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Rpubs link comes here: https://rpubs.com/s3240003/bechdel

Introduction

Disproportionate gender representation in the film industry is an interesting issue to many.

The Bechdel test is a tool to measure the representation of women in film. A film is said to pass the test when the following criteria are met:

• The film contains at least two named women,
• These women have a conversation with each other, and
• The conversation is not about a man.

This study will investigate the association of the gender of a film’s writers, and the film’s score on the Bechdel test.

Problem Statement

Is a film’s result on the Bechdel test associated with the gender of the film’s writers?

A Chi-Squared test of association will be used to test this association.

Data

In order to address the question posed by this study, a number of data sources were utilised. Data was sourced from the following:

• The Bechdel test website: On this website users submit assessments of films against the criteria of the Bechdel test. A data set containing all assessed films and their corresponding scores was used. Films in this dataset are also cross referenced to IMDb using unique IMDb ID numbers. IMDb is a database containing the information of over 6 million films.
• IMDb. A number of IMDb datasets were used, these included:
  • ‘title.crew.tsv.gz’: contains the unique ID number of writers and directors for all film titles in IMDb.
  • ‘name.basics.tsv.gz’: Contains details of writers and directors, sorted by a unique ID number.

Gender data for writers and directors is not included within publicly available IMDb datasets. Due to the number of writers credited in the assessed films, it was not possible to individually check and assign a gender to each person. genderize.io was used to predict the gender of each writer, based on their first name, as extracted from IMDb (Adapted from FiveThirtyEight, 2017, The Next Bechdel Test)

Data Cont.

Each film in the Bechdel dataset has a score of between 0 and 3, depending on the number of Bechdel test criteria that it met. A film was only considered to Pass the Bechdel test if it passed each of the 3 rules set out by the test. All films scoring less than 3 were deemed to Fail.

First names of writers were extracted and processed through genderize.io, the predicted gender and corresponding probability associated with that prediction were joined with the Bechdel dataset.

If the gender of a writer could not be predicted, or a gender was predicted with a probability of less than 90% (as output by genderize.io), the observation was filtered out of the dataset.

A film was considered to have female representation if at least one writer that worked on that film was female. All remaining Films that did not meet this criteria were considered to only have Male representation.

The resulting data set contained 7835 unique films, each with a Bechdel test result (Pass/Fail) and an assessment of the Writer gender representation (Male/Female)

Data Cont.

The following variables are of importance to this study:

• imdbid: a unique identifier for films in IMDB databases, also used in the Bechdel dataset.
• score: ordered factor with 4 levels ranging from 0 to 3. This is the number of bechdel test rules that the film passed. This variable is available in the Bechdel dataset.
• binary: a factor with 2 levels, PASS and FAIL. This is a conversion of the score variable into a binary pass/fail output.
• role: in the final dataset there may be two observations for each film. One for those with the role ‘director’ and one with the role ‘writer’
• representation: a factor with 2 levels, Male or Female. This is the assessment of what gender is represented for the corresponding ‘role’ in the observation.

Descriptive Statistics and Visualisation

In this investigation each observation represents a unique film, each with a determined gender representation (Male/Female) and a binary result on the Bechdel test (PASS/FAIL)

Observations with questionable values, such as those with genders predicted with a probability of correctness being less than 90%, were filtered out of the data set.

It can be observed that a higher proportion of films that pass the Bechdel test appear to have female representation among its writers compared to male representation. See the next slide for this visualised on a bar chart.

Descriptive Statistics and Visualisation Cont.

bechdel_complete <- read.csv("Data/bechdel_complete.csv", stringsAsFactors = TRUE)
barplot(table(bechdel_complete$representation,bechdel_complete$binary)%>%prop.table(margin = 2),ylab="Proportion Within Group",
        ylim=c(0,1),legend=rownames(table(bechdel_complete$representation,bechdel_complete$binary)%>%prop.table(margin = 2)),beside=TRUE,
        args.legend=c(x = "top",horiz=TRUE,title="Representation"),
        xlab="Representation")

Descriptive Statistics Cont.

A summary of the data is presented in the tables below. These tables include a raw count of all observations:

t1 <- table(bechdel_complete$representation,bechdel_complete$binary)
t2 <- table(bechdel_complete$representation,bechdel_complete$binary)%>%prop.table(margin = 2)
knitr::kable(t1)

and also the proportion of films with Male and Female representation among writers, by Bechdel score:

knitr::kable(t2, digits = 2)

Hypothesis Testing

A Chi-squared test of association was used to test for a statistically significant association between the gender of a films writers and the films result on the Bechdel test.

It was assumed that if a film had at least one female writer, that constituted female representation.

This statistical test assumes that no more than 25% of the cells have expected counts below 5. This assumption was met.

\(H_0\): There is no association in the population between the gender of a films writers and the films result on the Bechdel test.

\(H_A\): There is an association in the population between the gender of a films writers and the films result on the Bechdel test.

Hypothesis Testing Cont.

To test \(H_0\), the Chi-square statistic (\(\chi^2\))is calculated, where \(O_{ij}\) is the observed count in the \(i^{th}\) row of the \(j^{th}\) column and \(E_{ij}\) is the expected count assuming no association.

\(r_{i}\) refers to the total count of the \(i^{th}\) row and \(c_{j}\) is the total count of the \(j^{th}\) column. \(n\) is the total number of observations.

\[\chi^2 = \sum(O_{ij} - E_{ij})^2/E_{ij} \]

\[E_{ij} = n(r_{i}/n)(c_{j}/n)\] These values can be computed by R…

Hypothesis Testing Cont.

Observed Values:

chi <- chisq.test(table(bechdel_complete$binary, bechdel_complete$representation))
knitr::kable(chi$observed, digits = 2)

Expected Values:

knitr::kable(chi$expected, digits = 2)

These expected values can now be used to calculate the test statistic \(\chi^2\)…

Hypothesis Testing Cont.

chi

## 
##  Pearson's Chi-squared test with Yates' continuity correction
## 
## data:  table(bechdel_complete$binary, bechdel_complete$representation)
## X-squared = 426.89, df = 1, p-value < 2.2e-16

This \(\chi^2\) value of 426.89 is compared against the critical value, \(\chi^2_{crit}\):

qchisq(p = .95,df = 1)

## [1] 3.841459

\(p\) value:

chi$p.value

## [1] 7.725228e-95

\(H_0\) can be rejected as \(\chi^2 >\chi^2_{crit}\) (426.89 > 3.84) and the \(p\) value of <0.001 is below the 0.05 level of significance.

Discussion

A Chi-squared test of association was used to test for a statistically significant association between the gender of a films writers and the films result on the Bechdel test. The results of this test found a statistically significant association, \(\chi^2 = 426.89, p < .001\). The results of this study suggest that films that had female representation among its writers was more likely to pass the bechdel test when compared to those films without female representation.

This suggests that if at least one female is on a film’s writing team, that film is more likely to achieve a basic standard of female representation in film as set out by the rules of the Bechdel test, compared to those films that have no female writers.

Discussion Cont.

There are two major limitations with this study:

• The need to predict gender of a writer based on their first name. While only predictions with a >90% probability of being correct were retained, there is still a possibility that genders were erroneously assigned to some writers.
• The Bechdel test website allows users submit an assessment of a film containing the film’s score on the bechdel test. This assessment is subjective. Each assessment has a comments section where users debate the accuracy of the assessment, which cna lead to a moderator changing the score. This comment section is not captured by the Bechdel test database and was not considered by this study.

Future studies should consider:

• Identifying, or attaining approval to use data sources that contain the gender of people in a film’s crew.
• Utilise the comments section of the Bechdel test website to further refine Bechdel test scores assigned to films used in the investigation
• Consider assessing the association of other variables, such as lead actor gender, director gender, budget, or gross profits, against a films score on the Bechdel test.

References

• IMDb Internet Movie Database (2020). title.crew.tsv.gz. Retrieved September 28, 2020, from IMDb website: https://datasets.imdbws.com/
• IMDb Internet Movie Database (2020). name.basics.tsv.gz. Retrieved September 28, 2020, from IMDb website: https://datasets.imdbws.com/
• Bechdel Test Movie List (2020). getAllMovies database. Retrieved September 28, 2020, from Bechdel Test Movie List website: https://bechdeltest.com/?list=all
• FiveThirtyEight (2017). The Next Bechdel Test. https://projects.fivethirtyeight.com/next-bechdel/