Statistical analysis on film data dates back at least to the 1970s, with Barry Salt's initial work applying quantitative statistical analysis methods to cinematic data. His work is a good place to start.
Salt, B. (1974). Statistical style analysis of motion pictures. Film Quarterly, 13-22.
Salt, B. (1992). Film style and technology: History and analysis (2rd edition). Starword. (Last 3rd edition is in 2009)
Salt's book Moving into Pictures was later on reviewed by Buckland (2008).
Buckland, W. (2008). What does the statistical style analysis of film involve? A review of Moving Into Pictures: More on History, Style, and Analysis. Literary and Linguistic Computing 23, 219-230.
Selected recent work:
Baxter, M.(2014). Notes on cinemetric data analysis. (Posted by author)
Baxter, M. (2013). Evolution in Hollywood editing patterns. Cinemetrics Website. (Posted by author)
Cutting, J.E., DeLong, J.E. and Nothelfer, C.E. (2010): Attention and the evolution of Hollywood Film film. Psychological Science 21, 440-447.
Cutting, J.E., Brunick, K.L., DeLong, J.E., Irichischi, C., &Candan, A.(2011). Quicker, faster, darker: change in Hollywood film over 75 years. i-Perception, 2(6), 569.
Smith, T.J., Levin, D. and Cutting, J.E. (2012): A window on reality: perceiving edited reality. Current Directions in Psychological Science 21, 107-113.