Location and spread in shot length distributions
The typical characteristics of the distribution of shot lengths in a motion picture are:
- The distribution is decidedly non-normal – it is positive skewed. Although it is possible to conceive of a film that would have a normal or even a negative distribution of shot lengths this does not occur in fact, and I have never come across any film in which the shot lengths were not positively skewed.
- The distribution will include some outlying data points that are far from the average value (the mean or the median shot length).
An additional characteristic worth exploring is the linear relationship between the average value of a shot length distribution and the spread of the data around that value. Figures 1 to 6 plot the average value (the mean and the median shot lengths) of the 50 Hollywood films I used in my analysis of the impact of sound technology on film style (20 silent and 30 sound) against three measures of absolute dispersion – the standard deviation, the interquartile range, and the median absolute deviation. The coefficient of determination is given as a measure of the linear relationship between location and spread. The correlation coefficients for all the comparisons are significant at the 95% level.
Figure 1 Mean shot length v. standard deviation for silent Hollywood films produced from 1920 to 1928 inclusively (n = 20).
Figure 2 Median shot length v. interquartile range for silent Hollywood films produced from 1920 to 1928 inclusively (n = 20).
Figure 3 Median shot length v. median absolute deviation for silent Hollywood films produced from 1920 to 1928 inclusively (n = 20).
Figure 4 Mean shot length v. standard deviation for sound Hollywood films produced from 1929 to 1931 inclusively (n = 30).
Figure 5 Median shot length v. interquartile range for sound Hollywood films produced from 1929 to 1931 inclusively (n = 30).
Figure 6 Median shot length v. median absolute deviation for sound Hollywood films produced from 1929 to 1931 inclusively (n = 30).
In general the linear relationship between location and spread for these films is evident, but may be quite weak. The strongest linear relationship occurs between the median shot length and the median absolute deviation, and the strength of these relationship increases from the silent to the sound era. In both cases there is a substantial proportion of the variance that is unexplained, but overall films with greater median shot lengths exhibit greater variation in their shot lengths.
The relationship between the mean shot length and the standard deviation shows weaker linearity, with approximately one-third of the variance unexplained for both groups of films although there is a small increase in the strength of the relationship from the silent to the sound eras.
The relationship between the median and the interquartile range (IQR) for the sound films shows a weak linear relationship for the sound films, but only a very weak relationship for the silent films – although the r is significant (t  = 4.1090, p = 0.0007), over half the variance in the IQR is unexplained. R2 for the silent films is 0.4840 and for the sound films is 0.7490, though why such a difference should occur for this relationship and not for the others is a mystery. There is clearly something about the relationship between the median shot length and the interquartile range in the sample of silent films that requires further exploration.
We can say that for Hollywood films of the 1920s and early silent period the average shot length of a motion picture increases so does the variability of shot lengths. As expected, for skewed data sets the linear relationship between measures that do not rely on a mathematical relationship to the mean are the strongest. It seems likely that other groups of films will exhibit similar relationships between measures of location and spread (although perhaps not for the median and the IQR), but it will take further studies to test this hypothesis.
Posted on November 12, 2009, in Cinemetrics, Film Studies, Film Style, Hollywood, Silent cinema, Statistics and tagged Cinemetrics, Film Studies, Film Style, Silent cinema, Statistics. Bookmark the permalink. 5 Comments.