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 [18] = 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.

The relative dispersion of shot lengths

Studies comparing the change in shot length distributions in Hollywood films with the coming of synchronous sound have focused on measures of central location – the mean or median shot length of a film. The change in the mean shot length from the silent to sound era has been put at approximately six seconds, although this figure is suspect due to the asymmetrical nature of shot length distributions; while the change in the median shot length has been estimated at 2.9 seconds. Similar attention has not been paid to the change in the dispersion of shot lengths that also occurred in the shift from silent to sound cinema. In fact, it is common for mean shot lengths to be presented with no measures of dispersion at all and this severely hampers any useful interpretation of the results.

In my study of the impact of sound on shot length distributions I noted that the interquartile range of sound films was greater than those of silent films, indicating that there is greater variation in the shot length distributions of the sound films. While this method of comparing the variation of shot length distributions is perfectly fine, it is not perhaps the simplest method and using measures of relative dispersion may prove easier to interpret.

Measures of Relative Dispersion

In order to compare the relative dispersion of shot length distributions, three measures of relative dispersion were calculated for each film from a sample of Hollywood silent films produced from 1920 to 1928 inclusive (n = 20) and from a sample of sound films produced in Hollywood from 1929 to 1931 inclusive (n = 30) (see my earlier study for the descriptive statistics of these films). The mean values of each coefficient for the two samples were compared using a t-test assuming unequal variances. Calculations were conducted using Microsoft Excel 2007 and GraphPad Instat v3.10 (2009).

The three measures of dispersion considered are the coefficient of variation (CV), the quartile coefficient of dispersion (QCD), and the coefficient of median deviation (MD). The relative measures of dispersion for the silent films are presented in Table 1 and for the sound films in Table 2.

TABLE 1 Relative measures of dispersion for Hollywood silent films, 1920 to 1928

TABLE 2 Relative measures of dispersion for Hollywood sound films, 1929 to 1931

Coefficient of variation

The coefficient of variation is the ratio of the standard deviation to the mean:

CV = SD/M

The coefficient of variation for the sound films (M = 1.1912, SD = 0.2319) is greater than those silent films (M = 0.9015, SD = 0.1393), t (47) = 5.5217, p = <0.0001. On this measure of dispersion, the shot lengths of a Hollywood sound film are more dispersed by almost a third (32.14%) than the silent films.

Quartile coefficient of dispersion

The quartile coefficient of dispersion is calculated using the lower (Q₁) and upper (Q₃) quartiles of the shot length distribution:

QCD = Q3-Q1/Q3+Q1

The quartile coefficient of dispersion for the sound films (M = 0.5748, SD = 0.0617) is greater than those silent films (M = 0.4833, SD = 0.0522), t (45) = 5.6409, p = <0.0001. On this measure of dispersion, the shot lengths of a Hollywood sound film are more dispersed by almost a fifth (18.83%) than the silent films.

Coefficient of median deviation

The coefficient of median deviation is the ratio of the median absolute deviation from the median shot length (MAD) to the median shot length [1]:

MD = MAD/Median

The coefficient of median deviation for the sound films (M = 0.5825, SD = 0.0680) is greater than those silent films (M = 0.4735, SD = 0.0473), t (47) = 6.6813, p = <0.0001. On this measure of dispersion, the shot lengths of a Hollywood sound film are more dispersed by almost a quarter (23.01%) than the silent films.

Discussion

All three measures of relative dispersion provide similar results, but the coefficient of median deviation is the most reliable.

While the coefficient of variation makes complete use of the data and is the best understood of measures of relative dispersion, it relies on the mean shot length. As the distribution of shot lengths in a motion picture is typically positively-skewed with a number of outlying data points, the mean shot length is an unreliable statistic of film style. Consequently, the coefficient of variation can be expected to overestimate the dispersion of shot lengths in a film as the mean value is pulled towards the higher end of the distribution.

The quartile coefficient of dispersion is not dependent upon the mean shot length and so provides a more robust estimation of relative dispersion than the coefficient of variation. A drawback is that it uses only a limited amount of information in calculating the coefficient, and as a film may feature shot lengths that are much greater than the upper quartile it may underestimate the actual dispersion of shot lengths.

Like the quartile coefficient of dispersion, the median deviation does not use the mean shot length and can be relied upon as a more robust measure of relative dispersion. The median deviation has an advantage over the quartile coefficient of dispersion in that it uses more of the data by calculating the absolute deviation of each shot length from the median rather than relying on just two positional values. The quartile coefficient of dispersion can be regarded as an estimator of the coefficient of median deviation for the films looked at here.

In conclusion, we can say that with the introduction of synchronous sound to Hollywood in the late-1920s we not only see an increase in the median of the shot lengths of a motion picture, but also an increase in the variation shot lengths of sound films relative to silent films. Using the coefficient of median deviation we can estimate that increase to be of the order of 23%.

Notes

1. The coefficient of median deviation is based on the coefficient of mean deviation, but replaces the average absolute deviation with the median absolute deviation in order to prevent extra weight being given to shots of duration that are unusually long.

The impact of sound on film style

This post is the last of three draft papers that apply statistical analysis to questions of film style. This I focus on the impact of sound technology on shot length distributions by examining the change in the median shot length and the interquartile range. You can access the pdf here: Nick Redfern – The impact of sound technology on Hollywood film style, and the abstract is presented below.

Quantitative analyses of the impact of sound technology on shot lengths in Hollywood cinema have claimed that, with the coming of sound, the mean shot length increased from ~5s to ~11s, and that this indicates a major change in film style as cutting rates slowed. However, the mean shot length is not a robust statistic of film style due to the positive skew of the data and the presence of outlying data points in shot length distributions. The median shot length is shown to be a more robust statistic unaffected by shape of shot length distributions, and the impact of sound technology on Hollywood is analysed through looking at the median shot lengths of silent films produced between 1920 and 1928 (n = 20, median = 4.4s [95.86% CI: 3.7, 5.1]) and sound films produced from 1929 to 1931 (n = 30, median = 6.9s [95.72% CI: 5.9, 8.7]). The results show that there is an increase in shot lengths in the early sound era (Mann-Whitney U = 32.5, P = <0.0001, PS = 0.0542), but that this change is much less than that described by studies using the mean shot length (HLΔ = 2.9s [95% CI: 1.8, 4.1]). Looking at the interquartile ranges of the silent films (median = 4.8s [95.86% CI: 4.3, 5.7]) and the sound films (median = 10.7s [95.72% CI: 8.8, 12.1]), we see that there is an increase by HLΔ = 5.6 seconds (95% CI: 4.1, 7.1), indicating that shot lengths in sound films show greater variation than those of the silent era (Mann-Whitney U = 4, P = <0.0001, PS = 0.0067).

As before, I’ll leave this up for a while before submitting it to a journal (if I can find one), so feel free to comment.

Shot Length Distributions in the Chaplin Keystones

This week I have another draft of a Cinemetrics paper, this time looking at shot length distributions in Keystone films starring Charles Chaplin and directed by Chaplin, Mack Sennett, Mabel Normand, George Nichols, and Henry Lehrman. You can download the pdf here: Nick Redfern – Shot Length Distributions in the Chaplin Keystones, and the abstract is given below.

Cinemetrics provides an objective method by which the stylistic characteristics of a filmmaker may be identified. This study uses shot length distributions as an element of film style in order to analyse the films by five directors featuring Charles Chaplin for the Keystone Film Company. A total of 17 Keystone films are analysed – six directed by Chaplin himself, along with others directed by Henry Lehrman, George Nichols, Mabel Normand, and Mack Sennett. Shot length data was collected for each film and then combined to create data sets based on the studio style and for each director. The results show that for the distribution of shot lengths in Keystone films starring Chaplin (1) there is no significant difference between films directed Chaplin and the overall Keystone model; (2) there is no significant difference between Chaplin’s films and those of Lehrman, Nichols, and Sennett; (3) there is a significant difference between the films of Normand and the Keystone model but the effect size is small; and (4) there is a significant difference between Normand and the other Keystone filmmakers but the effect size of these differences is again small. This study shows that the distribution of shot lengths can be used to identify how the style of an individual filmmaker relates to a larger group style; and that, in the specific case of the Keystone Film Company, it is the studio style of fast-paced, slapstick comedy that determines the distribution of shot lengths with little variation present in the films of individual filmmakers.

As before, any comments and suggestions are welcome (as is the pointing out of glaring errors).

The raw data was collectde by examining the films frame by frame in my editing software, and can be accessed in a Microsoft Word Document here:

For Microsoft Word 97-2003 (x.doc): Nick Redfern – Shot length distributions in the Chaplin Keystones – data

For Microsfoft Word 2007 (x.docx): Nick Redfern – Shot length distributions in the Chaplin Keystones – data

Claude Hamilton Verity

This post introduces some facts and resources about the life and work of Claude Hamilton Verity, and engineer from Leeds, whose work on synchronous sound in the cinema deserves far greater mention that it gets (in histories of British cinema in particular). Included are some basic facts, some references to where Verity does appear in research on film, patents to Verity’s sound technologies, and some contemporary pieces that refer to Verity’s work.

Claude Hamilton Verity was born at Leeds in May 1880, the youngest child of Edwin and Ann Verity. Edwin Verity was an ironmonger with a workshop at . Edwin was one of the Verity Brothers who had a large premises on The Calls by Leeds Bridge. Edwin later took premises round the corner at 168 & 169 Briggate as a hardware merchant. It was these premises that Claude was later to use as his workshop, and are now Bar Fibre. These premises are also located approximately 200 metres from the building at Leeds Bridge, where Le Prince shot his footage of traffic at the Corner of Briggate, Swinegate, and The Calls.

Claude was brought up in Roundhay in the north of the city – an affluent part of Leeds that was also home to Louis le Prince and the Whitley family in the 1880s. The 1901 census has Verity listed as a student at a College of Agriculture and resident at Downton, Wiltshire. He also seems to crop up in Seacombe, nr. Liverpool, as an engineering draughtsman c.1910, and there is an engineer called Claude Hamilton Verity living in Scarborough in 1912, who is presumbaly the same person. He later moves to Harrogate (where his mother’s family were from), and then Harpenden, Hertfordshire.

Verity held many patents, including improvements to stoves, revolving doors, electric radiators, clouderising coal dust, low-temperature carbonisation, and ‘apparatus for the inhalation of medicated vapours.’ All of this suggests that he was a skilled engineer, who could turn his hand to many different things. There is also a book published in 1928, titled Industrial Prosperity, and authored by a Claude H. Verity, but I have not yet confirmed the identity of the author. It is Verity’s patents in the synchronising of sound and pictures that are of main interest to film scholars, and the following is a chronological list of the relevant patents:

• The synchronisation of machines for recording and reproducing sounds & movements. GB103407, Verity, C. H. May 11, 1916.
• Synchronization of Machines for Recording and Reproducing Sounds and Movements. Claude Hamilton Verity, of Leeds, England.  No execution date.  Filed May 23, 1917, Serial No. 170,531.  Classification 352/23. This is a US patent.
• Synchronisation of machines for recording and reproducing sounds and movements. GB165489, Verity, C. H. Jan. 28, 1920.
• Improvements in or relating to gramophones and like sound reproducing machines. GB207222, Verity, C. H. July 21, 1922
• Synchronisation of machines for recording sounds and movements and for reproducing such sounds and movements by phonograph and kinematograph. GB318847, Verity, C. H. June 5, 1928.
• Apparatus for reproducing synchronously recorded disk records and kinematograph films. GB318688, Verity, C. H. June 19, 1928.

Figure 1 Verity’s registration marks for resynchronising cut sound film (GB318688)

• Means for the synchronisation of broadcast wireless sounds and kinematograph films. GB320881, Verity, C. H. July 23, 1928.
• Improvements relating to the synchronous reproduction of picture films and disk sound records. GB321624, Verity, C. H. Aug. 13, 1928.
• Improvements relating to phonograph disc recording & reproducing machines and means for driving and synchronising same with kinematograph apparatus. GB322561, Verity, C. H. Sept. 24, 1928.
• Improvements relating to electric pick-up supports for gramophones and means for indicating the position of the needle in the record groove and to facilitate synchronous reproduction with picture projection. GB324411, Verity, C. H. Oct. 22, 1928.

Most of these patents relate to sound-on-disk systems, but Verity’s appears to have adopted an approach that is less dependent upon the technology and focuses more on the operator’s problem of keeping sound and image together. It’s a very human approach to a technological problem : for example, the 1920 patent for the  Synchronisation of machines for recording and reproducing sounds and movements uses two rows of lamps to indicate when the operator has achieved the union of sound and image by manipulating motors to bring the projector and the sound mechanism together, and which will tell the operator when they start to go out of synch.

Verity’s work attracted international attention: one newspaper report from 1922 talks about a German patent, but I haven’t been able to find this; while Verity was crossing the Atlantic to work with the Vitapgraph Company in New York. Altman (1992) mentions Verity’s arrival in New York and his demonstration of the synchronisation of music and talking pictures

Figure 2 The Ellis Island register shows Verity was met by the vice-president of the Vitagraph Co. as he disembarked from the Aquitania in 1923.

From reports in the local Yorkshire press, Verity’s system worked well and was popular. Verity apparently first demonstrated his talking pictures at the Royal Hall Theatre in Harrogate on 30 April 1921, before moving to London in June/July 1921, and then at the Albert Hall, Leeds in the first weeks of April, 1922.

A contemporary description gives an indication of how image, music, and dialogue were brought together.

Leeds Mercury, 27 June 1921

‘TALKING’ PICTURES

LEEDS MAN’S SYNCHRONISM INVENTION

The latest development in singing and talking pictures was explained at a demonstration on Saturday at the Philharmoinc Hall, London.

The inventor, Mr. Claude Verity, of Leeds, claimed to be able to synchronise perfectly the spoken word and the lip movements by the players shown on the screen.

By Mr. Verity’s system it is claimed to be possible to synchronise speeches, sounds, music, or anything that is at present being done at any of the London theatres – opera, drama, musical comedy, or revue. The inventor does not do away with the orchestra; his object is to synchronise the spoken word or song, the orchestra accompanying the gramophone while the movements are thrown on the screen.

The two productions shown on Saturday, ‘A Cup of Beef Tea’ and ‘The Playthings of Fate,’ proved that the invention has great possibilities.

The public interest in talking pictures can be gauged from this announcement of Verity’s 1922 shows in Leeds, which gives the size of the audience for the initial Harrogate run.

Yorkshire Evening Post, 3 April 1922

FILM AND GRAMPOHONE

PROGRAMME TO DEMONSTRATE A LEEDS MAN’S INVENTION

Mr. C.H. verity, the inventor of the apparatus which has made the synchronisation of film and gramophone a practical proposition, is the head of a Leeds firm of hardware manufacturers and merchants. He is presenting his talking and singing pictures at the Albert Hall, Leeds, this week. Entertainments will be given each evening, and on three afternoons. The programme consists of the first film productions under the Verity system of synchronisation.

Mr. Verity claims that the cost of these productions will be no greater than that of the majority of silent films, because it is cheaper to help out scenes and actions by words than by the multiplication of dumb show. There are interesting possibilities in the production of talking pictures in these days when the demand is all for novelty and originality in entertainment. Four performances recently given in Harrogate attracted over 5600 people.

As another report indicates, the road to the synchronisation of sound and image was long and expensive, and it is important to remember that Verity was not a research scientist for a large corporation but ran a hardware manufacturers in the centre of Leeds.

Yorkshire Evening News, 1 April 1922

SPEAKING FILMS

LEEDS MAN’S SYSTEM PATENTED IN GERMANY

SYNCHRONISATION ACHIEVED

Mr. Claude H. Verity, the Leeds inventor, is making a bold bid to enlist the sympathies of the public in his talking and singing pictures. He claims that he has definitely and absolutely solved the problem of the synchronisation of the voice with the picture on the screen.

For over three years he has been perfecting his idea, and so fa it has entailed a cost of £7000, but now to quote his own words: ‘With my system of synchronisation I can guarantee to keep this relation of sound and lip movement under synchronous control to within one-twenty-fourth of a second for any length of time.’

Next week at the Albert Hall, Leeds, the local public will have its first opportunity of judging the merit of the invention.

The solving of the problem of synchronisation was proved and admitted by the critics at Mr. Verity’s first trade show in Harrogate. There was criticism, Mr. Verity says, not in regard to the question of synchronisation, but in regard to the sound productions of the gramophone used.

CLAIM ADMITTED

Mr. Verity has given many trade shows in various parts of the country, and never once has his claim to have solved the synchronisation problem been doubted. The only thing he needs he points out, is what might be termed a super-gramophone, and in this connection it may be stated, Mr. Verity has gone some way to meet this need.

By the means of electric amplification and a new design of gramophone horn, the inventor ensures that the spoken word is clear and easily distinguishable.

Very shortly a company is to be formed, and with the necessary financial backing the invention should not fail to succeed.

Mr. Verity claims that everything in the way of singing or speaking can be synchronised by means of his method. He also wishes to make it clear that he does not intend to work on the lines of a monopoly in regard to his invention.

PATENTED IN GERMANY

Mr. Verity does not suggest that the whole programme in all the countless picture-houses should be entirely devoted to ‘talking pictures;’ he introduces the idea with a view to an enjoyable variation in the programme.

The ‘Yorkshire Evening News’ is able to add that Mr. Verity has now had his ‘talking-picture’ idea patented in Germany. This is itself proof that he has not encroached on any previous idea on this point. The German system of granting patents is different to the British system.

Here a patent is granted after a search through British patents only; in Germany the patents of all nationalities are first scrutinised.

For all this effort, Verity does not get much of a mention in histories of British cinema, but he is mentioned on occasion. As noted above, Altman (1992) mentions Verity’s visit to the US and he features in The New York Times Encyclopedia of Film (1984),  which suggests that there are references in the New York press to the demonstrations of the Verity system. There is also a reference to Verity’s trip to New York in Gramophone in October 1926, albeit a reference that is inconclusive (I haven’t found the original report):

The problem of synchronizing films and records has been solved if we are to believe the reports of the demonstration of the Vitaphone in New York. There is an excellent and full account of the problem and of the solution in the Wireless World for September 15th. Three years ago we reported the departure of Mr. Claude Verity, who was experimenting in the subject, for America ; but it is not said whether he is at the bottom of the Vitaphone. It is the Western Electric Co.’s patents which have made the synchronization possible, worked in conjunction with Warner Brothers’ Pictures Inc (22).

Verity is also mention by M. Jackson Wrigley (1922: 115-116), who refers to the ‘invention of a synchronizer by Mr. Claude H. Verity, a Harrogate engineer, enables the operator, by simply sliding a knob, quite independently of observing the screen, to work synchronization to 1-24th of a second.’

References

Altman, D. (1992) Hollywood East: Louis B. Mayer and the Origins of the Studio System. New York: Carol Publishing Group.

Jackson Wrigley, M. (1922) The Film: Its Use In Popular Education. London: Grafton.

The New York Times Encyclopedia of Film, edited by Gene Brown New York: New York Times Books, 1984

Improvements relating to electric pick-up supports for gramophones and means for indicating the position of the needle in the record groove and to facilitate synchronousreproduction with picture projection

United Kingdom GB324411, Published 1930-01-22, Claude Hamilton Verity
324,411. Verity, C. H. Oct. 22, 1928.

Power functions and the mean relative frequency of shot scales in motion pictures

UPDATE (26 October 2009): This post has been getting a lot of traffic recently, and I think it is important to point the reader in the direction of a follow up post (here) where I point out that while the use of rank-frequency plots is useful for analysing film style (see here, for example) the power laws approach is not. This is not to say that films or groups of films will not be described by a non-linear power model, but other non-linear models (logarithmic, exponential) are also evident and there does not seem to be any general rule for which model can be applied to specific types of films (e.g. genres, eras, etc.). In general, a power laws approach to the distribution of shot scales is not going to get you anywhere – certainly not to the extent that I suggest in this post. I’ll leave this post here because there is still some useful information, and it’s also nice to see how wrong you can be.

Power functions describe a wide range of social phenomena, from the distributions of city size to the popularity of websites, the citations of academic papers, and the frequency of words in the corpus of a language (Schroeder 1991: 33-38, 103-119; Newman 2005). While power functions have been used for over half a century in analysing language and communication (e.g. Zipf’s law) they have yet to be applied to the empirical analysis of film style. This brief survey looks at the applicability of power functions in describing the distribution of the mean relative frequency of shot scales in the films of two directors – Alfred Hitchcock and Fritz Lang – whose careers encompass both European and Hollywood filmmaking.

Data on the frequency of shot scales was collected from the Cinemetrics database. Seven shot scales were used – big close-up, close-up, medium close-up, medium shot, medium-long shot, long shot, and very long shot (see Salt 2006). The relative frequency of shot scales in a motion picture was calculated by dividing the frequency with which each scale occurred by its normalising value (~500), and this data was then ranked from the event of the highest frequency to the lowest. The average value of the seven ordered relative frequencies was taken to give the mean relative frequency of each shot scale, thereby removing the problem of films that have zero frequency for a particular shot size. This data was then used to calculate predicted values for linear regression (f(x) = ax+b, where a is the slope and b is the intercept of the regression line) and power regression (f(x) = cx^α, where c is a constant equal to the frequency of the most frequently occurring scale and α is the exponent of the distribution such that Σ f(x) = 1). The coefficient of determination (R²) was used as a measure of goodness-of-fit for the predicted mean relative frequencies to the empirically observed values.

Data on shot scales was taken from the Cinemetrics database for 43 films directed by Alfred Hitchcock between 1925 and 1963, of which 23 were produced in the UK between 1925 and 1939; and from 21 films directed by Fritz Lang between 1919 and 1955, of which 11 were produced in Germany between 1919 and 1933. The results are presented in Table 1, and show that power regression provides the better model only for Lang’s German films, while for the other classes the linear model is superior. These results can be seen clearly in Figures 1-4, in which the observed values and the linear and power regression lines are plotted on linear axes. (The power regression line is straight when the log rank is plotted against the log frequency).

Table 1 Linear and power regression for the films of Alfred Hitchcock and Fritz Lang

Table 1 also shows that while the distribution of the mean relative frequencies of shot scales in the films of Alfred Hitchcock are consistent for his British and Hollywood films, there is a change in Lang’s style in his shift from Germany to Hollywood. It is also worth noting the similarity in the figures of R² for both linear and power regression for Hitchcock’s and Lang’s Hollywood films, which suggests that both filmmakers are working within a consistent institutional style (such as classical Hollywood cinema) rather than auteurist idiosyncrasies. The value c is the mean relative frequency with a rank of 1, and this too is similar for Hitchcock and Lang’s Hollywood films, reinforcing the idea of an institutional style. This does not, however, account for why Hitchcock’s British films are so similar to his Hollywood movies. It is possible that German cinema in the 1920s was different from British and Hollywood cinema in general, and that British films style was influenced by Hollywood, but a larger scale study is needed to resolve these questions.

Figure 1 Linear and power regression for the mean relative frequency (MRF) of shot scales in Alfred Hitchcock British films, 1925-1939

Figure 2 Linear and power regression for the mean relative frequency (MRF) of shot scales in Alfred Hitchcock’s Hollywood films, 1940-1963

Figure 3 Linear and power regression for the mean relative frequency (MRF) of shot scales in Fritz Lang’s German films, 1919-1933

Figure 4 Linear and power regression for the mean relative frequency (MRF) of shot scales in Fritz Lang’s Hollywood films, 1936-1956

Table 1 also shows that while the distribution of the mean relative frequencies of shot scales in the films of Alfred Hitchcock are consistent for his British and Hollywood films, there is a change in Lang’s style in his shift from Germany to Hollywood. It is also worth noting the similarity in the figures of R² for both linear and power regression for Hitchcock’s and Lang’s Hollywood films, which suggests that both filmmakers are working within a consistent institutional style (such as classical Hollywood cinema) rather than auteurist idiosyncrasies. The value c is the mean relative frequency with a rank of 1, and this too is similar for Hitchcock and Lang’s Hollywood films, reinforcing the idea of an institutional style. This does not, however, account for why Hitchcock’s British films are so similar to his Hollywood movies. It is possible that German cinema in the 1920s was different from British and Hollywood cinema in general, and that British films style was influenced by Hollywood, but a larger scale study is needed to resolve these questions.

This survey has shown that while power functions can be used to describe the distribution of mean relative frequencies of shot scales in motion pictures, they cannot be applied universally and linear functions may provide a better means of modelling film style. These distributions may be used as a measure of film style in order to distinguish between different groups of films. However, this approach cannot tell us what changes in the use of shot scales have occurred. It is necessary, then, to look more closely at where the continuities and discontinuities lie. As I have shown elsewhere, in there is a shift in the use of particular shot scales in the films in the films of Hitchcock and Lang when they arrive in Hollywood (Redfern 2009, unpublished). For both directors we find that there is a shift from distant shots to closer framing. Armed with the knowledge that different regression models explain the distribution of the mean relative frequencies of shot scales for Hitchcock and Lang prior to their arrival in Hollywood, we can extend this argument to state that: (1) Hitchcock’s Hollywood films feature closer framing than his British films, but there is no change in the distribution of the mean relative frequencies of the scale overall; and, (2) Lang’s Hollywood films feature a large change in the distribution of the mean relative frequencies as well as a shift to closer framing. In Lang’s German films it is the long shot that dominates, while in his Hollywood films there is no single shot scale that determines the films’ style.

References

Newman, M.E.J. (2005) Power laws, Pareto distributions, and Zipf’s law, Contemporary Physics 46 (5): 323-351.

Redfern, N. (2009) Shot scales in the films of Fritz Lang.

Redfern, N. (unpublished) Cinemetric analysis of shot types in the films of Alfred Hitchcock.

Salt, B. (2006) Moving into Pictures: More on Film History, Style, and Analysis. London: Starwood.

Schroeder, M. (1991) Fractals, Chaos, and Power Laws: Minutes from an Infinite Paradise. New York: W.H. Freeman & Co.

Does the Heftberger Correlation exist?

Cinemetrics is the statistical analysis of film style (Salt 1974), and has the potential to make a significant contribution to film studies in identifying trends in film style (shot length distributions, shot scales) that will allow scholars to explore questions of individual style, genre, studio style, national differences, and changes in style over time. However, the potential of cinemetrics is hamstrung by the poor quality of the statistics practised by film scholars. For example, in a discussion of Salt’s (2006) survey of shot length distributions, Buckland (2008) recently confused the coefficient of determination (R² as a measure of goodness-of-fit of a regression line) with the correlation coefficient (r) – although the two are intimately related. Similarly, O’Brien (2005: 88-93) has argued that the introduction of sound technologies in Hollywood and France in the late-1920s led to an increase in average (mean) shot lengths (ASL) but does not employ any tests (e.g. t-test, one-way ANOVA, chi-square, or their nonparametric equivalents) to determine if changes in ASL are significant, does not provide confidence intervals for estimates of ASL in a particular country or time period, and does not consider the use of the median as a measure of central tendency or data transformations for skewed shot length distributions. Here I discuss a particular mis-application of statistics in the analysis of film style: the so-called Heftberger Correlation between cutting rate and type of motion represented in Man with a Movie Camera (Dziga Vertov, 1929).

The Heftberger Correlation

The herculean effort of a meticulous statistical analysis of Vertov’s Man with a Movie Camera (MWMC) offers the potential for a rich and detailed understanding of this complex film’s intricate style, and has been undertaken by Yuri Tsivian, Adelheid Heftberger, Barbara Wurm, and Gunars Civjans. As a part of this project, data has been produced that covers the distribution of shot lengths for each reel and for the film overall, for the use of point-of-view shots, and for the relationship between shot length and the type of motion represented by the film. It is as a statistic of this last element of film style that the Heftberger Correlation (HC) has been proposed as a measure (Cinemetrics 2008).

The researchers hypothesised that the cutting rate would increase with the intensity of movement within a shot, which was defined as belonging to one of seven categories: black frames (BF), fast motion (camera) (FastC), fast motion (naturally) (FastN), freeze-frame (FF), no motion (NM), normal motion (naturally) (NormalN), and slow motion (camera) (SMC). Once the dataset employed was reduced to exclude the category BF, it was claimed that there is a correlation between cutting speed and intensity of motion. For MWMC, the value for HC including NM is 0.2, and excluding NM it is 0.4. A further step was to remove the category FF, so that only data for shots with movement were included to give the Particular Heftberger Correlation (PHC), and is was claimed that this produced a stronger correlation but no figure was supplied. The conclusion arrived at by the researchers is that (1) the HC exists; (2) the HC for MWMC is weak and nonlinear; and (3) the PHC is MWMC is stronger than the HC and is linear.

It is far from clear what statistical processes have been used in the calculation of the HC and the PHC, and I have been unable to reconstruct the process by which the above quoted values for HC were derived. The researchers themselves acknowledge that the processes involved in producing the plots of shot length and intensity of movement in Figure 1 are not ‘mathematically sound,’ and it is precisely these plots that are employed as justification that the HC exists. It does not appear to have occurred to anyone involved that the lack of mathematical ’soundness’ would present a problem in employing a statistical analysis.

Figure 1 The Heftberger Correlation in Man with a Movie Camera (1929) (Source: http://www.cinemetrics.lv/movie.php?movie_ID=2311, accessed 9 April 2009)

What is clear is that correlation is not an appropriate statistical method to be employed in this analysis. Correlation is a method of analysing if pairs of variables are related and the strength of that relationship. The pairing of the variable is important: each point on the graph represents a value on the x-axis and a value on the y-axis For example, if we measure the height and weight of ten people, we will have ten pairs of data, with each pair consisting of a measure of height and a measure of weight – it is the relationship between these measures that we call a correlation. The Heftberger Correlation does not exist simply because it is not possible to calculate a correlation for pairs of data when the number of categories of motion intensity is seven and the number of shots in the film is 1729 – there are no pairs of data to correlate. Data does not appear to be ordinal – although order exists for some categories (FastC is quicker that SMC) it does not exist for others (BF) and the distinction between some categories is not ordinal (FastC and FastN). The data labels used in Figure 1 must be considered nominal and a re not tractable. The decision to proceed despite the lack of mathematical ’soundness’ is compounded by a lack of understanding of the mathematics of correlation.

The appropriate statistical approach to be used in analysing the relationship between shot length and motion intensity is to look at the variance of shot lengths in each category. In this case the data does not meet the requirements for a parametric one-way analysis of variance (ANOVA), and a logarithmic transformation of the data is no help either. The best approach, therefore, is to employ a nonparametric analysis of variance of ranks using a Kruskal-Wallis test and Mann-Whitney U as a post-hoc test (α = 0.05).

Shot length data was sorted by category of motion intensity, and the descriptive statistics are presented in Table 1.

Table 1 Shot length data for motion intensity in Man with a Movie Camera (1929)

In analysing this data I include only four of the motion categories: FastC, FastN, NM, and NormalN. The distribution of shot lengths in these categories are represented in Figure 2.

Figure 2 Distribution of shot lengths in FastC, FastN, NM, and NormalN in Man with a Movie Camera (1929)

BF is excluded as the data includes several shot lengths of 0.0 seconds (due to a technical error in data collection); while the number of shot lengths in FF (13) and SMC (32) are too small to be reliable. The results show that there is a statistically significant relationship between shot length and intensity of motion (H_c = 289.7, P = <0.0001); and the post-hoc tests show that each category is significant different from one another (Table 2).

Table 2 Pairwise comparisons of shot length/motion intensity data for Man with a Movie Camera (1929) (Mann Whitney U, P-values only (Bonferroni Corrected α = 0.0083))

These results show that Tsivian, et al. were correct in their hypothesis that there is a relationship between shot length and motion intensity in Man with a Movie Camera; in fact, the results presented here indicate that this relationship is stronger than that identified by the HC. Focussing on the median shot length (see Table 1), we can see that FastC (0.4 seconds) has a quicker cutting rate that FastN (0.9s), while NormalN has a value of 2.8s. Although they were not included in the above test, median shot length increases as motion slows in SMC (3.7s) and FF (4.0s), and this confirms the overall relationship between shot length and motion intensity. Only NM does fit this overall pattern, with a median shot length of 2.2s. Data for BF is unreliable at the low end where shot lengths equal 0.0s.

Conclusion

Ben Goldacre, the GP and journalist who publishes the Bad Science blog (see Goldacre 2008), has made a distinction between scientific medicine and alternative therapies that employ scientific terms inaccurately to sound ’sciency.’ The Heftberger Correlation sounds good, it sounds scientific, it sounds statistical; but it is not based on a sound understanding of statistical methodology. Following Goldacre, I think this use of statistical terminology should be labelled ’sciency’ rather than science and film scholars should be discouraged from declaring the existence and relevance of such ’statistics’. It is incumbent upon film scholars to understand the statistical methods that they wish to employ in cinemetrics and to respect the use statistical terminology. Cinemetrics can make a positive contribution to film studies, but before it can be good film studies it must first be good statistics.

References

Buckland, W. (2008) What does the statistical style analysis of film involve?,
Literary and Linguistic Computing 23 (2): 219-30.

Cinemetrics (2008) http://www.cinemetrics.lvmovie.php?movie_ID=2311, accessed 9 April 2009

Goldacre, B. (2008) Bad Science. London: Fourth Estate.

O’Brien, C. (2005) Cinema’s Conversion to Sound: Technology and Film Style in France and the U.S. Bloomington: Indiana University Press.

Salt, B. (1974) Statistical style analysis of motion pictures, Film Quarterly 28 (1): 13-22.

Salt, B. (2006) Moving into Pictures: More on Film History, Style, and Analysis. London: Starwood.

The distribution of picture halls in Leeds, 1910 to 1939

The Cinematograph Act, 1909, placed the regulation of the exhibition of motion pictures in the hands of local authorities. In Leeds (as in many other British cities), the Watch Committee of the City Council was responsible for licensing and regulating places of exhibition in the city. The proceedings of this committee and the Council in general provide a great deal of information on the development of exhibition in the city, including data on the location of theatres, the licensees. Here, data from the council proceedings is used to map the development of motion picture exhibition in Leeds from 1910 to 1939 (see Preedy 2005 for an overview). By looking at the income from the issuing of cinematograph licenses we can follow how the size of the exhibition market in the city changed over time, and this information is presented in Figure 1. The development of motion picture exhibition after the introduction of the Cinematograph Act, 1909, in Leeds can be divided into three phases: a period of rapid growth from 1910 to 1913; a first wave of expansion from 1913 to the early 1920s; and a stable period from 1921 to the beginning of World War Two. Changes in the distribution of picture halls are examined by looking at four years – 1914, 1922, 1931, 1939 (see Table 1) – that are (roughly) evenly spread across the three decades covered.

Figure 1 Revenue from licenses issued under Cinematograph Act, 1909 (Source: Leeds City Council Accounts)

The first phase in the development of motion picture exhibition in Leeds after 1909 is primarily comprised of the licensing of existing premises. The first picture hall to be licensed was the Coliseum on Cookridge Street. It is interesting to note that an early decision of the Watch Committee was to license premises that had been exhibiting moving pictures prior to the passage of the 1909 Act without requiring them to meet the safety measures specified, particularly the need to isolate the projector from the auditorium. For the most part these premises were the larger theatres in the city (including the Empire, the Hippodrome, City Varieties, and the Queen’s), and so were already subject to licenses for music and dancing. Also among this group were public halls (e.g. Salem Central Hall, Albert Hall).

Although some purpose built theatres were opened prior to 1913, the majority of the licensed premises are converted premises. The Cottage Road Cinema, Headingly, opened in 1912 (and is arguably the oldest continually operating theatre in the world) at the site of a former stable (and later garage) built in 1835. The Palace Cinema at Eyres Avenue, Armley, was opened as a cinema following the decline of the skating rink in the same premises – although the rink did not entirely disappear, and the site appears to have been dual use for a number of years. Early demands of the Watch Committee focus on the safety aspects of the new entertainment, with routine demands for fire extinguishers, panic bolts, improvements to ventilation and lighting, and the clearing of all aisles – all subject to the inspection of the Chief Constable and the City Engineer. Occasionally, licenses were granted on the submission of plans; and the whole business of licensing theatres appears to have taken up a significant amount of the committee’s time: on 22 October 1912, the minutes of the Committee show that nine resolutions were passed, all of which related to the exhibition of motion pictures.

Early cinema proprietors were also converts: the Cottage was operated by Owen Brooks and George R. Smith, the former being a photographer; and Allan Nield, another photographer, ran the Malvern Picture House in Beeston and the Hill Crest in Harehills at one time or another. In fact, Brooks and Nield appear to have lived close to one another in the Beeston/Dewsbury Road area, along with other proprietors such as the confectioner Frederick S. Brier. Another cluster of proprietors develops on the other side of the city in Roundhay (once home to inventor of the cinema, Louis Le Prince), including the lithographic printer Charles Lightowler who opens a theatre in Hunslet near his print works; Arthur Cunningham, a household furnisher; and Harry Bagges Hylton, a builder. Other trades of proprietors include a rag merchant, a ladies’ tailor, Pattern makers, a city councilor and the secretary to the City Council, and a number of estate agents. Typically, then, in this early phase the proprietor of a Leeds cinema was a local businessman with the funds to spend on exhibiting motion pictures. The large theatres in the city centre were already part of existing entertainment chains or already had in place a management structure that could be easily adapted, and the licensees of these shows are more often managers than proprietors.

The boom in picture halls in Leeds takes off in 1913, with a surge in the number of new builds and this is reflected in the increase in license fees collected by the council. That a second increase follows in 1921 suggests that the First World War interrupted the growth of the exhibition market in the city. The distribution of picture halls in Leeds in January 1914 is presented in Figure 2. The high number of licensed premises in the city centre is unsurprising; but it should be noted that this number includes premises used for alternative entertainments (i.e. theatres, public halls, church halls, etc.) and these ‘other use premises’ account for approximately half of the picture halls in this part of the city. The number of licensed premises in the city centre in which the exhibition of motion pictures is the primary purpose of the building is then no greater than in other parts of Leeds. Attending the cinema in the city can be associated with other leisure activities that are not present in the single-use theatres in areas outside the civic centre. It is outside the city centre that purpose-built cinemas are to be found, while in the centre premises are adapted and converted, but these picture halls are distributed unevenly across the city. Hunslet and Holbeck are both densely populated areas comprised primarily of back-to-back housing and industrial premises, but the former has a substantially greater number of theatres. Over time, the distribution becomes more even (see Figures 3-5) and by 1922, Holbeck has gone from three cinemas to six while Hunslet has gone from nine to six.

Clues as to why the distribution of picture halls in the city adopted this pattern shortly after the introduction of the Cinematograph Act in 1909 can be found in the trade directories for Leeds. What this comparison reveals is that the distribution of picture halls is – to a significant extent – a matter of convenience for the proprietors. For example, the Imperial Picture House at 79 Kirkstall Road opened by William Ogden and William Fielding in 1913 is located next door to the workshop (at 77 Kirkstall Road) of William Ogden, tinplate manufacturer. Kelley’s 1911 directory for Leeds lists 10 Alpha Street, Hunslet, as the premises of Harry Rodger, estate agent; while the council minutes reveal that the conversion of this property for the purpose of exhibiting motion pictures under license to Rodger was approved (subject to modifications) on 10 February 1911. Joseph Battersby, a marine store dealer at Place’s Road in Cross Green in 1911 is listed as the licensee of the East End Picture Hall at the same location in 1914. Clifford Lax, owner of a building company and estate agent based on Harehills Lane, opened the Harehills Picture House at the corner of Roundhay Road and Harehills Lane. Lax built a number of cinemas in Leeds, and appears to have entered the picture trade after building theatres for others.

What is also notable comparing the distributions of 1914 to 1939 is the overall consistency in the distribution: the exhibition market in Leeds is remarkably stable, and it is only towards the end of World War Two that closures become common. Even then, most areas of the city continue to have at least one theatre until well into the 1960s. The transition to sound had no impact on the distribution of theatres in the city. The years surrounding the introduction of sound show much less variation in license income (Figure 1), but this appears to be a short-lived phenomenon. The majority of the theatres open in 1922 are open in 1931. The costs of converting to sound may have been high – as many historians of the cinema have noted (see, for example, Jancovich et al. 2003 and Hanson 2008) – but this does appear to have perturbed exhibitors in Leeds: comparing the list of licensed theatres from 1927 and 1931 we see that one site has disappeared from the list while two have been added. In fact, of the fifty seven picture halls in Leeds licensed in 1914, 33 are still operating in 1939. In the latter phase, there is also the spread of motion picture exhibition into areas of the city away from the main metropolitan core (such as Meanwood, Middleton, and Moortown), accompanied by an expansion of the city boundaries that can be seen to contribute to the increase in council revenue from licensing.

Most the cinemas in the city in 1914 are individually controlled, and many cinemas remain independent until well after World War Two. Overtime, the presence of theatre chains becomes more marked. Some are national circuits (Provincial Cinematograph Theatres, Gaumont British), with several smaller, local chains. By 1911, Charles P. Metcalfe and Thomas Thompson own two cinemas – though they soon break up their partnership. Goldstone Cinemas Ltd operate a number of picture houses in the South and East of the city, opening the Victoria in Burmantofts in 1912 (replaced by the Star in 1938), the Wellington Picture House in 1920, and the Regal in Hunslet after 1927. John Robert Sharp runs two picture halls under the name Atlas in Sheepscar and Kirkstall, although he finds himself frustrated by the demands of the Watch Committee in refusing his applications changes to his auditorium (although the precise nature of the requested changes are not made clear). Often, when the decision of the Committee is not to the applicant’s satisfaction, a solicitor is brought in to argue a case, but this appears to have been a largely unsuccessful strategy.

More prosperous areas (e.g. Roundhay) have no theatres, although this should not lead us to assume that there are no middle class patrons. It appears likely that working class audiences attended the cinemas in their area of Leeds, while middle class audiences attended the larger theatres in the city. Parts of modern day Leeds that do not appear here (e.g. Horsforth, Otley, etc) were also well served with cinemas, but did not come under the control of Leeds City Council until much later.

Table 1 Premises licensed by Leeds City Council (Annual licenses) under the Cinematograph Act 1909

Figures 2 to 5 chart the change in distribution of licensed picture halls in Leeds from 1914 to 1939. In each case, data was taken from the annual renewal of licenses list published by the Watch Committee of Leeds City Council in January of each year.

Figure 2 Distribution of premises licensed by Leeds City Council, 7 January 1914

Figure 3 Distribution of premises licensed by Leeds City Council, 4 January 1922

Figure 4 Distribution of premises licensed by Leeds City Council, 7 January 1931

Figure 5 Distribution of premises licensed by Leeds City Council, 4 January 1939

KEY: ARM – Armley; BEE – Beeston; BRA – Bramley; BUR – Burmantofts; BUY – Burley; CHA – Chapel Allerton (including Chapeltown); CRG – Cross Gates; CRN – Cross Green; HAR – Harehills; HEA – Headingly; HOL – Holbeck; HUN – Hunslet; KIR – Kirkstall; LEE – Leeds; MEA – Meanwood; MID – Middleton; MOO – Moortown; SHE – Sheepscar; STA – Stanningley; WOO – Woodhouse; WOR – Wortley.

References

Hanson, S. (2008) From Silent Screen to Multi-screen: A History of Cinema Exhibition in Britain since 1896. Manchester: Manchester University Press.

Jancovich, M., Faire, L., and Stubbings, S. (2003) The Place of the Audience: Cultural Geographies of Film Consumption. London: BFI.

Preedy, R.E. (2005) Leeds Cinemas. Stroud: Tempus Publishing Ltd.