Following on from last week’s post on shot length distributions in the short films of Laurel and Hardy (here) and a piece on shot length distributions in German cinema (here) from last month, this week I add to a post from last year that looked at the relationship between different measures of location and spread (see here).

This post uses different methods from the earlier one: the measure of scale used is Qn, Spearman’s rank correlation coefficient is used to describe the linear relationship, and the trendline in the graphs is fitted using RMA regression rather than OLS.

In Table 1 we see that there is a strong correlation between the median shot length and Qn in each year for the German films, and this can be seen more easily in the graphs below. The correlation is less strong for the films produced in 1929, and these are the silent films in this sample. As we are using different statistics the results to the Hollywood films are not directly comparable, but the same difference between the silent and sound films is apparent in both samples.

Table 1 Spearman’s rank correlation coefficient for German films produced between 1929 and 1933, inclusive

Figure 1 Median shot length v.Qn for German films produced in 1929 (n = 12).

Figure 2 Median shot length v.Qn for German films produced in 1930 (n = 11).

Figure 3 Median shot length v.Qn for German films produced in 1931 (n = 14).

Figure 4 Median shot length v.Qn for German films produced in 1932 (n = 17).

Figure 5 Median shot length v.Qn for German films produced in 1933 (n = 13).

We see the same patterns when we look at the relationship between the same two statistics for the Laurel and Hardy movies. For the silent films produced between 1927 and 1929 inclusive (n = 12), we find that Spearman’s r = 0.7702, p = 0.0034. For the sound films produced from 1929 to 1933 inclusive (n = 20), Spearman’s r = 0.9525, p = <0.0001. Again we see that there is a relationship between the median as a measure of location and Qn as a measure of scale, and again this relationship is stronger for the sound films than for the silent films.

Figure 6 Median shot length v.Qn for silent short films of Laurel and Hardy, 1927 to 1929 (n = 12).

Figure 7 Median shot length v.Qn for sound short films of Laurel and Hardy, 1929 to 1933 (n = 20).

Although I have only looked at three samples of films, the relationship between location and spread noted here does appear to be relative consistent. This is useful for comparing . In ‘Some Notes on Cinemetrics III’ (here), I pointed out that using non-robust statistics can lead to false conclusions about the differences in style between two films: using the standard deviation, the lognormal shape factor, or the median/mean ratio all indicated that shot lengths in Lights of New York (1929) were more widely dispersed than shot lengths in Scarlett Empress (1934), when this was not in fact the case. Robust statistics clearly indicated than the opposite is true – namely, that shot lengths in Scarlett Empress showed greater variation. By looking at the median shot lengths of these films we would not only have been able compare their measures of location, we would have been able to make an intuitive assessment about the usefulness of measures of spread: as the median of Lights of New York (5.1s) is lower than that of Scarlett Empress (6.5s) – and possessing the knowledge that there appears to be a strong correlation between location and spread – then we could have immediately seen that there was a problem when the measures of spread indicated that shot lengths in the former were more widely dispersed than in the latter when we should have (rightly) suspected the opposite. Using the medians in this way provides us with a simple check to see if we are going to make a fundamental error in our use of statistics to describe film style, and will allow us to be more careful in making decisions about how to go about the statistical analysis of film style and how to interpret those results.

 Year n Spearman’s r p 1929 12 0.8733 0.0021 1930 11 0.9816 <0.0001 1931 14 0.9504 <0.0001 1932 17 0.9093 <0.0001 1933 13 0.9848 <0.0001