Graphing UK box office performance

The UK Film Council box office archive has a large amount of financial data on the performance of films released in the UK, including the weekend gross, total gross, the number of screens, etc. Unfortunately this data is only available for several weeks for UK films, as once a film drops out of the top 15 weekend grosses data is no longer provided. This does, however, make it possible to understand how UK films perform at the box office, and how the few non-UK films that last more than a few weeks in the top 15 compare against them. This data can be very revealing.

For example, although individual films may make or lose money according to their budget and their success in finding an audience, most UK films released in the UK follow the same pattern of decline in their weekend gross (the 3-day weekend from Friday to Sunday) and growth in their cumulative total gross. (Here I have removed any gross from preview screenings to make direct comparisons between patterns in the 3-day gross easier). In general, the decline of the 3-day gross over successive weeks follows an exponential pattern while the growth in the cumulative gross follows a logarithmic pattern. We can see that the longer a film is on release the less money it is able to wring from its audience, and that over time the graphs for both the weekend and total gross flatten out. This makes it possible to see the importance of the opening weekend to a film in a way that it is not really possible by simply reporting the record breaking figures. As I will show below, the opening weekend records are of less interest than the relationship between consecutive weeks on release.

This gives rise to a distinctive graph shaped like a blade or a bird’s beak, and in Figures 1 to 4 such graphs are provided for four UK films. The trendlines are exponential for the 3-day gross and logarithmic for the cumulative total gross, and in each case the coefficient of determination is provided. These four cases illustrate a general pattern that can be used to describe the box office performance of British films, but occasionally the 3-day gross may be better fitted by a power regression curve (where the decline after the opening weekend is very steep [e.g. Venus (2006)]), or a logarithmic curve (where the decline is marginally less than might be expected [e.g. Miss Potter (2006) – although the difference here is very marginal: R² (exp) = 0.9364, R² (log) = 0.9665]).

Figure 1 Box office data for Quantum of Solace (2008)

Figure 2 Box office data for The Duchess (2008)

Figure 3 Box office data for Angus, Thongs, and Perfect Snogging (2008)

Figure 4 Box office data for The Dark Knight (2008)

While the above graphs may be thought of as representing the general pattern of performance for UK films at the UK box office, visualising data in this way makes it possible to identify those films that buck the trends in gross performance. For example, in Figures 5 and 6 we have two films (Atonement [2007] and The Boy in the Striped Pyjamas [2008]) that experienced a far less severe decline in their 3-day gross. In both these films, the 3-day weekend gross declines in a linear pattern indicating that, unlike The Dark Knight say, these films were able to draw an audience in a much more consistent fashion over the first eight week of their release. In fact, for The Boy in the Striped Pyjamas the weekend gross increases from week 3 to 4. However, in both cases the total gross continued to grow at a logarithmic rate suggesting that this continuing strong performance was not replicated during the period Monday to Thursday for each week of release.

Figure 5 Box office data for Atonement (2007)

Figure 6 Box office data for The Boy in the Striped Pyjamas (2008)

On other occasions, we can find exceptional patterns that indicate the very strong success of films at the box office. Mamma Mia! (2008) was the top performing film at the UK box office in 2008 and is the number grossing film in the history of the UK cinema. Plotting the 3-day and cumulative total gross for this film requires two graphs (Figure 7), and reveals that the 3-day gross declined at an exponential rate, while the total cumulative gross grew at a linear rate. This suggests that the weekend box office performance is of less importance to the sustained success of Mamma Mia! than the attendance of audiences during the week.

Figure 7 Box office data for Mamma Mia! (2008)

Avatar (2009) looks set to beat Mamma Mia! to the all-time number one spot at the UK box office by Sunday after only 8 weeks on release. Looking at the linear trend for the total gross this is hardly surprising (Figure 8). What is remarkable is the absence of any trend for the 3-day gross data. This is due to the timing of the films release in the UK: the film was released on 18 December 2009 (excluding previews) and so it crossed the Christmas holiday period. This is important as, unlike the rest of the world, cinemas in the UK are closed on Christmas Day, and as this fell on a Friday in 2009, with the Boxing Day bank holiday held over to Monday 28 December, the ability of the audience to access the film at the weekend was severely restricted. This is why there is a large drop from week 1 to week 2 followed by a large increase to week 3. The film has proved to be remarkably resilient at the weekend with a rise from week 4 to week 5, and over the period of release so far it is only the Christmas weekend when the 3-day gross has fallen below £4.7 million. Due to the continuing sustained performance at the weekend there is no trendline that can be adequately fitted to the data. Avatar really is unlke any film released at the UK box office.

Figure 8 Box office data for Avatar (2009)

Getting data out of cinemetrics

The Cinemetrics database has a lot of shot length data that you can access freely, but it is not necessarily in the form in which you can get the most out of it. Although some summary statistics are given (mean, standard deviation, minimum, maximum) are given, we may want other statistics (e.g., the median and the median absolute deviation, the lower and upper quartiles, the geometric mean and multiplicative standard deviation) from the data. You may also want to produce some different graphical representations of shot length data (box plots, empirical distribution functions) than the polynomial graph that Cinemetrics automatically produces. In order to calculate these statistics we need to have the value of each shot length.

Various scholars have calculated mean shot lengths by counting the number of shots in a film, and then dividing the running time by this figure. This is useless because you only get the mean shot length (which is not a helpful statistic when shot length data is typically skewed), and you do not get any measure of the dispersion around the mean. It is also a lot of effort for very little reward, as there is very little you can do with this one figure. Having the length of each shot is always preferable, and reports of statistics of film style  done using the count and divide method should be viewed with suspicion.

But never fear – the Cinemetrics database has the length of each shot within it. You just need to get at that data. I have described this procedure in an earlier post (here), but it will be useful to repeat it. First, you need get some data, and for the purposes of this demonstration we will use Charlie Chaplin’s His New Job (1915). (The data for this film at the Cinemetrics database is here). Next you need to disconnect the data in the web page from the software that draws the graph, and you can do this by working offline: in your browser, go to the File menu and click ‘Work offline’ (you may need to disconnect from the internet, and if you are on a network this may present its own problems). Now tell the web page to redraw the graph (e.g. set the height to ‘300 pix’ and click Redraw) – a lot of red text should appear, but will not be able to disappear (see Figure 1). This is all the shot length data for the film.

Figure 1 Shot length data becomes visible for His New Job (1915) by separating the data from the Cinemetrics software

Now you can see your data, what should you do with it? Well you could type it into a spreadsheet, which isn’t too bad for His New Job as it only has a total of 175 shots. With practice and patience, you can quickly and accurately enter a lot of data in a spreadsheet. This is, however, a laborious and time-consuming process, and while you can save your work and come back to it later, it soon becomes tedious if a film has a lot of shots or if you are working with data fro a lot of films.

What is needed is a quicker method, and if you are using Microsoft Excel then the following procedure can be used. (If you are using a different spreadsheet, then what follows may still be easy to do but you will need to work out the precise details according to how the spreadsheet and its functions are set up). I’m using Excel 2007 here, but earlier versions will have the same functions that are used here.

The first step is to get the shot length data on to the screen as outlined above.

The next step is to select the red text, and copy and paste it into Excel. How you paste the data is important: right-click on the cell in which you want to paste the first line of the data and select Paste Special, and then in the dialogue box that opens select Text, and click OK. What you should be left with is a spreadsheet with all the text from the Cinemetrics web-page, in which every line of text occupies a single cell in the spreadsheet (see Figure 2).

Figure 2 Text pasted into an Excel spreadsheet.

Now the shot length data is in our spreadsheet, but is not in a usable form due the presence of the text in the same cell. For example, cell B4 in Figure 2 contains “Shot Length: 4.8 sec.”, and we only want the numerical part of this cell (the “4.8″). Using the Replace function we can eliminate the text and be left with just the numbers. In Excel 2007, the Replace function is located on the far-right of the Home tab, or you can open the dialogue box by pressing CTRL+H. (Earlier versions of Excel will have a similar function located in one of the drop-down menus). Once you have opened the Replace function dialogue box, enter “Shot length: ” into the Find what box and leave the Replace with box empty (see Figure 3). Click Replace All.

Figure 3 Using the Replace function to eliminate text and leave behind data

Repeat this process by entering ” sec.” into the Find what box, leave the Replace with box empty, and click Replace All. You should now be left with a spreadsheet in which the shot length data remains without any text. This makes it possible for Excel to recognise the numbers as numbers, and is much quicker than typing all the data out.

But we need to complete a final step before the shot length data is in its final form, and this relies upon using the VLOOKUP function in Excel. If we are trying to save time, we don’t want to waste effort deleting all the rows between the shot length values, and using VLOOKUP we don’t have to.

First, number all the cells from 1 to whatever so that the data for each shot length falls in a cell that is a multiple of 4 (assuming advanced data entry into the Cinemetrics database – for simple data entry the shot length data won’t land in every fourth cell and you will need to adjust the numbering accordingly, either way the same principle applies). See Figure 4 for an example. This can be done very quickly using Excel’s Autofill function.

Figure 4 Numbering data cells

Now we need to tell Excel to look up the value of every fourth cell, using VLOOKUP (which means Vertical Look-up). (If you’re not sure how the VLOOKUP command works, check the helpfile in Excel). To do this, create a number list of multiples of four starting at 4, again using Excel’s Autofill function. This list needs to include every multiple of four that corresponds to a shot length in the data, and as there are 175 shots we need to go to 700 (i.e. 4 multiplied by 175). In the cell next to the number 4 in this new list type in the VLOOKUP command:

=VLOOKUP(E4, A:B, 2, False).

This tells Excel to find the value in cell E4 (in this case “4″) in the array comprised of columns A and B (where our numbered data is) and to return the value in the second column (i.e. column B) wherever there is an exact match (the “False” command). This returns the shot length of the first shot and is “4.8.” Drag to fill the formula in to next cell for each multiple of four, and what you end up with is the shot length data in an easy to use form (see Figure 5). (Actually, you need to select this data, Copy, and Paste Special and past the data into a new column as Values, otherwise it will copy and paste the formulas).

Figure 5 Shot length data in a form ready to use

Once you’ve set up your spreadsheet with the VLOOKUP commands you will not have to repeat this step each time you load new data into Excel, but you will have to do the find and and replace steps each time.

Now you are ready to anlayse the shot length data!

It is a simple method, and once you’ve tried it you will soon find that it is very easy to get a lot of data very quickly, thereby speeding up your research.

Shakespeare and national identity

Although he died centuries before the invention of the cinema, the impact of William Shakespeare on the most popular art-form of the twentieth century has been profound. There have been many adaptations of his plays, but Shakespeare’s influence goes much further than simply adapting his works: his plays have been a source of inspiration for filmmakers in a number of ways and references to Shakespeare and his plays crop up in a variety of unexpected moments. The titles of two films by Alfred Hitchcock are drawn from Shakespeare (Rich and Strange (The Tempest) and North by Northwest (Hamlet)). The St. Crispin’s Day speech from Henry V has also been used as the source of the title for the HBO/BBC World War Two Series Band of Brothers (2001), and also features in Tombstone (1993).

The two most commonly referenced speeches are from Richard II and Hamlet, and both have been employed in the contexts of British and American cinema, respectively, to articulate ideas about national identity.

This England

In the history of British cinema, it is John of Gaunt’s speech from Richard II (Act 2, Scene 1) that has been a source of inspiration for filmmakers. Several films have taken their titles from this speech, mostly produced during World War II: This England (1923 & 1941), The Demi Paradise (1943), This Happy Breed (1944). More than any other moment in the history of drama, it is John of Gaunt’s evocation of that has captured the image and imagination of the nation.

This royal throne of kings, this scepter’d isle,
This earth of majesty, this seat of Mars,
This other Eden, demi-paradise,
This fortress built by Nature for herself
Against infection and the hand of war,
This happy breed of men, this little world,
This precious stone set in the silver sea,
Which serves it in the office of a wall,
Or as a moat defensive to a house,
Against the envy of less happier lands,
This blessed plot, this earth, this realm, this England,

Perhaps the most famous performance of this speech on film is that of Leslie Howard in The Scarlet Pimpernel (1934). To secure the escape of Lady Blakeney, Sir Percy surrenders himself to Chauvelin and as the firing squad is readied he reflects on the England he is leaving behind. Soft in focus and long in take, Howard’s performance of this speech adds a third dimension to the foppish Blakeney and the cunning Pimpernel and is very much the best scene in the film. This scene, perhaps more than any other in pre-war British cinema, establish the qualities of the English gentleman that also feature in films such as The Drum (1938), The Four Feathers (1939), Sanders of the River (1935), and the like; and does so with greater economy and far less bombast than in these other films.

Lindsay Anderson also employs this speech in Britannia Hospital (1982) – albeit for a very different effect. As the staff tour the hospital in preparation for a royal visit, pointing the various iniquities of life in modern Britain (militancy of trade unions, the unfairness of the class system, the corruption and insanity of authority, and many others), they come across a patient – ‘our greatest foreign minister since Palmerston’ – (played by Arthur Lowe) who all of a sudden sits bolt upright in bed, quotes Richard II, and promptly dies. Quite what Anderson wants us to make of this is not clear, and the scene lasts only 50 seconds. Anderson is pointing to the difference between the image of the nation articulated by John of Gaunt and the reality of Britannia Hospital, but this may be matter of exposing the hypocrisy of a British national identity that clings to an unrealistic idea of itself; or we may see it as the death of a once great England, that has been reduced to such a low status and has clearly lost something it once had. Depending on how you interpret it, the scene may be nostalgic, but there is no mourning a once great man, and the former foreign minister is covered with a bed sheet and the words, ‘Pity – he would have appreciated a visit.’

Since Britannia Hospital, the speech has disappeared from British cinema screens; while Richard II has tended to disappear from school curricula, which seem to focus almost exclusively on Hamlet and Romeo and Juliet. It seems unlikely now that audiences would be familiar enough with Richard II for a scene like that at the end of The Scarlet Pimpernel to work with the same power.

It should also be noted that Muriel Box directed a film called This Other Eden (1959), about a town in Ireland that wants to erect a statue to a member of the IRA. Apparently, this was the first Irish film to be directed by a woman. Cork University Press published a monograph on this film in 2001 by Fidelma Farley as part of its Ireland into Film series. I have not seen this film, but the title is very suggestive of the political relationship between the British and the Irish.

Hamlet in Hollywood

Hamlet’s ‘To be or not to be’ soliloquy (Act 3, Scene 1) has been referenced by Hollywood cinema on many occasions. The titles of numerous films have been drawn from the text: To Be or Not to Be (1942 & 1983), What Dreams May Come (1998), and even Star Trek VI: The Undiscovered Country (1991). While the Lubitsch’s and Johnson’s To Be or Not to Bes are comic farces, the other two films both share a sense of crossing over into the unknown (death and the afterlife, or a peace treaty with your mortal enemies). Star Trek VI was released in after the fall of the Berlin Wall, and the peace treaty between the Klingons and the Federation mirrors this breaking down of a long-standing barrier.

What connects these films is that they exist at the frontier, an idea that has been central to American exceptionalism and national identity. The ‘frontier thesis’ of Frederick Jackson Turner has been one of the most enduring concepts n the study of American History since its original publication in the 1890s. For Turner, it is the frontier that defines America:

The frontier is the line of most rapid and effective Americanization. … the frontier promoted the formation of a composite nationality for the American people. The coast was predominantly English, but the later tides of continental immigration flowed across the free lands. … The growth of nationalism and the evolution of American political institutions were dependent on the advance of the frontier ([1893] 1956: 1-2, 10-11).

The frontier is a place of becoming – it is where America became America, and it is this sense of becoming that occupies Hamlet. Faced with the murder of his father he must come to terms with himself and decide what he will do. This is Hamlet’s moment of becoming, of transformation, of crossing the frontier into adulthood and the future.

Perhaps the most unique example of this idea of transformation, becoming and the frontier is John Ford’s My Darling Clementine (1946) (Figure 1). Tag Gallagher (1986:232-233) discusses the role of Hamlet in this film, but does not say anything of great interest. He writes that, the ‘pretentiousness of inserting Shakespeare into a western mirrors the advent of culture into the wilderness, and is both undercut and underscored by staging the soliloquy on a saloon table with a drunken actor (Alan Mowbray) and an uncomprehending savage audience (the Clanton boys).’ To call this scene pretentious is, I think, to miss the importance of the idea of the frontier, and Gallagher’s subsequent analysis is very literal:

To be or not to be – that is the question:
Whether ’tis nobler in the mind to suffer
The slings and arrows of outrageous fortune,
Or to take arms against a sea of troubles
And, by opposing, end them.

Wyatt, of course, opposes troubles (ought he to?), and Clementine and the Clantons also decide to take action. But Holliday prefers

To die, to sleep⎯
No more – and by a sleep to say we end
The heartache and the thousand natural shocks
That flesh is heir to – ‘tis a consummation
Devoutly to be wished.

Is not Wyatt in a kind of ‘sleep?’ Holliday in a nightmare? Clementine in a kind of dream?

I generally think that Gallagher’s book on Ford is quite an interesting one, but this is rubbish. He simply assigns qualities referred to in the speech to characters in the film, and generates no insight whatsoever.

Figure 1 Hamlet’s ‘To be or not to be ‘soliloquy in My Darling Clementine (1946)

The use of Hamlet in this scene may be interpreted in several ways. The placing of high culture in the low surroundings of a saloon does contrast the civilised and the barbaric. The film has, along with just about every other  western, been interpreted as a shift from wilderness to garden, from barbarity to civilisation, and so we can see this as an instance of the becoming of the west. Hamlet is a metaphor for the transformation of American society at the frontier. At the same time, we have Doc Holliday who finishes the speech when the actor falters, and so we may this speech as a meditation on Doc’s mortality. Like Hamlet, Doc must face up to the future and determine a course of action. He must decide if he is to go on as a drunkard and a gambler, or if he will take a stand for what is right. The coughing fit that ends his performance reminds us of the short time he has left, and so his decision must be interpreted in terms of his own impending frontier – death. We would not expect to find Shakespeare in a western – it is certainly not a common part of the genre, but in My Darling Clementine it is one of the most important. This scene is a moment of pause, in which we are invited to reflect on the central question Shakespeare poses – ‘To be or not be’ – and to consider the nature and consequences of that becoming. For the west it is the transformation of the wilderness into civilisation, for America it is the becoming of a nation, and for Doc it is a decision on a path to righteousness.

References

Gallagher, T. (1986) John Ford: The Man and His Films. Berkeley, CA: University of California Press.

Turner, F. J. ([1893] 1956) The significance of the frontier in American history, in G. R. Taylor (ed.) The Turner Thesis Concerning the Role of the Frontier in American History. Boston: D.C. Heath & Co.: 1-18.

Cognitive film theory: a bibliography

This weeks post is a bibliography of materials on the subject of cognitive film theory I have amassed on and off over the past few years. Although it contains some 355 items it is neither exhaustive nor up to date, although it should be accurate (barring any changes in the URLs for web-based resources). I’m sure most of what is there is well-known to those interested in this area, but there is almost certainly something you will not have come across before.

The file can be downloaded here as a pdf: Nick Redfern – CognitiveFilmTheoryBibliography1-19.

Finally, to bring to your attention an interesting article I came across recently on the subject of Luchino Visconti and Federico Fellini in Frontiers of Neurology and Neuroscience and their series on the impact of neurological disorders on famous artists, which looks at the impact of strokes on the creativity of two of Italy’s greatest filmmakers.

Dieguez, S., Assal, G., Bogousslavsky, J. (2007) Visconti and Fellini: from left social neorealism to right-hemisphere stroke, Frontiers of Neurology and Neuroscience 22: 44-74.

The acclaimed Italian directors Luchino Visconti and Federico Fellini had very different life trajectories that led them to become major figures in the history of cinema. Similarities, however, can be found in their debuts with the neorealist genre, their personalities, creative styles and politicocultural involvement, and ultimately in the neurological disease that struck them at the end of their careers. Both suffered a right-hemispheric stroke that left them hemiplegic on the left side. We review their life and career to put that event into perspective, and then discuss its aftermath for both artists in the light of our current knowledge of right-hemispheric functions. Visconti showed a tremendous resilience following the accident and managed to direct several films and plays as an infirm, whereas Fellini had to put an end to his career but still was able to display his talents to the neuropsychologists that treated him. A speculative account is given of the links between right-hemispheric symptomatology and the premorbid personality of these highly prolific patients.

PMID: 17495505

The transferable belief model in film and games studies

This post is another draft paper, this time focusing on the difference between ergodic and non-ergodic texts and so is of relevance to games studies as well as film studies. I use an approach that I don’t think has been applied to either of fields yet: the transferable belief model, which is a mathematical theory of evidence. Hopefully soon I will be able to outline how this model will be of use in film studies in more depth, along with considering its relationship to Bayesian approaches to modelling viewer behaviour. The idea is to apply these models to the empirical analysis of the beliefs of real spectators so that it may be possible to make some statements about how we understand films that are more than theoretical but which have a solid evidential basis. The article can be downloaded as a pdf file here:Nick Redfern – Credal and pignistic reasoning in ergodic and non-ergodic texts.

Abstract

This paper discusses the difference between ergodic and non-ergodic texts by considering the different levels of reasoning required of an agent in each case. The difference indentified between such texts is based on the distinction between credal and pignistic reasoning in the transferable belief model. It is argued that non-ergodic texts require an active agent to reason about the state of the world, and thus operate at the credal level; while ergodic texts require that the belief function of an agent be transformed into a probability function for the purposes of decision making, and therefore entail both credal and pignistic reasoning. The difference between ergodic and non-ergodic texts considered in these terms is illustrated through comparing narratives from the CSI: Crime Scene Investigation franchise.

Connecting the regional and the global in the UK film industry

This weeks post is a draft of an article that I started writing a awhile ago and has driven me up the wall for several months, as most of it has been finished for quite some time but I never could quite get it done. The piece is about regional film production in the UK, and the ways in which this production is connected within the UK and beyond. It represents an attempt to enumerate the different types of films produced in the UK’s regions in the absence of any official statistics on the geography of film production in the UK. The abstract is presented below and the pdf can be down loaded here: Nick Redfern – Connecting the regional and the global in the UK film industry.

Abstract

Film policy in the United Kingdom is comprised of two complementary strands: the development of regional production clusters and the positioning of the UK as a film hub in the global film industry. Thus article examines the relationship between the regional, national, and global scales in feature film production in three UK regions – Northern Ireland, Scotland, and the South West of England – from 2004 to 2006. The results indicate that connections between the regions of the UK and the global film industry are limited; and that where they do exist these connections are either directly to or mediated through London, which functions as the dominant centre of distribution and finance – and therefore decision-making – in the UK film industry. Northern Ireland, by virtue of its cultural and economic relationship to the Republic of Ireland, stands out as a region in which its connections to other major decision-making centres are as important as its connections to London. The results suggest that while UK film policy has sought to redistribute the productive capacity of the industry, the autonomy of regional production centres remains limited.

Measures of central tendency in Cinemetrics

Barry Salt has made several assertions about the nature of film style and the use of statistical methods in the analysis thereof. Chief among these are:

• That the mean shot length accurately describes the distribution of shot lengths in a motion picture.
• That the lognormal distribution is a ‘ruling distribution’ of film style.
• That a shape factor of 0.9 is characteristic of shot length distributions, or that it lies in the interval 0.7 to 0.9.
• The median shot length can be estimated as either equal to mean * 0.6 or equal to mean / exp(0.5σ²), where σ is the shape factor.

Here I subject each of the above claims to scrutiny by testing them against specific data sets for defined populations, and I examine the methodology proposed by Salt in detail.

The mean shot length as a statistic of film style

Salt (1974) proposed that the mean shot length be used as a statistic of film style for shot length distributions. However, the distribution of shot lengths in a motion picture is typically characterised by two features: (1) it is positively skewed, and (2) there are a number of outlying data points that are far from the mean. (I say typically because there is no reason why the shot lengths of a film could not be distributed normally or negatively skewed, but I have not come across such a film). While the mean is the best measure of location for distributions that are symmetrical or near-symmetrical, it is a poor statistic when the data is asymmetrical (i.e. the data is skewed). The mean is not a robust statistic. When we say that a statistic is ‘robust,’ we mean that it is not influenced by data points that are very different from all the rest (outliers). The mean is very sensitive to such outliers and this can pull the mean away from the centre of the data creating a skewed data set: it has an asymptotic breakdown point of 0.0. The asymptotic breakdown point is a measure of the proportion of the data that can be given arbitrary values before the statistic becomes arbitrarily bad (Geyer 2006). So for the mean, the proportion of outlying data points in a sample that the mean can cope with is zero – just a single outlier can wreck the mean as a measure of central tendency, and in the distribution of shot lengths in a motion picture we can expect to find many outliers.

The asymmetrical nature of shot length data also limits the type of statistical tests that can be employed in statistical analysis [1]. Many tests require the assumption (amongst others) that the data is normally distributed. Tests which require an assumption to be made about he underlying probability distribution of the data are called parametric tests. However, for skewed data sets with a number of outliers, the assumption of normality does not hold, and the results of employing parametric tests will be unreliable. As no data is actually distributed normally, small deviations from the true normal distribution can be tolerated, but when we are dealing with shot length distributions we find that the deviations from normality are very large.

These problems may be overcome by using the median shot length as a statistic of film style. the median locates the middle of a data set by dividing the data in two, so that half the data is equal to or less than the median and half is equal to or greater than the median. The median locates the centre of any data set irrespective of shape, and is a more robust statistic than the mean: it has an asymptotic break down point of 0.5.

As we will be unable to use parametric statistical tests to analyse the data, we can turn to nonparametric tests which do not require the same assumptions to be met. Such tests, for example, make no assumption about the distribution of the data, and are often referred to as distribution-free tests. Thus, the two-sample independent t-test requires that the data in both samples be normally distributed; this is not the case for its nonparametric equivalent, the Mann Whitney U-test. This does not mean, however, that nonparametric statistics are assumption-free tests, and it is still necessary to make sure that the assumptions of each test can be met (e.g. that data is independently and identically distributed). As they require fewer assumptions about the nature of the data nonparametric tests are less powerful than their parametric equivalents, but when the requirements for the parametric tests cannot be met they provide a much better alternative than no analysis at all.

The mean shot length should never have been suggested as a statistic of film style. The median is a far superior statistic given the skewed nature of shot length distributions, and analysing film style using this measure of central tendency will provide results that are far more reliable than if we used the mean.

Do motion pictures have lognormal shot length distributions?

An alternative to using the median shot length is to apply a transformation to data in order to remove the skew from the data. Such transformations include raising the value of a data point to a power or taking the reciprocal of a data point, and there are many others. A common transformation employed is to take the logarithm of a data point, which may produce a lognormal distribution. A random variable (X) is said to be lognormally distributed if its logarithm (log [X]) is normally distributed. If the shot length data for a film is lognormally distributed then we have an advantage over the median shot length, as knowing the underlying probability distribution will allow us to use the more powerful parametric statistical tests. However, just as the parametric tests are unreliable when the assumption of normality is not, the same is true if the assumption of lognormality is not met.

The lognormal distribution and the mean shot length

Salt proposes that (1) the mean shot length is the appropriate statistic of film style and that (2) the shot lengths of a motion picture are distributed lognormally (2006: 389-396). However, these are conflicting claims. If the mean shot length was a reliable statistic of film style then we would not need the lognormal distribution: the reason we apply a logarithmic transformation to the data is because the mean does not provide a robust measure of the central tendency of the data in its original scale. Applying a logarithmic transformation to data allows us to recover the symmetry of the data, which we would not need to do if it were already symmetrical. To be specific, it is the arithmetic mean shot length that is incompatible with the lognormal distribution. The arithmetic mean is what we normally refer to when we say ‘mean:’ it is the sum of the data points divided by the number of data points in the sample. The arithmetic mean is NOT the measure of central tendency of the lognormal distribution. If we wish to locate the centre of the lognormal distribution then we use the geometric mean.

Logarithms are useful because they make complicated procedures like multiplication into simple operations like addition. For example, instead of multiplying two numbers together we can simply add their logarithms and by transforming the result back into the original scale we have our answer:

a * b = c ,

is the same as

log (a) + log (b) = log (c).

It does not matter which logarithm you use so long as you are consistent and use the correct method to back-transform the result. The two main logarithmic transformations are the common logarithm (log₁₀ [X]), which uses base 10; and the natural logarithm (ln [X]), which uses base e.

Now, if we transform the length of each shot in a film (X) into its logarithm (log [X]), we can calculate its average in the usual way – that is, we add up all the logarithms and divide by the number of shots. Transforming the average of the logarithms back into the original scale will give us the geometric mean. In the original scale, this is the equivalent of multiplying all the shot lengths together and then taking the nth root, where n is the number of shots in the film. As we are using multiplication instead of addition, the geometric mean of lognormally distributed data is clearly going to be very different from the arithmetic mean. In fact, the geometric mean of a data set will always be less than the arithmetic mean (unless all the data points are equal).

In Table 1, the shot length data (X) for A Busy Day (Charles Chaplin, 1914) is presented along with the natural logarithm of each shot (ln [X]). (This film has a shot length distribution that is lognormally distributed – Shapiro-Wilk: w = 0.9783, p = 0.6556). The film is 340.4 seconds long and includes 38 shots (once title and dialogue cards have been removed). The arithmetic mean shot length of A Busy Day is 340.4 divided by 38, and equals 9.0 seconds. The sum of the logarithms is 65.4763, and dividing this figure by 38 gives 1.7231. Transforming this figure back into the original scale gives us a geometric mean of 5.6 seconds.

TABLE 1 Shot length data in the original scale (X) and its natural logarithm ln (X) for A Busy Day (1914)

One of the reasons people get confused with the lognormal distribution is because, unlike the normal distribution, its expected value (E[X]) and its measure of central tendency are not the same. (For the normal distribution, the expected value and the measure of central tendency are both the arithmetic mean). The expected value of a Lognormal distribution is equal to the exponentiate of the geometric mean plus half the variance: E[X] = exp(μ+0.5σ²). For A Busy Day, the mean of the logarithms (μ – the geometric mean) is 1.7231 and the variance (σ²) is 1.0259. If we add the geometric mean to half the variance (1.7231 + 0.5129) we get 2.2360. Transforming this value back to the original scale (the exponentiate) we get 9.4 seconds, which is approximately equal to the arithmetic mean shot length, and we know this does not locate the centre of the shot length distribution for this film. For a Lognormal data set, the geometric mean will be approximately equal to the median. We know that the median will locate the centre of any data set, and for A Busy Day the median shot length is 4.9 seconds – much closer to the geometric mean than the arithmetic mean. (Finding the median of the logarithms (1.5813) and then converting back to the original scale is equal to the median shot length. Using the median of the logarithms gives a poorer estimate of the expected value (8.1 seconds) than the geometric mean). For a discussion see Olsson (2005).

The shot length data for A Busy Day is presented above, so you can do this for yourself. NB: I calculated the variance for this film using Microsoft Excel’s function for finding the population variance (=VARP(array), where the denominator is n), while using the sample variance function (=VAR(array), where the denominator is n-1) will give E[X] = 9.5 seconds [2]. It should also be noted that, while Excel 2007 has a function for calculating the geometric mean (=GEOMEAN(array)), this will only work for up to 255 data points (and for earlier versions of Excel considerably less). Transforming each shot length to its logarithm and then finding the average will work for any sample size in Excel.

It is clear that the arithmetic mean shot length should never have been proposed as a statistic of film style. If, as Salt claims, shot lengths are lognormally distributed resulting from the multiplication of independent factors, then it is necessary to use a multiplicative central tendency and this is the geometric mean shot length. It is necessary to choose between two claims: are we going to claim that the arithmetic mean shot length is the best statistic of film style or are we going to claim the shot lengths are lognormally distributed? Since we already know that the arithmetic mean is not a robust statistic for skewed data sets and we have already resorted to using the logarithms of the data, it would seem obvious to jettison the arithmetic mean and to use the geometric mean as our statistic – assuming, of course, that the shot lengths of a motion picture are lognormally distributed.

This would, of course, mean that every time the arithmetic mean shot length has been quoted as a statistic of film style, it is simply wrong.

Is the assumption of lognormality justified for the distribution of shot lengths in a motion picture?

In Salt (2006: 389-396), the ‘generality of the Lognormal distribution for shot lengths in movies’ is asserted but not demonstrated. Examples of some films that are claimed to have Lognormal shot length distributions are featured alongside some films for which this claim is not made, but the extent to which these claims can be generalised is in unclear. Salt admits that the sample in this study is not representative due to the presence of a number of films with very large mean shot lengths [3], and so on what is the claim that a lognormal distribution can be usefully used to model shot length distributions based? We do not know from which population the sample is drawn or what the sample size is. A further problem is that it is not clear what Salt defines as a film in which the shot lengths are lognormally distributed. The coefficient of determination is presented as a measure of goodness-of-fit, but there is no decision rule stated as to what value of R² can be considered ‘good.’ We do not actually know from this if the lognormal distribution is reliable enough to use in the analysis of film style, because we do not know how common it is for films to have lognormal distributions. Despite these problems, Salt has since made a much stronger claim that the lognormal distribution is a ‘ruling distribution’ of film style [4]. This claim assumes that at least a majority of films will have shot lengths that are lognormally distributed, although this has not yet been demonstrated.

Other probability distributions have been used in modelling shot lengths. Fujita (1989), for example, surveyed 32 educational television programmes and found that an Exponential distribution provided a good fit for the shot lengths in 30 cases. The Weibull, Gamma, and Poisson distributions (amongst others) have all been proposed as the best model for the shot lengths of motion pictures (Cotsaces et al. 2009, Taskiran and Delp 2002, Truong and Venkatesh 2005, Vasconcelos and Lippman 2000). Indeed, Salt (1974) used the Poisson distribution to model shot lengths, and also found films in which this hypothesised distribution did not hold.

It is a simple matter to estimate the proportion of films with a Lognormal distribution, and this is experiment is conducted below.

Sample

The samples used are the fifty films that I analysed earlier in my study of the impact of sound technology on the median shot lengths in Hollywood cinema. These films are divided into two samples: silent films produced between 1920 and 1928 inclusive (n = 20); and sound films produced from 1929 to 1931 inclusive (n = 30). The descriptive statistics for each film can be found by referring to my earlier paper.

Method

The shot lengths of each motion picture in the samples are transformed into their natural logarithms. The lognormality of the data is then tested using the probability plot correlation coefficient (PPCC) employing a Blom plotting position, with a significance level of 0.05 (Looney and Gulledge 1985, see my earlier post on how to do this). Where the PPCC for a film was just under its critical value, the result is checked using a Shapiro-Wilk test (α = 0.05).

The proportion of films with lognormally distributed shot lengths is then calculated, along with an approximate 95% confidence interval using the adjusted Wald method (Agresti and Coull 1998). This will be our estimate of the proportion of films that have lognormal distributions for the populations from which the samples are drawn.

Calculations were performed using Graphpad online calculators and PAST 1.89 (2009). The critical values for the PPCC can be accessed at the NIST website.

Results

The results of the PPCC test for the silent films are presented in Table 2, and for the sound films in Table 3. Only one film needed to be checked using the Shapiro-Wilk test: Behind the Make-up is not lognormally distributed (w = 0.9873, p = 0.0184).

TABLE 2 Sample size and PPCC (α = 0.05) for silent films produced in Hollywood, 1920 to 1928 inclusive

TABLE 3 Sample size and PPCC (α = 0.05) for sound films produced in Hollywood, 1929 to 1931 inclusive

Of the twenty silent films, six have Lognormal shot length distributions, and the proportion of silent films produced in Hollywood from 1920 to 1928 inclusive with a Lognormal distribution is estimated to be 0.30 (0.14, 0.52).

Of the thirty sound films, thirteen have Lognormal shot length distributions, and the proportion of sound films produced in Hollywood from 1929 to 1931 inclusive with a Lognormal distribution is estimated to be 0.43 (0.27, 0.61).

While some films do have shot lengths that are lognormally distributed, Salt’s statement that the lognormal distribution is a ‘ruling distribution’ of film style cannot be justified. In fact, in neither sample is there a majority of films with a lognormal distribution. If an analysis of film style is conducted using the assumption of then it is likely that the results will be unreliable.

The geometric mean is a superior measure of central tendency for skewed data sets with lognormal distributions. However, as no evidence has been presented that would justify the assumption that shot lengths are lognormally distributed the use of the geometric mean is questionable. Again, the median shot length is available as an alternative that can be used reliably as it locates the centre of a distribution as the middle ranked value in a data set, and does not rely on an underlying probability distribution.

Do shot length distributions have a characteristic shape factor?

Each theoretical distribution is described by a set of parameters. The Lognormal distribution is described by the parameters and the shape factor, σ. Salt has claimed that the characteristic shape factor for the Lognormal shot length distributions of a motion picture is ~0.9 [5]. The relevance of this claim is lessened by the fact that there is no evidence to justify the claim that shot lengths are lognormally distributed. This claim is different to the one made in Salt (2006: 393), where it was asserted that the shape factor will lie in the interval 0.7 to 0.9.

Again, it is a simple matter to test both these claims.

Hypotheses

The first research question we are addressing here is ‘the lognormal shape factor of a shot length distribution is 0.9.’ The statistical hypothesis is:

• H₀: the shape factor (σ) = 0.9

The second hypothesis we will address is the claim that ‘the lognormal shape factor of a shot length distribution will lie in the interval 0.7 to 0.9.’

Sample

The two samples of Hollywood films used above are employed in this test.

Method

The shape factor for each film is determined by maximum likelihood estimation (MLE) for the lognormal distribution. The mean value of σ for each data set is then calculated, and compared to the hypothesised value of 0.9 using a one sample t-test. A p-value of less than 0.05 is considered significant. The proportion of films with σ in the range 0.7 to 0.9 is then calculated, along with an approximate 95% confidence interval using the adjusted Wald method

MLE is performed using online calculators (Wessa 2008), and the t-test is performed using Microsoft Excel 2007. Graphpad online calculators were used to produce the confidence intervals for the proportions.

Results

The Lognormal shape factor for each film is presented in Table 4 for the silent films and Table 5 for the sound films.

TABLE 4 Lognormal shape factors for silent films produced in Hollywood, 1920 to 1928 inclusive

TABLE 5 Lognormal shape factors for sound films produced in Hollywood, 1929 to 1931 inclusive

The mean shape factor of the silent films is 0.7437 (SD = 0.0617), and is significantly lower than the hypothesised value of 0.9, t (19) = 11.3303, p = <0.0001.

The mean shape factor of the sound films is 0.9411 (SD = 0.1066), and is significantly greater than the hypothesised value of 0.9, t (29) = 2.1134, p = 0.0433.

If we take Salt’s alternative claim that σ will lie in the interval 0.7 to 0.9, then we can say that for the silent films this is a much more useful estimate, with a proportion of 0.70 (0.48, 0.86) in the specified interval. For the sound films, however, it is less good with a proportion of 0.47 (0.30, 0.64).

The hypothesised shape factor of 0.9 is not a good estimate for either sample, while the specified range of 0.7 to 0.9 is only a reasonable estimate for the silent films and even then we can expect over one-quarter of the films to lie outside this interval.

The claim that there is a characteristic shape factor for the distribution of shot lengths in a motion picture is not supported by the evidence.

When is a mean shot length not a statistic?

There are clearly serious problems in using the arithmetic mean shot length as a statistic of film style, and  Salt has tried to shift the justification for keeping the mean shot length to the argument that it can be used to estimate the median shot length [6]. To further add to the confusion of using the arithmetic mean with the lognormal distribution, we now have the claim that the mean shot is both the desired statistic of film style and is desirable as a means of estimating the median. Why, if the mean shot length is the statistic we desire, do we need these methods of estimating the median? Why, if the median can be estimated from the mean, has no one ever used this estimated median to describe changes in film style? As before, it is a question of competing claims: it is either the mean or the median, as they are different for skewed data sets, and not both. As it is a simple matter to demonstrate that the mean shot length is not a robust statistic, then it should be disposed of. Again, if the mean shot length is not the desired statistic of film style, then it would be necessary to admit that every time the mean shot length has been quoted in books and journal articles, this was wrong.

This is all very well, but it begs a fundamental question: is the estimated median any good?

Can the median shot length be reliably estimated from the mean shot length?

Salt proposes two methods for estimating the median shot length from the arithmetic mean shot length, which, for the sake of simplicity, I shall refer to as Method A and Method B:

• Method A: median = mean * 0.6
• Method B: median = mean / exp(0.5σ²), where σ is the shape factor.

This two methods should produce approximately the same results when σ = 0.9.

Again this is simply an assertion and Salt provides no data or results to back up this claim.

Sample

The two samples of Hollywood films used above are employed in this test.

Method

For clarity, the following symbols are used:

• Med is the true value of the median shot length.
• Med_A is the estimate of the true value of the median using Method A.
• Med_B is the estimate of the true value of the median using Method B.

As Salt claims that σ = 0.9, using Method B is immediately problematic as I have already demonstrated that this is not a good estimate of the shape factor of the films in the two samples. In order to allow for this Method B is used twice – once where σ = 0.9, and once where σ is the MLE-derived value in Tables 4 and 5.

The value of Med_A or Med_B is considered a good estimate for Med if it is included in the 95% confidence interval of Med. Note that this is not the same as saying that Med_A or Med_B will be equal to Med – only that they will estimate Med if they lie within an interval with a specified confidence level. These methods will therefore introduce some error into any analysis even when they are good estimates, but this error will be known.

The confidence intervals for the median were calculated using the binomial method. It is important to remember that while the shot length data itself is not binomially distributed, the median shot length is determined by its rank in the ordered sample. Therefore, when we calculate the confidence interval for a median were apply the binomial method to the ranks of the ordered data and then transpose this on to the ordered data – i.e. calculate the rank of the lower (j) and upper (k) limits of the interval for the proportion 0.5 and then the shot lengths that are ranked jth and kth in the ordered data. The binomial method is NOT applied to the shot lengths themselves. Using the binomial method tends to produce a conservative interval, but all the intervals are at least 95% and no film has a confidence interval greater than 96.41% [7]. See Curwin and Slater (2008: 296) for a simple introduction on how to do this and the large sample approximation.

The proportion of good estimates is calculated, along with an approximate 95% confidence interval using the adjusted Wald method.

Results

The results for the sample of silent films are presented in Table 6, and for the sound films in Table 7.

TABLE 6 Median estimation for silent films produced in Hollywood, 1920 to 1928 inclusive

TABLE 7 Median estimation for sound films produced in Hollywood, 1929 to 1931 inclusive

For the silent films, Method A produces a result that lies in the confidence interval of the true median only 4 times out of twenty (P = 0.20 [0.04, 0.37]). If we use this method we can expect our estimate to be outside the given confidence interval 80% of the time. Method B fares better for the silent films when σ = 0.9: out of twenty trials, the estimate was within the confidence interval for the true median on 13 occasions (P = 0.65 [0.43, 0.82]) – but this still means that it provides a poor estimate for approximately 1 in 3 films. When σ is the value derived by MLE, then the number of estimates that fall in the confidence interval of the true median is zero.

For the sound films, Method A provides a good estimate on 21 out of 30 occasions (P = 0.70 [0.52, 0.83]); and for Method B (σ = 0.9), the median is also well estimated 21 times. When σ is the value derived by MLE, then the number of estimates that fall in the confidence interval of the true median is 25 (P = 0.83 [0.66, 0.93]). These three methods when applied to the sample of sound films provide good estimates for the same film on 14 occasions, two methods provide good estimates on a total of twelve occasions (but it was not necessarily the same two for each of these twelve films), and on one occasion only a single method provides a good estimate. There are three films for which no method provides a good estimate. The different methods, then, provide different results for the same films.

The different methods proposed by Salt perform inconsistently across the two samples, and also produce different results when applied to the same sample. Overall, neither method provides a sound means of estimating the median shot lengths, and relying on median shot lengths estimated by these methods in the analysis will incorporate a large degree of error into the results as at least 17% of those estimates can be expected to lie outside the 95% confidence interval of the true median.

Summary

Salt has made a number of assertions about the appropriate methodology for the statistical analysis of film style. When this methodology is examined in detail, and these claims are subject to statistical hypothesis tests, they cannot be justified:

• The mean shot length is not a reliable statistic of film style. The median and the geometric mean are both more reliable measures of central tendency for shot length distributions that are positively skewed with outlying data points.
• There is no evidence that the majority of films have shot lengths that are lognormally distribution, let alone any evidence to support the claim that the lognormal distribution is a ‘ruling distribution’ of film style. Consequently, the use of the geometric mean as a measure of central tendency is less reliable than that of the median.
• There is no evidence to support the claim that the characteristic shape factor of the distribution of shot length in a motion picture is 0.9; while the claim that the shape factor will lie in the interval 0.7 to 0.9 produces inconsistent results across the samples examined here, with between a quarter and a half of the films outside this interval.
• The methods for estimating the median shot length from the mean shot length are inconsistent, and are not sufficiently reliable. Use of these methods to estimate the median from the mean shot length will introduce a large amount of error into a study.

The implications for film studies are depressing. The mean shot length has been used as statistic of film style for over thirty years in a number of publications by a number of prominent film scholars (e.g. Barry Salt, David Bordwell, Warren Buckland, Charles O’Brien, Yuri Tsivian, Colin Crisp, etc.). Unfortunately all this research is simply wrong, and as these studies have been further cited by other scholars this mistake has been multiplied. There is now a whole range of so-called ‘statistical analyses’ of film style out there, but none of it is, in fact, correct. The statistical analysis of film style can make a significant and positive contribution to our understanding of the cinema, but this first requires an understanding of statistics. Before the statistical analysis of film style can be good film studies, it must first be good statistics. Good statistics is the one thing we do not have at present. This problem goes back 35 years and the introduction of the mean shot length as a statistic of film style.

What is truly disheartening is that the mistakes made by film scholars in this area are elementary: in the UK, knowing when to use the mean and the median is GCSE statistics. The current specification for the AQA statistics syllabus clearly requires students – not university professors with Ph.D.s, but 14-16 year old school pupils – to understand the ‘advantages and disadvantages of each of the three measures of location [mean, median, mode] in a given situation,’ and to provide a ‘reasoned choice of a measure of location appropriate to the nature of the data and the purpose of the analysis.’ You can even get extra marks if you discuss the geometric mean! Any basic statistics course will tell you that you need to cite measures of dispersion alongside measures of central tendency. Every text book ever written on the subject discusses the meaning of the word ‘significant’ in the context of statistics. The application of statistics in film studies falls below these basic standards.

Do not take my word for it. Go and learn some statistics, or ask a statistician to show you how to do it. Get some data and do the analyses for yourself – and by analysis I mean actually formulate the hypotheses and do the tests rather than simply asserting two numbers are different and that this is ‘significant.’ Do not simply quote statistics when you do not know what from what population the sample was drawn, or when you do not know what the statistics are supposed to describe, or when you do not know what decision rule was employed, or when you do not know what tests were used. There really is nothing difficult about any of this.

Nulius addictus judicare in verbia magistri

Notes

1. I have assumed that film scholars will be using statistical tests to test hypotheses about data, but I have not actually come across anyone who has used a single statistical test in film studies. It is typical for film scholars to cite some means (without any accompanying measure of dispersion), and then simply to assert that a difference does or does not exist and that such a result is ‘significant.’ What they mean by ‘significant’ is not clear, but this is a term with a precise meaning in statistics and should not be abused. The statistical analysis of film style is scarcely statistics.
2. The reason for using the population variance is to be consistent with the MLE values given for σ, which were calculated based on the population standard deviation.
3. See Salt’s comment to my post ‘Testing Normality in Cinemetrics‘ dated 21 May 2009.
4. See Salt’s comment to my post ‘The impact of sound on film style‘ dated 25 September 2009. Note that in his comment to this post and the one cited above in note 3 Salt gives two different sets of figures for a set of 40 films I tested by the same method here, and that he gets both of them wrong. I can only assume that he has counted some films that appear in different posts twice. For the record (1) this is not a representative sample drawn from a population (2) there are 40 films in the table, and (3) half the films (20) have lognormal shot lengths. If we add the fifty films above to those forty films (remembering to remove the ones that overlap) we have a total set of 81 films of which 35 have lognormal shot lengths.
5. See Salt’s comment to my post ‘Location and spread in shot length distributions‘ dated 15 November 2009.
6. See Salt’s comment to my post ‘The impact of sound on film style‘ dated 25 September 2009.
7. A method for constructing exact confidence intervals for the median has been described by Bonnet and Price (2002), and there is a spreadsheet that can be downloaded to do this automatically. By all accounts this should be a better method than the binomial, but I have not been able to get hold of a copy of the article in which this method is described and so I am reluctant to use it without first understanding how it works.

References

Agresti A and Coull B 1998 Approximate is better than ‘exact’ for interval estimation of binomial proportions, The American Statistician 52: 119-126.

Bonett DG and Price RM 2002 Statistical inference for a linear function of medians: confidence intervals, hypothesis testing, and sample size requirements, Psychological Methods 7 (3): 370-383.

Curwin J and Slater R 2008 Quantitative Methods for Business Decisions, sixth edition. London: Thomson Learning.

Cotsaces C, Nikolaidis N, and Pitas I 2009 Semantic video fingerprinting and retrieval using face information, Signal Processing: Image Communication 24 (7): 598-613.

Fujita K 1989 Shot length distributions in educational TV programmes, Bulletin of the National Institute of Multimedia Education 2: 107-116.

Geyer CJ 2006 Breakdown point theory notes, http://www.stat.umn.edu/geyer/5601/notes/break.pdf, accessed 9 December 2009.

Looney SW and Gulledge TR 1985 Use of the correlation coefficient with normal probability plots, The American Statistician 39 (1): 75-79.

Olsson U 2005 Confidence intervals for the mean of a lognormal distribution, Journal of Statistics Education, Volume 13, Number 1, www.amstat.org/publications/jse/v13n1/olsson.html, accessed 18 November 2009.

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. Starwood, London.

Taskiran CM and Delp EJ 2002 A study on the distribution of shot lengths for video analysis, SPIE Conference on Storage and Retrieval for Media Databases, 20-25 January 2002, San Jose, CA. Available online: http://ctaskiran.com/papers/2002_ei_shotlen.pdf, accessed 7 August 2009.

Truong BT and Venkatesh S 2005 Finding the optimal temporal partitioning of video sequences, Proceedings of IEEE International Conference on Multimedia and Expo, 6-9 July 2005, Amsterdam, Netherlands: 1182-1185.

Vasconcelos N and Lippman A 2000 Statistical models of video structure for content analysis and characterization, IEEE Transactions on Image Processing 9 (1): 3-19.

Wessa P 2008 Maximum-likelihood lognormal distribution fitting (v1.0.2) in free statistics software (v1.1.23-r4), Office for Research Development and Education, http://www.wessa.net/rwasp_fitdistrlnorm.wasp/, accessed 15 November 2009.

Buckland on Spielberg

Although credited to Tobe Hooper, it is widely held that the director of this film was in fact Steven Spielberg, who also wrote and produced the film. In Directed by Steven Spielberg: Poetics of the Contemporary Hollywood Blockbuster, Warren Buckland undertakes what he calls a statistical analysis of a group of films in order to solve the riddle of who directed Poltergeist (2006: 154-173) [1]. Buckland sets out his intentions for this chapter clearly:

Through a shot-by-shot analysis, I use statistical methods to compare and contrast Poltergeist to a selection of Hopper’s and Spielberg’s other films,’ in order to ‘determine how Poltergeist’s style conforms to and deviates from Spielberg’s and Hooper’s filmmaking strategies (155).

Here I review the statistical approach adopted by Buckland. Specifically, I address four issues: the design of the study; the statistical methodology employed; the presentation of the results; and the conclusions drawn.

I do not address the rest of the book, and my critique is limited only to the chapter that deals with the statistical analysis of Spielberg’s and Hooper’s films.

The study

Buckland’s analysis compares Poltergeist to two films directed by Spielberg (ET and Jurassic Park) and one film (The Funhouse) and one TV movie (Salem’s Lot) directed by Tobe Hooper. It is reasonable that we would want to compare the work of interest (Poltergeist) to the work of the two possible directors, but alarm bells should be ringing already.

First, Poltergeist was released in 1982 – the same year as ET, while The Funhouse was released in 1981, and Salem’s Lot was aired in 1979. Jurassic Park, however, was released in 1993; and so while four of the works in question are contemporary with one another, one is from a decade later. Is it reasonable to assume that Spielberg’s style remained unchanged from 1982 to 1993 so that a direct comparison is possible? It is not unreasonable to suggest that Spielberg’s style did not change from ET to Jurassic Park, but equally it is not unreasonable to expect that it did. In the period 1901 to 1912, Picasso moved through his blue, rose, and cubist periods – might we not expect Spielberg to also have developed as a filmmaker over the course of a decade? What impact might new filmmaking techniques and technologies developed throughout the 1980s have had on his film style? We might expect the results to reflect the fact that the exemplars for Hooper are contemporary with Poltergeist, while this is only the case for one of the Spielberg films.

Furthermore, of the five films considered, four were produced for release into cinemas, while Salem’s Lot was produced for television. Might we not expect the results to reflect the fact that Poltergeist was made for cinemas like the two Spielberg films, while this is only the case for one of the Hooper films, and so indicate a difference in media rather than director? Buckland addresses this a note to the chapter (173, n.2), where he points out that the percentage of medium close-ups in Salem’s Lot is consistent with that in The Funhouse – although he simply asserts this and does not perform any test of this hypothesis (see below). It is the case that there is no significant difference between the proportion of medium close-ups in Salem’s Lot (0.33 [0.28, 0.39]) and The Funhouse (0.36 [0.30, 0.42]) (Z = 0.6459, p = 0.5183), but there is a significant difference between the proportion of reverse angle shots (see Table 2 below). Buckland’s justification for using a TV movie is, then, very weak indeed and open to challenge.

There is the potential for bias in the study, and it is not clear that it can set out to do what it claims. This is the result of failing to establish the style of Hooper and Spielberg before conducting a comparison of the two. Is Spielberg consistent over the course of a decade in his use of film style? Is Hooper consistent in his style when moving between film and television? Buckland states that a pattern of film style is ‘created by a director’s sensibility, or intuition, a series of consistent habits that constitute a director’s style’ (158), but he has failed to demonstrate that this is actually the case for either Spielberg or Hooper.

Statistical methodology

Sampling

Buckland’s data is taken from only the first thirty minutes of each film, and this has the potential to distort the results. This sampling strategy requires the assumption that rest of the film will be of similar style to the first half hour – not necessarily an unreasonable judgment but equally one which may turn out to be unjustifiable. As I have shown elsewhere, calculating the mean shot length on the basis of the first thirty minutes of a film may under- or over-estimate the true value. This may be attributed to a film reaching a dramatic climax, for example, where the pace of the editing may increase relative to the early portion of a film, which may have longer shots and scenes for exposition. Equally, when calculating the proportion of shots that are of a particular scale we may find that the style changes as the film progresses.

Estimation

A flaw in Buckland’s presentation of his results – and a general flaw in the use of statistics in film studies in general – is the confusion of statistics with parameters. It is worth reading Mark Schuster’s paper ‘Informing Cultural Policy: Data, Statistics, and Meaning’ (Schuster 2002) before proceeding with any statistical analysis because he sets out some fundamental principles of statistical analysis in a clear and accessible manner. First, he makes a distinction between data and statistics:

It has become quite common to treat the words ‘data’ and ‘statistics’ as synonyms. We prefer the word ‘statistics,’ perhaps, when we wish to signal seriousness of purpose; but we prefer ‘data’ when we don’t wish to threaten the system that is being measured.

But statistics and data are not the same. Statistics are measures that are created by human beings; they are calculated from raw data by people who are wishing to detect patterns in those data. We calculate means, modes, standard deviations, chi-squared statistics, slopes of regression lines, correlation coefficients, and so on; we aggregate in a wide variety of ways, we eliminate outliers, we normalize calculations, we truncate time series. In short, we generate mathematical summaries that we think are appropriate to the questions with which we are grappling at a particular moment in time. And we have debates about which statistic will capture better the particular element of human behavior in which we are interested.

This is why it is not only silly but perhaps even dangerous to say that we will ‘let the data speak for themselves.’ We calculate statistics from data in order to say something about them.

Schuster then goes on to make a distinction between statistics and parameters:

Statistics are mathematical summaries of the relationships we observe in the data we have actually been able to collect, often from systematically drawn samples. Parameters are mathematical summaries of the relationships that we would observe if we were able to collect complete and accurate data about the behavior of entire populations. Statistics are estimates of parameters. In the end, we are interested in parameters, but statistics are the best we can do.

Statistics and parameters are often distinguished by the use of different symbols: roman letters are used for statistics, while Greek letters are used for parameters. For example, the sample correlation coefficient r is an estimate of the population coefficient ρ, and the sample standard deviation s is an estimate of the population standard deviation σ.

Buckland – like everyone else writing about the statistical analysis of film style – presents statistics as parameters and not as estimates of parameters. For example, on the basis of the first thirty minutes of ET, Buckland states that the mean shot length is 6.25 seconds. Now, for the first thirty minutes of ET we can take this to be a parameter (it describes all of the data in the first half hour), but if we want to use this figure to describe the whole film then it is a statistic (an estimate of the parameter for the whole film). Unfortunately, as a statistic it is useless because it is not accompanied by any measure of the error of the estimate – the mean shot length is presented without a standard deviation or standard error to indicate the variability of the data, or confidence intervals to indicate the possible values of the true mean shot length. Is 6.25 seconds a good estimate of the mean shot length for ET? We do not, and on the basis of the information provided by Buckland we cannot, know.

This problem arises due to the way in which the mean shot length of a film is often calculated: the running time is divided by the number of shots. This method will tell you what the mean shot length is, but it does not make it possible to calculate any other statistics because the actual duration of each shot is not known. For example, the standard deviation is calculated by subtracting the mean of a data set from each value in the data set, but if you do not know the value of each data point then this is not possible. Consequently, we have no measure of the variability of the data, and this makes any subsequent analysis impossible. I cannot assess the validity of Buckland’s claim that, because in order to perform the appropriate statistical tests (a t-test for independent samples or one-way ANOVA, depending on how you choose to compare the films) require the standard deviation. (However, see below on the non-normal nature of shot length distributions). Nor can I calculate confidence intervals for the mean shot length because this again would require the standard deviation [2].

The unusual thing is that Buckland must have, in fact, determined the length of each shot – he presents data on the proportion of shot lengths that lie in the range 1-3 seconds, for example. He also presents the skew of the shot length data for each film, and the calculation of this statistic would require knowing the duration of each shot. Why, if this information is available, was not included in the study?

The skew of each film in Buckland’s study is large, and this begs the question why the mean shot length is used as a statistic of film style when the shot length distributions for each film are asymmetrical. A true normal distribution will have a skew of zero, but life is never convenient and a dataset will almost never have a true normal distribution. Some (but not all) statistic textbooks recommend that the assumption of normality is valid when the skew is greater than -0.8 and less than 0.8. If the skew lies outside this interval, then the assumption of normality is not valid. For the five films in Buckland’s study, the skew values are 2.7, 2.7, 5.5, 5.6, and 4.1. As I have shown elsewhere, the median is a more robust statistic when dealing with  data sets that are positively skewed with outlying data points, as shot length typically are. A statistic is ‘robust’ if it is not influenced by outliers – the mean is very sensitive to outliers and just a single value that is very different from the rest of the data can wreck the mean as a measure of central tendency. The median is not affected in this way. The mean shot length should not have been used as a statistic of film style, and the conclusions Buckland draws on the basis of the mean shot length are worthless.

Testing

Buckland alerts the reader his chapter on Poltergeist will involve a detailed analysis involving the thorough use of statistics:

I need to warn the reader that this chapter contains a lot of number crunching and statistical testing, which are necessary if we want to make an informed judgment about the creative force behind Poltergeist. The results of my analysis may surprise you (155).

What statistical tests are employed in this analysis?

None.

The statements Buckland makes about the style of each director and their relation to Poltergeist are simply assertions based on whether one number is similar to another. There is no statement of what is considered to be a statistically significant result – i.e. there is no value for α and no decision rules – and so there is no means by which we can judge the reliability of the results.

This is all the more bizarre because in Elsaesser and Buckland (2002) we find the following statement:

… some films such as Poltergeist have disputed authorship (was it directed by Tobe Hooper or Steven Spielberg?). By systematically analyzing the parameters of the shots in Poltergeist, and then comparing the results to samples from Hooper’s and Spielberg’s other films, it may be possible to identify the film’s authorship (defined in terms of mise en shot, that is, the parameters of the shot). Of course, because we move from descriptive to inferential statistics, then the result can never be certain, but only predicted with a degree of probability. Only the descriptive aspect of the analysis remains beyond doubt.

On a cautionary note, the variables chosen to determine a director’s style need to be valid (…). Secondly, the results need to be statistically significant, rather than due to chance occurrence. Many statistical tests are in fact tests for significance.

Why, then, does Buckland not employ any tests of statistical significance, when clearly he is at least aware that such tests exist? It all sounds very good, but in practice there is little of substance.

To demonstrate how this analysis could have been I look at the proportion of different types of shots in the five films in the study. The obvious test for comparing the use each director of certain types of shots is the Z-test of two proportions, but the Fisher Exact Test can also be used. For an explanation of how to do the Z-test for two proportions, see David M. Lane’s Hyperstat website. For an explanation and online calculator for the Fisher Exact Test (as well as many other calculators), see the Graphpad website (The Fisher Exact Test is under the heading ‘Categorical data’).

For example, Buckland states that:

On average, 58 per cent of Hooper’s shot scales fall within the ‘big close-up to medium close-up’ range; for Spielberg, the figure is only 45 per cent. In Poltergeist, 55 per cent of the shot scales fall within this range, significantly closer to Hooper than Spielberg (164-165).

What does ‘significantly’ mean in this paragraph? There are several problems here. First, in statistics ‘significant’ has a specific (if controversial) meaning – it defines the amount of evidence required to reject a null hypothesis (though quite how you interpret this evidence depends on your preference for the Fisher or Neyman-Pearson approach to hypothesis testing, or the hybrid of the two). However, we cannot judge the significance of Buckland’s claim in these terms – we have a statement that sounds like statistics but is in fact not. We have (again) the presentation of averages without measures of dispersion or confidence intervals, and no significance test is performed. In the above paragraph, the use of the term ‘significant’ sounds good, but it is, from the point of view of statistics, meaningless: how close does ‘close’ have to be to be ‘significant?’ What procedure will we use to calculate ‘close?’ The main problem is that the issue is presented back to front: in statistical hypothesis testing, we always test the null hypothesis of no difference. This is not what Buckland describes: he says that the proportion for Hooper is significantly nearer to that of Poltergeist than the proportion for Spielberg. But how do we frame a statistical hypothesis to express this? A simple way is to compare the proportion for each director against that of Poltergeist. We state our hypotheses:

• The null hypothesis is: ‘the proportion of close-ups (big close-ups to medium close-ups) in Poltergeist is equal to that of the films directed by Hooper/Spielberg.’

The significance level is set at 0.05 – this means that if we get a p-value that is equal to or less than 0.05 we will say that there is a statistically significant difference, and if the p-value is greater than 0.05 we will say that there is no statistically significant difference. This our decision rule. The p-value is NOT the probability that a hypothesis is true – it is the probability of getting a result that is equal to or more extreme than that observed if the null hypothesis is true. Essentially it is a measure of incorrectly concluding that there is a statistically significant difference based on the data in front of you. It is important to remember that a statistically significant result is not a practically significant result, and how the former relates to the real world situation you are analysing requires careful interpretation. A significance test of the above hypothesis will not tell us why there is or is not a difference; but if we assume that the decisions of filmmakers determine the style of a film and that different filmmakers making different decisions will have different styles we must first determine if such a difference can be said to exist. Statistics is one method of doing this, but not the only one.

To answer the question as to which director is closer to Poltergeist and which is further away we need to address the effect size of the difference. A significance test will us if there is a statistically significant difference and the effect size will tell us how big that difference is. Unfortunately, there is not enough data to be able to do this for Buckland’s experiment. Nonetheless, it is important to be clear that the p-value does not tell you the size of a difference.

The results of a Z-test of proportions for our hypotheses at a significance level of 0.05 are presented in Table 1.

TABLE 1 Proportion of close-ups (big close-ups to medium close-ups) (α = 0.05)

In Table 1, we have a lot of information. The first column (P) gives the proportion of close-ups (big close-ups to medium close-ups) in the three data sets, with the confidence interval in the second column so that we know the error of the estimate. The third column (Difference) calculates the difference between the sample for each director and the sample for Poltergeist, and the fourth column is the confidence interval for this difference. (This will give us some limited understanding of ‘closer,’ but is not the same as the effect size). The fifth column gives the result of the Z-test and the sixth column is the p-value. Note that for Hooper the p-value is greater than 0.05, and so we say that there is no statistically significant difference between Hooper and Poltergeist. For Spielberg, the p-value is less than 0.05 and so we say that is a statistically significant difference between this director and Poltergeist. Buckland’s conclusion is vindicated by the statistical analysis – but without defining the hypotheses, without the statistical test, and without defining what we mean by significance we are just guessing, and guessing is not research.

How good are Buckland’s other guesses? We can find out by performing statistical tests on a range of stylistic elements for which Buckland provides data. For the rest of these tests I will not explicitly state the hypotheses and typically hypotheses in research papers will be implicit rather than explicit; but the null hypothesis (unless otherwise stated) in each case is of the form ‘the proportion of x in film y is equal to the proportion of x in Poltergeist.’ The test used in each case is the Z-test for two proportions, and the significance level is 0.05.

In Table 2 we can see the results of applying the Z-test to the proportion of reverse angle shots; and what they tell us is that there is no statistically significant difference between Poltergeist and ET, Jurassic Park, or The Funhouse, while there is a significant difference between Poltergeist and Salem’s Lot. It is possible that, as a television programme (viewed on a smaller screen in the intimate setting of the home) Salem’s Lot uses reverse angle cuts in a different way to motion pictures designed to be viewed on a cinema screen. This is a hypothesis that can be tested statistically if you have the data: do films made for television have a greater proportion of reverse angle cuts than film made for theatres? If so, then the decision to include a made-for-television, which Buckland justifies on the basis of one element of film style (see above), is flawed and the results will reflect the difference between to media and not two directors. Either way, looking at this element of film style leads us to no firm conclusion about who could be considered the author of Poltergeist.

TABLE 2 Proportion of reverse angle shots in Poltergeist against four films (α = 0.05)

The same is also true when we look at the proportion of low angle shots (Table 3). The results show that there is no significant difference between the proportion of low angle shots in Poltergeist and ET or The Funhouse, but that there is a significant difference between the proportion of low angle shots in Poltergeist and Salem’s Lot and Jurassic Park. There is no conclusion that we can draw here about the authorship of Poltergeist.

TABLE 3 Proportion of low angle shots in Poltergeist against four films (α = 0.05)

We also cannot draw any conclusion based on the proportion of high angle shots (Table 4), which shows a significant difference between Poltergeist and ET, but no significant difference between Poltergeist and the other three films.

TABLE 4 Proportion of high angle shots in Poltergeist against four films (α = 0.05)

Buckland argues that the proportion of shots with a low camera height in Poltergeist is more akin to the films of Spielberg than Hooper; and if the former did not actually direct Poltergeist then Buckland suggests (reasonably) that this may have been a creative suggestion from one filmmaker (Spielberg) to another (Hooper). The results of the Z-test show that Poltergeist has a significantly different proportion of low camera height shots from The Funhouse or Salem’s Lot, and we may conclude that a proportion of 0.53 is certainly unusual for what we know about Hooper’s film style. There is no significant difference between the proportion of low camera height shots in Poltergeist and ET, and we could conclude that placing the camera at this height was a creative suggestion that originates with Spielberg if it were not actually his decision, were it not for the fact that Jurassic Park shows a statistically significant difference from Poltergeist. Buckland’s argument that ‘we can infer that the decision to use so many low camera heights in Poltergeist was Spielberg’s suggestion, which constitutes one of the pieces of advice he offered to Hooper on the set’ (163) is demonstrably false because we cannot, in fact, conclude from the results in Table 5 that the use of low camera height shots in Poltergeist is typical of Spielberg. Note that the confidence interval for the proportion in ET does not include the proportion for Jurassic Park, and vice versa.This example demonstrates clearly why it is necessary to perform statistical test and not simply make assertions based on the fact that one number is more like a second number than another: 0.42 looks close enough to 0.53 to for Spielberg’s influence be plausible – especially when the proportions for the Hooper films 0.29 and 0.33 – but the Z-test leads us to the alternative conclusion. This does not mean that Spielberg did not influence Hooper’s decision to place the camera at a low height – but it is not a statistically sound conclusion.

TABLE 5 Proportion of low camera height shots in Poltergeist against four films (α = 0.05)

Things are clearer when we look at the proportion of moving shots: there are significant differences between Poltergeist and the two Spielberg films, but no significant difference between Poltergeist and the two Hooper films. In isolation, we might interpret this as a clear indication of that Poltergeist was directed by Hooper. However, when interpreted in relation to the other types of shot Buckland includes this serves only to confuse the issue.

TABLE 6 Proportion of moving shots in Poltergeist against four films (α = 0.05)

Again, the proportion of shots in the range 1-3 seconds (Table 7) seemingly paints a clear-cut picture of that Hooper did direct Poltergeist. Taken with the moving shots, we might argue that the only elements of film style that can distinguish one filmmaker from another are these two statistics – but this is a highly selective interpretation of the available evidence and it would be necessary to explain why reverse angle shots, low angle shots, etc., should not be used. As Buckland bases his interpretation on all the available data, then the results in Table 7 are inconclusive when viewed in the context of the rest of the data. We can only conclude that there are some differences between some of the films on some measures.

TABLE 7 Proportion of shots in the range 1-3 seconds in Poltergeist against four films (α = 0.05)

All of this assumes that Hooper’s and Spielberg’s films are stylistically different from one another, but is this, in fact, the case? For example, if we compare the proportion of shots in the range 1-3 seconds in ET and Jurassic Park against The Funhouse and Salem’s Lot (see Table 8), we find that we cannot simply distinguish between Spielberg and Hooper as film directors. Neither Salem’s Lot nor The Funhouse shows a significant difference from ET, while both films are significantly different from Jurassic Park. We might conclude, therefore, that the director of Jurassic Park was not the same director of Salem’s Lot and The Funhouse; but, if we did so, would we not also need to consider the possibility that the director of ET did direct Salem’s Lot and The Funhouse? This is made even more complicated by the fact that ET shows no significant difference for the proportion of shots in the range 1-3 seconds from Jurassic Park (Z = 1.4443, p = 0.1487) and that there is no significant difference between Salem’s Lot and The Funhouse (Z = 0.2371, p = 0.8126). Should we then conclude that the director of ET also directed The Funhouse, Salem’s Lot, and Jurassic Park, but that the director of Salem’s Lot, The Funhouse, and ET did not direct Jurassic Park? Buckland describes these films as being of ‘undisputed authorship’ (157), and certainly there is no reason to think that director in each case has been inaccurately credited – but is there any statistical evidence to support this? Is statistics even able to answer this question?

TABLE 8 Z-test of the proportion of shots in the range 1-3 seconds in four films (α = 0.05)

Presentation

One of the problems with Buckland’s analysis is that it is difficult to follow. This is due the poor presentation of the data, which is organised by film rather than by variable. As a result we find the relevant statistics for reverse angle shots on five different pages, and have to spend time hunting and organising this data. This makes it difficult to easily compare and contrast the different stylistic elements. Hopefully you will have found the tables produced here clear and simple to understand, with all the relevant data easily to hand. In Table 2, for example, the proportion of reverse angle shots in each film is presented together in a single column so that rather than having to flip from page to page you can get all the data. It is far easier to identity patterns by looking at the data when it is presented side-by-side.

This might seem like a small and pedantic point, but if you want to present the reader with a detailed statistical analysis, then you have to make it clear for them to follow and to understand. It is especially irritating given that the use of diagrams in the book’s other chapters is clear and easy to understand. It raises questions about the ability of Buckland, his readers, and the editors at Continuum to deal with statistical information – why, when everything else appears to be have been done so much better, was the presentation of the statistics done so badly?

Conclusions

Buckland concludes that Hooper was the director of Poltergeist, but that Spielberg had an input on key stylistic decisions. This seems to me to be an entirely plausible description of the working relationship between two filmmakers who fulfilled the roles of director (Hooper), and producer and screenwriter (Spielberg). However, it is not a conclusion that can be reached through a statistical analysis of some elements of film style.

A further problem lies in the way in which the research question behind the chapter is framed. Buckland asks who the author of Poltergeist is: Spielberg or Hooper. This assumes an all-or-nothing conception of authorship that is parceled out to one of two pre-selected individuals. What if the answer is neither (or even both)? What if there is no such thing as authorship in the cinema? Or if such a thing does exist, what if it cannot be identified by the statistical analysis of those elements of film style and can only be located in the non-quantifiable, such as mise-en-scene? We are also assuming that a statistically significant  difference reflects the practical difference the decisions of a filmmaker has on film style – not necessarily an unreasonable assumption but one that needs to be considered in the design of the experiment.

We could just drop the authorship question entirely and ask who, on the basis of the results presented here, should be credited as the director of Poltergeist? (These two questions are presented as equal by Buckland and there is no reason not to do this, but they could be separated). Well, some measures would seem to favour Spielberg, while others would favour Hooper. We certainly cannot apportion some role of direct creative agency as ‘author’ based on statistics if we cannot use those statistics to say who, in fact, directed the film! Table 9 summarises whether the proportion of different shot types is different for each film against Poltergeist, and we can see that there is no consistent pattern for these elements of film style.

TABLE 9 Statistically significant differences in shot types between Poltergeist and four films (Z-test for two proportions, α = 0.05)

We might also question the results that do indicate significant differences, which may have a higher than expected error rate due to the multiple tests used. We have assumed a significance level of 0.05, which means that at least one significant result could be expected even though there is no practical difference. We can therefore assume that at least one ‘YES’ in Table 9 is a false positive, but we cannot know which one. One method is to correct the significance level to take multiple testing into account, thereby reducing the critical p-value. This would make our decision rule much more stringent, and some of the significant differences above would be re-classed as ‘not significant.’ For the 20 hypothesis tests presented in Table 9, a corrected p-value of 0.0025 would keep the expected error rate at 5% for the whole experiment.

On the back cover of Directed by Steven Spielberg we find the promise that,

Buckland also uses poetics to answer once and for all the question: did Spielberg really direct Poltergeist? The reader will discover whether Poltergeist should remain a Tobe Hooper film, or whether it should be added to Spielberg’s canon.

If we adopt a statistical approach, what can we conclude about the roles of Spielberg and Hooper in the production of Poltergeist? Well, nothing, it turns out, and the reader will discover nothing. The results of the tests presented above are too inconclusive, too topsy-turvy, and too open to conflicting interpretations to justify the conclusion that either Spielberg or Hooper should be credited as author or, indeed, as director. All data is open to multiple interpretations, but we should at least be able to (1) explain the logic behind a particular interpretation, (2) give reasons why one interpretation is to be considered to be better than another, and (3) subject that interpretation to further scrutiny. As I have shown here, Buckland’s study fails on all three counts due to the potentially flawed design of the study, the lack of a statistical methodology and the failure to provide all the necessary information, and the difficulty in understanding the data presented due to its poor organisation.

Summary

Buckland makes bold claims for his chapter on Poltergeist, and promises that the results of his analysis may surprise the reader. Unfortunately, there is little surprising about the standard of the statistical analysis in this book, and the mistakes Buckland makes are the same mistakes that have been made for over thirty years in film studies. For example, no one to my knowledge has ever conducted a statistical test or provided a confidence interval when making statements about film style while quoting things like average shot lengths or the proportion of a type of shot in a film; and Bordwell and Thompson (1985) made precisely the same mistake about the use of the term ‘significant’ Buckland makes 21 years later. Statistics are presented as parameters, and there are no measures of dispersion or confidence intervals. The wrong statistics are used, when the data clearly indicate the necessity to use alternative methods.

Notes

1. Unless otherwise stated, all page references are to this chapter.
2. Charles O’Brien (2005: 83) does provide standard deviations for some data, including standard deviations for some of Barry Salt’s data that do not appear to be in Salt (1992), but makes no reference to them and performs no statistical tests.

References

Bordwell D and Thompson K 1985 Toward a scientific film theory, Quarterly Review of Film Studies 10 (3): 224–237. Available online: http://www.davidbordwell.net/articles/Bordwell_Thompson_QuarterlyRevFilmStud_vol10_no3_summer1988_224.pdf, accessed 18 November 2009.

Buckland W 2006 Directed by Steven Spielberg: Poetics of the Contemporary Hollywood Blockbuster. London: Continuum.

Elsaesser T and Buckland W 2002 Studying Contemporary American Film: A Guide To Movie Analysis. London: Arnold. The chapter on the statistical analysis of film style can be accessed online: http://www.cinemetrics.lv/buckland.php, accessed 18 November 2009.

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 1992 Film Style and Technology: History and Analysis, second edition. London: Starwood.

Schuster M 2002 Informing cultural policy – data, statistics, and meaning, International Symposium on Cultural Statistics, UNESCO Institute for Statistics, Observatoire de la culture et des communications du Québec, Montréal, Québec, Canada, October 21 to 23, 2002. Available online: http://www.culturalpolicies.net/web/files/74/en/Schuster.pdf, accessed 18 November 2009.

Brassed Off

This piece is a slightly re-written version of a paper I gave on regional identity in Brassed Off in March 2007. I am including it here because I think that it is a good example of how the study of British cinema very quickly achieves a critical orthodoxy about some films, and the way in which several film scholars immediately lapsed into the stereotype of the North of England as the ‘land of the working class’ that has been with us since the nineteenth century (see the reference to Rob Shields) suggests a lack of critical imagination. I think that there is more to be said about the changing status of the community in Brassed Off, and that this film provides an excellent opportunity to explore the relationship between economy and culture, and class and region. The one dimensional critical approach of various scholars of British cinema have, I think, missed something interesting about how this film seeks to express identity. They are all to obsessed with class and gender to attend properly to the question of social space in the film, but it is the film itself that suggests we need to go beyond old conceptions of the North (based on economy and class) and to consider the new (based on culture and space).

 

In this paper I argue that in Brassed Off it is the cultural utopianism represented by the Grimley Colliery Brass Band that overcomes the alienation and economic decline of a Yorkshire mining community. The film is typically approached as a narrative about class and gender; albeit one that problematises those categories with the advent of post-industrial society in the United Kingdom. As such, the film is defined as a portrayal of ‘working class life’ (Hallam 2000: 261) and ‘Old Labour collectivism’ (Monk 2000: 277) that draws upon the ‘iconography of working-class realism’ (Leach 2004: 63-64) in presenting ‘a last throw of the dice for a powerful element in the construction of the identity of large parts of the industrial north of England’ (Blandford 2007: 28). This ‘crisis of post-industrialism’ is cast as ‘the crisis of masculinity’ in late twentieth century Britain (Marris 2001: 47), evident in ‘its treatment of the alternately dying, impoverished, and isolated male body’ (Luckett 2000: 95), and its ‘certain level of nostalgia for a fading masculinity’ (Blandford 2007: 29). Crisis is, however, overcome with ‘a certain utopianism about the possibility of collective action’ (Hill 2000: 183). Brassed Off, then, is seen to play out ‘a drama in which male social and emotional bonds once associated with the workplace and the working man’s club are threatened, mourned, struggled for, and finally restored’ (Monk 2000: 282).

The uniformity of critical opinion regarding Brassed Off reflects the north of England’s ‘intensified “sense of place,”’ which, as Rob Shields (1991: 208-230) had demonstarted, has adpoted a ‘consistent form since the nineteenth century in the popular imagination as the “land of the working class.”’ However, in the contemporary era this sense of place is challenged, as the north as ‘land of the working class’ is made problematic by the decline of industry and the transformation of labour. Consequently, the significance of a Yorkshire regional identity in the film has been overlooked, and here I argue that Brassed Off narrates a transformation in the basis for social identity in the town of Grimley from a solidarity based on social class to one based on identification with a regional identity. The ‘social and emotional bonds’ of working class, male culture are mourned, but are not, in the final scenes of the film, restored. As this regional identity is identified with a brass band, it is equally a shift from economy to culture. The identification with the region is located within the nation, and the film represents the affirmation of a British national identity through the expression of a regional, Yorkshire identity.

Brassed Off

The issue of regional identity emerged in a number of British films released between 1992 and 2002, including The Englishman Who Went Up a Hill but Came Down a Mountain (Christopher Monger, 1995), Blue Juice (Carl Prechezer, 1995), and 24 Hour Party People (Michael Winterbottom, 2002) (Redfern 2005a, 2005b, 2007), but no British film released during this period exemplifies the alienation of the regions from the centre, the transformation of work, and the demand to see regional cultures validated in the life of the nation better than Brassed Off.

Alienation most obviously features in the film in the decision to close the Grimley colliery. The report produced by Gloria that demonstrates the pit’s profitability goes unread by the management as it is revealed that the decision to close the pit was taken some two years before the miners voted for redundancy. Gloria’s belief that she could make a difference, that her work would enable both the management and the miners to make an informed decision is shown to be hopelessly naïve, suggesting that ‘down south’ they are unaware of the realities of life in the north. Though the miners vote for redundancy it is clear that it is merely a formality, a means for the management to retain control over the community’s future but to transfer responsibility on to the miners. The colliery manager, McKenzie, is shown to be different from the miners: he does not have a Yorkshire accent, he never shares the same space as the miners, does not try to cash in on the kudos the band brings to the colliery, and his office is spacious with wood panelled walls in contrast to the drab grey interiors of the spaces inhabited by the miners (e.g., the pub, Phil’s home). Andy, the youngest miner and band member, accurately predicts the outcome of the ballot will go four to one in favour of redundancy, because he is aware that although the miners want to keep the pit open they know that they have no real choice in the matter. Here the management are represented as gangsters: McKenzie’s seclusion in his office, his assistants hanging on his every word, and Gloria’s observation that he made the miners ‘an offer they couldn’t refuse’ link him generically to Don Corleone in The Godfather (Francis Ford Coppola, 1972). The alienation of the miners from this decision making process is evident in one sequence where the band’s performance of Rodrigo’s ‘Concierto de Aranjuez’ is heard over shots of a meeting between the management and the union leadership. The miners are excluded from this meeting but the use of music to obscure the negotiations makes the spectator aware of their absence and their lack of a voice in deciding their future. It is only through music that they are able to express themselves. The ease with which the miners are overlooked is revealed early in the film, as we see Ida and Vera, the wives of two of the band members, talking over the backwall of their terraced houses. The handling of space in a series of shot/reverse shot draws on the stereotypes of gossiping Northern women (e.g., from Coronation Street [Granada, 1961– ] and the paintings of Beryl Cook) and implies that they live in adjacent terrace houses. A wide shot then reveals to us that Ida and Vera do not live side by side but are divided by a backyard in which a former miner sits smoking and reading the paper.

As the narrative of Brassed Off centres on the closure of the colliery the economic aspect of the film is particularly strong. The loss of the pit simply means the absence of work and beyond coal mining there is no employment for the men of Grimley. For example, Simmo appears to have no job at all and appears to survive solely on what he can hustle playing pool, even referring to Andy as his ‘main source of income.’ The main focus of this part of the narrative is Phil and Sandra. Burdened by debt acquired during the 1984 miners’ strike, they are unable to keep the bailiffs from the door and eventually their possessions are seized. The bailiffs and the creditors they represent are symbolic of the Thatcher government, being insensitive and ignorant of the struggles of Grimley, and profit from their parasitic relationship to the miners. In order to raise extra money Phil is forced to perform as a clown, Mr. Chuckles. The birthday party at which he performs takes place in a middle class home, and the film contrasts this space (nicely decorated, carpeted, bright) with Phil’s house with its carpet and furniture stripped out. This house is also more modern than Phil’s 1930s dreary council housing and is unattainable to him, and this emphasises the relegation of heavy industry to the past. As McKenzie comments: ‘coal is history.’ On exiting, the mother is surprised to hear that he is a miner, to which he responds: ‘You remember ’em love. Dinosaurs, dodos, miners.’ This sequence is cross-cut with Sandra unable to pay for the family shopping, and relying on the charity of Vera, who, as the cashier, slips her a five pound note from the till. An exhibitionist shot of the table laid out with the birthday cake and other foods exposes a bounty that the miner’s lack. The one time we see one of the miners eat is when Andy takes Gloria to the fish and chip shop, which represents his idea of going ‘posh.’ (Other than this the men of Grimley appear to survive purely, and specifically, on bitter). Gloria comments sarcastically that if she knew they going to go this posh she would have got dressed up, and here the film notes the cultural and economic difference between the Grimley idea of ‘posh’ and that of someone who has just returned from the south of England. Phil’s other engagement as Mr. Chuckles takes place at a harvest festival, again contrasting the bounty of the middle class mothers and their children with the desperation of the miners.

The closure of Grimley colliery forces a shift in the conception of Yorkshire from one that is defined primarily in terms of economic activity to a definition that is culturally based. Moya Luckett argues that Brassed Off ‘ultimately exposes the Marxist truism that culture has no value without an economic infrastructure’ (Luckett, 2000: 96), but the film seeks to demonstrate that in the era of mass pit closures the colliery band is now more essential to the community of Grimley than ever before representing, pride, continuity, and unity. Originally founded in 1881, Danny states that through two world wars, three disasters, seven strikes, and one ‘bloody big depression’ the band ‘played on every flamin’ time.’ The continuity of the band is also evident in the continuity from one generation to the next: Danny’s son Phil is a trombone player, and Gloria turns out to be from Grimley and the granddaughter of the best bandsman and bravest miner Danny ever knew. She even has her grandfather’s flugel horn, and is accepted into the band by virtue of this historical and familial link. The final shot of the film focuses on Danny, who we know to be terminally ill, and a title tells us that, ‘Since 1984 there have been 140 pit closures in Great Britain at the cost of nearly a quarter of a million jobs.’ Brassed Off does not offer any solution to these problems and there are no miracle cures or last minute rescue packages, but the film is utopian in its representation of collective action through the band. Though Danny will die the memory of him will persist through the continuity of the band, and his picture will adorn the practise hall wall alongside Gloria’s grandfather.

Throughout the film there is a division of labour between the men and the women of Grimley, and this is reflected in the way in which social space is divided along gender lines. The men are associated with the pit, the pub, and the practise hall, while the women are shown in domestic situations (e.g., pegging out the washing, caring for children) or in service jobs (e.g., as a waitress, a pub landlady, a cashier, or nurses). Men and women are rarely shown together to occupy the same space: Harry and Rita pass one another outside their house, barely acknowledging each other’s existence; and, unable to cope, Sandra leaves Phil. The economic struggles of Grimley bring families to the point of collapse but through the band they are able to come together. At the Albert Hall the men and women of Grimley are reunited within a single space. Rita and Sandra are in the audience, where previously they have been scornful of their husbands’ interest in the band. With the men on stage and the women in the audience a division of labour remains in place at the end of the film. However, Gloria’s presence in the band suggests that it may be overcome. Gloria is the only female member of the band, and her arrival in Grimley prompts Vera and Ida to take an interest in their husbands’ activities. Gloria’s presence in the band also suggests that class differences may be overcome: it is Gloria who provides the money for the band to travel to London, thereby cleansing herself of the stain of being part of the management and readmitting her to the band. Hill argues that the film projects the image of a ‘populist alliance in which middle-class characters into the community represented by the working-class characters’ (2000: 184); but this alliance is not predicated on gender or class. With the colliery gone it is no longer a pre-requisite of band membership that the musicians be miners, and the grounds for membership is shifted to being from Grimley and this opens the way for a middle-class woman to become a member of the band. In his defiant speech at the Albert Hall, Danny reminds us that it is not music that matters but people. However, in stressing the pride, continuity, and unity the band has to offer Grimley following its economic decline, Brassed Off makes the case that music does matter because it represents the community.

Mike Wayne places Brassed Off into a category he describes as ‘anti-national national films.’

The films in this category are defined by their critique of the myth of community which underpins national identity; the myth that is of the deep horizontal comradeship which overlays the actual relations of a divided and fractured society. The myth of unity and shared interests is a powerful means of legitimising the social order. These films are national insofar as they display an acute attunement to the specific social, political, and cultural dynamics within the defined territory of the nation, but they are anti-national insofar as the that territory is seen as a conflicted zone of unequal relations of power (2002: 25).

It is certainly the case that in representing a mining community in Yorkshire, Brassed Off articulates the social, economic, and cultural dynamics of the UK as a ‘conflicted zone of unequal relations of power.’ The alienation and economic decline of the residents of Grimley is derived from these inequalities. However, the closing scene of the film does not critique the myth of a ‘deep horizontal comradeship’ but appeals to precisely that myth. On leaving the Albert Hall the band is seen riding on an open-top bus past the Houses of Parliament, and, like many films, the red London bus and Big Ben are used in Brassed Off to represent Britishness. By placing the band aboard the bus, the film symbolically places Yorkshire within the nation. It is in this sequence that the band plays Sir Edward Elgar’s Pomp and Circumstance No. 1, or as Danny refers to it (with grudging respect): ‘Land of Hope and Bloody Glory.’ The film thus appeals to the ‘deep horizontal comradeship’ of a British national identity whilst at the same time asserting the regional identity of Yorkshire, and the importance of that regional identity in the nation. Brassed Off may be read as an appeal to the nation not to forget that communities such as Grimley are a part of the nation, and though the traditional image of the North as an industrial heartland may no longer be applicable the intensity of identification with the North has not diminished.

Conclusion

Brassed Off is a British film – but its nationality is articulated through the representation of the regional in a harmonious relationship with the national. The alienation of a regional community can be overcome through the unification of the regional and the national, and in representing the Yorkshire region the films make the case for importance of the regional in the UK. Brassed Off dramatises the shift from traditional heavy industries to cultural industries and make the case that the rest of the UK needs to recognise this shift and reorient their ‘mental maps’ of the region. It also emphasises the vitality of a regional subculture; and that the nation should respect the uniqueness of Yorkshire, and recognise its contribution to the cultural life of the nation. In contrast to the anti-Thatcherite state of the nation films of the 1980s that questioned the validity of a national identity (e.g., The Ploughman’s Lunch [Richard Eyre, 1983]), Brassed Off has a positive outlook on the value of regional cultures, a British national identity, and the possibility of negotiating a more sympathetic relationship between the regional and the national.

Works Cited

Blandford, S. (2007) Film, Drama, and the Break-up of Britain. Bristol: Intellect.

Hallam, J. (2000) Film, class, and national identity: reimagining communities in the age of devolution, in J. Ashby and A. Higson (eds.) British Cinema, Past and Present. London and New York: Routledge: 261-273.

Hill, J. (2000) Failure and utopianism: representations of the working class in British cinema of the 1990s, in R. Murphy (ed.) British Cinema of the 90s. London: BFI: 178-187.

Leach, J. (2004) British Cinema. Cambridge: Cambridge University Press.

Luckett, M. (2000) Image and nation in the 1990s, in R. Murphy (ed.) British Cinema in the 90s. London: BFI: 88-99.

Marris, P. (2001) Northern realism: an exhausted tradition?, Cineaste 26 (4): 47-50.

Monk, C. (2000) Underbelly UK: The 1990s underclass film, masculinity, and the ideologies of “New Britain,” in J. Ashby and A. Higson (eds.) British Cinema, Past and Present. London and New York: Routledge: 274-287.

Shields, R. (1991) Places on the Margin: Alternative Geographies of Modernity. London: Routledge.

Redfern, N. (2005a) Regionalism and the Cinema in the United Kingdom, 1992 to 2002. Unpublished Ph.D. Thesis, Manchester Metropolitan University.

Redfern, N. (2005b) ‘We do things differently here:’ Manchester as a cultural region in 24 Hour Party People, EnterText 5 (2): 286-306.

Redfern, N. (2007) Making Wales possible: regional identity and the geographical imagination in The Englishman Who Went Up a Hill but Came Down a Mountain, Cyfrwmg: Media Wales Journal 4: 57-70.

Wayne, M. (2002) The Politics of Contemporary European Cinema: Histories, Borders, Diasporas. Bristol: Intellect Books.

3-D week on Channel 4

In September I wrote a piece on why I did not think that the future of home entertainment lay in 3-D television. This week, Channel 4 have been showing various programmes in 3-D, and so it seemed like the perfect opportunity to test the potential of the technology.

The results were more underwhelming than I had anticipated. No, really – I didn’t think it would be this bad.

The first programme of the week was ‘The Queen in 3-D,’ shown in two parts on Monday and Tuesday.It featured too affable gentlemen, Bob Angell and Arthur Wooster, who shot colour 3-D footage of the coronation in 1953. The programme was made of non-3-D sections where we got the history of the coronation, some talking-head segments, which were in 3-D, and the 3-D footage of the coronation. The pair of filmmakers appeared from time to time to ask us to put on or take-off our 3-D viewing spectacles. This take-them-off and put-them-back-on-again soon became irritating.

The stongest 3-D effect was in the talking-head segments, but it did not add anything to the social history of the coronation and the effect itself was disappointing. Things do not look any more real – if anything the 3-D effect was quite surreal as the image looked like a series of very flat layers stacked up one on top of the other. It did not have any depth or shape to it. The effect of spatial separation between these flat layers was evident (although, as I have said, not consistently), but it made me think of Ivor the Engine more than anything else. (For my non-UK readers under the age of 25, Ivor the Engine was an animated series created by Oliver Postgate in the 1950s and used stop-motion animation of cardboard cut-outs).

This image of Ivor the Engine was taken from the Walesonline page, where you can find an obituary of Oliver Postgate, who died in December 2008. Imagine this in 3-D, and you sort of get the idea.

The flatness of the image was all the more disappointing, as I have recently been re-watching the 3.5 hour long documentary on the making of Blade Runner (Ridley Scott, 1982) that is part of the Ultimate Collector’s Edition Blade Runner box set. This excellent documenatry has a great section with Douglas Trumbull and his fellow model makers, designers, matte painters, special effects cameraman, supervisors, etc. There is a great bit where they explain how they created the image of Los Angeles disappearing into the distance by using flat pieces of brass, so that the city is built up of layer upon layer of this model pieces to create a convincing experience of the immensity of the city. This old fashioned method creating in camera effects through multiple passes over a model landscape, gives a much better effect than 3-D. Obviously it is unfair to compare Channel 4 to the production of Blade Runner, but if we are going to hail 3-D as the future, then it should at least be an improvement on the technology of the past. When I get to see a 3-D landscape as good as that made in 1981, then we can talk about being impressed. Maybe James Cameron’s Avatar will be the film to take us there. But if the ‘last analogue film,’ as Blade Runner was referred to, can achieve such wonderful effects of depth and shape by using flat pieces of brass, 3-D faces a stiff challenge.

Matthew Yuricich’s matte paintings for Blade Runner are amazing, and better than 3-D. This image is taken from an interview with Douglas Trumbull over at Kipplezone, which is definitely worth checking out.

The 3-D effect in ‘The Queen in 3-D’ and the magic programme presented by Derren Brown that followed it was evident in some shots more than others, and this has been a problem through out the week – the inconsistency of the 3-D effect just doesn’t make it seem worth the while.Just as 3-D adds nothing to social history, I found that the magic tricks were harder to follow wearing the 3-D glasses. Also because 3-D television is so rare, I kept looking out for the 3-D effect and missed what was going on with the tricks themselves. I can see the appeal for magic shows to use 3-D – the lack of reality that was alienating in the documentary footage is ideal for illusions. It may that the future of 3-D in the home is limited to some genres of programming – but if this is the case, then selling the audience a new 3-D television is going to be that much harder.

I watched the first part of Flesh for Frankenstein (Paul Morrissey, 1973), which is every bit as bad as I remember, and found that even wearing the glasses I could see the amber and blue shapes on the image instead of the 3-D effect. The 3-D effect itself was very intermittent in this film, being quite strong in some shots but barely noticeable in others.

As my eyesight is pretty much perfect I don’t wear glasses or contact lenses, and I did not like the fact that I have to wear the 3-D spectacles. They very quickly became uncomfortable, and after a while I started to get a headache.

I also burnt my toast. The problem with 3-D in the home is that you do not just watch TV and do nothing else. Rather, the TV is on and has your attention some of the time, while various other things make competing demands on your attention. 3-D seems to depend on the viewer attending to the television screen and nothing else – which is fine in a cinema, where I have made the effort to go out and paid my money with the specific intention of watching the film. But at home I may be talking to another person who is either with me or on the phone, I may be attempting a crossword. My toast was burnt because my attention could not be divided so easily between the screen and the toast, and because I was wearing the 3-D glasses and couldn’t see what was happening. 3-D is all very well as a novelty for films, but once you actually try living a life it falls apart almost instantly.

In order to get the best effect, Channel 4 advised you to dim the lights. Well, I don’t have a light-dimmer switch – I have a light on-and-off switch. So now I am sitting the dark, on my own, watching a programme of which only a small part is actually 3-D (and even then the effect is inconsistent), wearing uncomfortable glasses that are giving me a headache, unable to see anything properly, and eating burnt toast.

Do you want to come from work and sit in the dark wearing 3-D glasses, ignoring your nearest and dearest while watching underwhelming television programmes? Of course not.

The future of home entertainment?

No.