser pulses with the electron bunch. In recent dielectric laser acceleration experiments, the laser pulse was shorter both temporally and spatially than the electron bunch. As a result, the laser is theorized to have interacted with only a small portion of the electron bunch. The detection of this phenomenon, referred to as partial population modulation, required a new approach to the data analysis of the electron energy spectra. A fitting function was designed to separate the accelerated electron population from the un-accelerated electron population. The approach was unsuccessful in detecting acceleration in the partial population modulation data. However, the fitting functions provide an excellent figure of merit for previous data known to contain signatures of acceleration. Show Partial Abstract