Flare occurrence is statistically associated with changes in several characteristics of the line-of-sight magnetic field in solar active regions (ARs). We calculated magnetic measures throughout the disk passage of 1075 ARs spanning solar cycle 23 to find a statistical relationship between the solar magnetic field and flares. This expansive study of over 71,000 magnetograms and 6000 flares uses superposed epoch (SPE) analysis to investigate changes in several magnetic measures surrounding flares and ARs completely lacking associated flares. The results were used to seek any flare associated signatures with the capability to recover weak systematic signals with SPE analysis. SPE analysis is a method of combining large sets of data series in a manner that yields concise information. This is achieved by aligning the temporal location of a specified flare in each time series, then calculating the statistical moments of the "overlapping" data. The best-calculated parameter, the gradient-weighted inversion-line length (GWILL), combines the primary polarity inversion line (PIL) length and the gradient across it. Therefore, GWILL is sensitive to complex field structures via the length of the PIL and shearing via the gradient. GWILL shows an average 35% increase during the 40 hr prior to X-class flares, a 16% increase before M-class flares, and 17% increase prior to B-C-class flares. ARs not associated with flares tend to decrease in GWILL during their disk passage. Gilbert and Heidke skill scores are also calculated and show that even GWILL is not a reliable parameter for predicting solar flares in real time.
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