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.

The relative dispersion of shot lengths

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

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

Measures of Relative Dispersion

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

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

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

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

Coefficient of variation

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

CV = SD/M

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

Quartile coefficient of dispersion

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

QCD = Q3-Q1/Q3+Q1

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

Coefficient of median deviation

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

MD = MAD/Median

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

Discussion

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

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

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

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

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

Notes

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

Establishing shots

The establishing shot is unique in the cinema in that it is distinguished not by its scale (e.g., medium long shot, close up) but by its function. Typically, this function is understood to involve the definition of on-screen space and on-screen spatial relationships. For example Karel Reisz and Gavin Millar describe an establishing shot in these terms:

Shot (usually long shot) used near the beginning of a scene to establish the inter-relationship of details to be shown subsequently in nearer shots (Reisz and Millar 1968: 399);

Equally we have the following definition:

A shot, usually at the beginning of a scene, that situates where and sometimes when the action that is to follow takes place before it is broken up through editing. Establishing shots also make clear the spatial relations among characters and the space they inhabit. … Establishing shots are usually long shots or extreme long shots, although not necessarily so (Blandford et al 2001: 86).

These definitions are fine as they go, but they do not capture something important about the role of establishing shots – they emphasise spatial qualities only whilst ignoring the role of establishing shots in organising the viewer’s comprehension of the narrative chain.

Two sequences

Two films provide examples with how sequences begin with a series of shots that do not define the space of the narrative, but nonetheless play an important role in preparing the viewer to receive narrative information.

Little Caesar (1931)

The action at “Little Arnie Gorch’s Casino” is comprised of thirty one shots, and plays an important role in setting up character relations in Little Caesar. The dramatic purpose of this scene is to define the relationship between a number of characters: to identify Rico, who desires the power and wealth of “Diamond” Pete Montana, as a violent liability at a time when the gangsters have been ordered to lie low by “Big Boy.” Rico’s designs on wealth and power are conveyed visually through a close-up shot from Rico’s point-of-view of “Diamond” Pete’s jewels and clothes. Dialogue is used to mark Rico out as a liability, as “Diamond” Pete says of him to Salvatore: ‘It’s guys like this torpedo of yours that cause all the trouble.’

The action of this sequence takes place in three spaces. Firstly, we are in the casino with the gamblers and the owner Little Arnie Gorch, who is informed that “Diamond” Pete is coming to see him (Figures 1-5). Then we move to the office of Little Arnie is the space where “Diamond” Pete first comes across Rico, and he explains that the crime commissioner McClure can’t be bargained with and therefore “Big Boy” has given the order to lie low (Figures 6-9 and 11-22). Finally, it is in the corridor outside the office where “Diamond” Pete and Rico come face to face, setting up the power struggle that will come later in the film (Figures 10 and 23-31).

The relevant narrative information in this scene is presented in the office and the corridor, but neither of these spaces is defined by the use of an establishing shot. The office is revealed to us as Little Arnie Gorch enters to see Salvatore and Rico waiting for him, but at no time during this sequence is there a shot long enough or wide enough to give the spectator an overall sense of the spatial extent of the room or the relationships between characters. At no point in the scene is ‘the inter-relationship of details to be shown subsequently in nearer shots’ established.

However, the scene does begin with two shots that show us we are in a casino and three shots of Little Arnie being informed that a meeting is taking place in his office. Why does the film begin the scene with in a space in which no narrative action will take place before moving to two other spaces, neither of which are established?

Figures 1-5 The opening shots of this sequence from Little Caesar let the audience know where we are and what is happening, but the action will not take place in the spaces we have so far been shown.

Figures 6-22 The scene then goes on to establish that Rico is a loose cannon who could make trouble for the “Diamond” Pete, who has come to tell the gangsters to lie low.

Figures 23-31 In the corridor Rico admires “Diamond” Pete’s finery and images himself taking over Pete’s role.

Pleasantville (1998)

An early sequence in Pleasantville comprises 14 shots (though I have only used 12 here – shots H and I are repeated), and sets up Tobey Maguire’s character as your typical shy high school student. The narrative of the film follows his character’s transformation into a more confident person having been sucked into a 1950s television show. The first seven shots (A-G) are of student’s arriving at school, but do not feature any characters who we will follow through the narrative. In fact, these seven shots reveal no narrative information whatsoever, and there is no dialogue until we see David in shot H. He appears to be asking the girl in shot I out on a date who would seem to be listening intently, but in shot J the distance between these two characters is revealed: David is in fact talking to no-one, and in shot K we see the girl is actually talking to some one else. The final shot of the sequence (L) is a very long shot of the school yard, and perhaps comes closest to the two definitions of the establishing shot given above except that it marks the end of this sequence rather than its beginning.

There is no shot in this sequence that establishes the spatial relationships of the narrative action that is to follow. There is no spatial continuity between shots A through G, and while H through L are spatially related we do not know how they are related to the earlier shots of this sequence.

The dramatic impact of this scene clearly depends on delaying the viewer’s awareness of the spatial distance between David and the object of his affections, but why then does it take so long to set up the sequence with seven shots that tell us nothing in particular about the narrative?

Figures A-H The opening seven shots carry no narrative information, while the remaining shots set up David’s character for the film

The role of the establishing shot

What is going on in these two films? Only shot L in Pleasantville comes close to the definition of an establishing shot, and yet in both sequences we have a series of shots that let the viewer know where we are. While it is certainly a part of the function of these shots (1-5 in Little Caesar, A-G in Pleasantville) to tell the viewer we are here, I think there is also an additional function of orientating the viewer in the narrative chain. These shots carry no narrative information, but they perform an important role in preparing the viewer to expect narrative information. The role these shots play is to alert and orientate the viewer – they say “here is a new sequence, pay attention.” In Little Caesar we also have dialogue to tell us what is going to happen in the rest of the sequence.

These types of preparatory gambits occur in language, and are called prefacing devices. Prefaces comprise a varied class of phenomena in the context of human interaction (gestures, micro-moments of silence, fully formed statements) that occur as prefatory components to bigger things to come (Streeck 1995). The function of a preface is to ‘foreshadow’ or ‘project’ something that comes after them, to bring into play and ‘prepare the scene’ (Sacks, Schegloff, & Jefferson 1974; Schegloff 1984). Prefaces enable others to anticipate intended actions and to respond accordingly, thus synchronizing the understanding of the participants (Goody 1995).

This is, I argue, what is happening in the opening five shots of Little Caesar: we are being prepared to receive narrative information through a combination of shots, titles, and dialogue. In Pleasantville, the opening of the sequence is unnecessarily long: the same effect could have been achieved with fewer shots but the delay of the reveal is also important here. The establishing portion of this sequence not only makes the viewer aware that something is going to happen but also contributes to the narrative effect by heightening the viewer’s expectation of events to come.

Shots such as those in Little Caesar and Pleasantville have a role to play in establishing a sequence but they do not meet the definitions of establishing shots given above. An alternative definition of an establishing shot should include the following components:

• The establishing shot occurs at the beginning of a sequence.
• The establishing shot does not necessarily occur in isolation, and we may find that we are dealing with establishing shots in any particular sequence.
• The establishing shot is non-scalar: it is not limited to long or very long shots, and can be of any focal depth and field of view.
• The establishing shot may set up the overall space of a scene that will subsequently be broken down through analytical editing, but this is neither a necessary not a sufficient requirement to define its role in establishing a sequence.
• The establishing shot serves to orientate the viewer to the flow of the narrative by alerting her to the beginning of a new sequence, but does not itself carry narrative information.

Persson (1998: 24) writes that ‘some cinematic conventions … are not totally arbitrary. They are designed with careful consideration to the socio-psychological makeup of the spectator in order to produce specific effects.’ Establishing shots are not arbitrary and have an important role to play in organising the viewer’s attention so that these specific effects may be achieved in the viewer by the film.

References

Blandford, S., B.K. Grant, and J. Hillier (2001) The Film Studies Dictionary. London: Arnold.

Goody, E.N. (1995) Introduction: some implications of a social origin of intelligence in E.N. Goody (ed.) Social Intelligence and Interaction: Expressions and Implications of the Social Bias in Human Intelligence. Cambridge: Cambridge University Press.

Persson, P. (1998) Towards a psychological theory of close-ups: experiencing intimacy and threat, Kinema: A Journal for Film and Audiovisual Media 9: 24-42.

Reisz, K., and G. Millar (1968) The Technique of Film Editing. London: Focal Press.

Sacks, H., E.A. Schegloff, & G. Jefferson (1974) A simplest systematics for the organization of turn-taking for conversation, Language 50 (4): 696-735.

Schegloff, E.A. (1984) On some gestures’ relation to talk, in J.M Atkinson and J. Heritage (eds.) Structures of Social Action. Cambridge: Cambridge University Press: 266-298.

Streeck, J. (1995) On projection, in E.N. Goody (ed.) Social Intelligence and Interaction: Expressions and Implications of the Social Bias in Human Intelligence. Cambridge: Cambridge University Press.

Prefaces comprise a varied class of phenomena in the context of human interaction (gestures, micro-moments of silence, fully formed statements) that occur as prefatory components to bigger things to come (Streeck 1995). The function of a preface is to ‘foreshadow’ or ‘project’ something that comes after them, to bring into play and ‘prepare the scene’ (Sacks, Schegloff, & Jefferson 1974; Schegloff 1984). Prefaces enable others to anticipate intended actions and to respond accordingly, thus synchronizing the understanding of the participants (Goody 1995).