Lecture 10

Visual summaries of data

Plots and tables

Dr Lincoln Colling

28 Nov 2022

Psychology as a Science

Plan for today

Why use tables and plots?

Tables

What makes a good table?
Frequency tables
Summary tables

Plotting basics

What makes a good plot?
Structure of a plot
Frequency plots
Summary plots

All plots and tables in the slides made in R

The Data

4,468 films pulled from IMDB.com
Inclusion criteria
- Rated at least 5,000 times
- Released in 2010 or later
Data available here

Of the 4,468 titles, 52 (1.16%) were produced, or co-produced by at least one African country, 3,009 (67.35%) by at least one country in the Americas, 1,058 (23.68%) by a country in Asia, 1,604 (35.9%) in Europe, and 153 (3.42%) in Oceania. The sum of these numbers is necessarily higher than the total number of titles in the data set, as one title can have multiple production attributions and so can count towards several “Continent” categories.

The number of IMDB ratings ranged from 5,003 to 2.03×10⁶, with a mean of 6.31×10⁴ and SD of 1.23×10⁵. The average user rating for a given title spanned the range 1–9.2; M=6.37, SD=1.02.

Information on estimated budget was only available for 2,170 of the titles in the data set: 18–3.56×10⁸, M=3.96×10⁷, SD=5.09×10⁷.

Why and when to use tables and plots?

Why

Plots and tables allow us to convey a lot of information using relatively small amounts of space
They structure the information we’re communicating so that it’s easier to understand than a wall of text
Good tables and plots are simply #aesthetic

When

Tables and plot are not just for reports
They are a good way of exploring data before analysis in order for us to get to know them
Not all plots and table we create should be put in reports/papers
If we are including them in reports/papers, they should be used to convey important information that would be cumbersome to convey in body text

Tables

Tidy way of presenting a lot of numbers
A good table should be easy to read, well-organised, and clear
Good for exploring and summarising data (this lecture), and presenting results (future modules)

Structural elements

Number: all tables should be numbered and the number should be referenced in paper/report
Title: should be descriptive
Header: clearly indicates what the data in each column mean
Body: logically organised into rows and columns
Note: optional, provides additional information necessary to correctly interpret data in the table

Frequency tables

Table 1
*Distribution of film titles by continent with absolute and relative frequencies*
Continent	N ^*	%^†
Africa	52	1.2
Americas	3,009	67.3
Asia	1,058	23.7
Europe	1,604	35.9
Oceania	153	3.4
Note:
Based on a sample of 4,468 full feature films released since 2010 with 5,000 or more ratings on IMDB.com.
^* Column does not add up to total number of titles, as a single title can have multiple continent attributions.
^† Percentage of total number of titles (does not add up to 100%).

Grouped frequency tables

Table 2
*Distribution of film titles by genres for Europe and the Americas*
	Americas		Europe
Continent	N ^*	%^†	N ^*	%^†
Drama	1,704	56.6	1,075	67.0
Thriller	1,142	38.0	620	38.7
Comedy	1,069	35.5	439	27.4
Action	779	25.9	363	22.6
Romance	551	18.3	325	20.3
Crime	547	18.2	295	18.4
Adventure	541	18.0	267	16.6
Other	2,934	97.5	1,548	96.5
Note:
Based on a sample of 4,468 full feature films released since 2010 with 5,000 or more ratings on IMDB.com.
^* Column does not add up to total number of titles, as a single title can have multiple genre attributions.
^† Percentage of total number of titles within given continent (does not add up to 100%).

Grouped frequency tables

Table 2
*Distribution of film titles by genres for Europe and the Americas*
	Americas		Europe
Continent	N ^*	%^†	N ^*	%^†
Drama	1,704	56.6	1,075	67.0
Thriller	1,142	38.0	620	38.7
Comedy	1,069	35.5	439	27.4
Action	779	25.9	363	22.6
Romance	551	18.3	325	20.3
Crime	547	18.2	295	18.4
Adventure	541	18.0	267	16.6
Other	2,934	97.5	1,548	96.5
Note:
Based on a sample of 4,468 full feature films released since 2010 with 5,000 or more ratings on IMDB.com.
^* Column does not add up to total number of titles, as a single title can have multiple genre attributions.
^† Percentage of total number of titles within given continent (does not add up to 100%).

Summary tables

Table 3
*Summary statistics of the measured continuous variables*
	N	Min	Max	M	SD	SEM
Average IMDB rating	4,468	1	9.2	6.37	1.02	0.02
Number of IMDB ratings	4,468	5,003	2.03×10⁶	6.31×10⁴	1.23×10⁵	5.25
Estimated budget (USD)	2,170	18	3.56×10⁸	3.96×10⁷	5.09×10⁷	106.75
Opening week grossing (USD)	2,842	63	3.57×10⁸	1.14×10⁷	2.52×10⁷	75.09
Runtime in minutes	4,387	45	321	109.22	20.33	0.07

Plots

Sometimes, a picture is worth a thousand words
Great for communicating information about data that takes a lot of space to explain in writing
Good graphics should be both clear and packed full of information

Structural elements

Number: just like tables, all plots should be numbered and the number should be referenced
Title: should be descriptive
Axes: clearly labelled, with sensible ticks along them, and units of measurement
Graphics: clear, well designed, good size
Legend: if graphical elements are used to distinguish levels of variables, legend must be provided
Note: optional, provides additional information necessary to correctly interpret the plot

Frequency plots

Good for exploring distributions of data
They are intended for you, the analyst, not for the readers of your paper/report
They can be nice but take up too much space, use up too much ink, and convey too little information

Histogram

Useful for plotting distributions of continuous variables only (interval and ratio)
Data need to be binned; width of individual bins is our decision, explicit or implicit

Code

df |>
  dplyr::distinct(title, .keep_all = TRUE) |>
  ggplot2::ggplot(aes(x = rating)) +
  ggplot2::geom_bar(fill = "steelblue") +
  ggplot2::labs(x = "Mean viewer rating", y = "Count") +
  ggplot2::scale_x_continuous(breaks = 1:10)

Figure 1: A histogram of the distribution of average viewer ratings in the sample

Density plots

Also for continuous variables only
Simulate what a histogram with infinitely narrow bins would look like

Code

df |>
  dplyr::distinct(title, .keep_all = T) |>
  ggplot2::ggplot(aes(x = rating)) +
  ggplot2::geom_density(fill = "#3d755b88", colour = "#3d755b") +
  ggplot2::labs(x = "Mean viewer rating", y = "Density") +
  ggplot2::scale_x_continuous(breaks = 1:10)

Figure 2: Density plots provide a smoother representation of the distribution of a variable

Bar charts

Visualise distributions of categorical data (nominal and ordinal)
They are still used for summarising data, so you’ll see a lot of them
Even the APA website shows them in their list of sample figures
But when you’re drawing your own plots there are better choices…

Simple bar chart

Code

df |>
  dplyr::distinct(title, country, .keep_all = T) |>
  dplyr::mutate(region = factor(region)) |>
  ggplot2::ggplot(aes(x = region)) +
  ggplot2::geom_bar(fill = "#00356888", colour="#003568") +
  ggplot2::labs(x = "Region", y = "Count") +
  ggplot2::theme(axis.text.x = element_text(angle = 30, vjust = 1, hjust=1))

Figure 3: A bar chart showing the number of films produced within a region

Note. Categorisation of countries into regions is based on World Bank Development Indicators.

Bar charts

Colour isn’t necessary here, but it’s at least meaningful (British Board of Film Classification labels)

Code

df |>
  dplyr::distinct(title, .keep_all=T) |>
  dplyr::mutate(cert = forcats::fct_explicit_na(cert)) |>
  ggplot2::ggplot(aes(x = cert, fill = cert, colour = cert)) +
  ggplot2::geom_bar() +
  ggplot2::labs(x = "BBFC Certificate", y = "Count") +
  ggplot2::scale_fill_manual(values = c("#2aa832", "#fab900", "#ef7910",
                               "#ef7910", "#ec5692", "#d8011e", "#007ec8", "#aaaaaa"),
                    guide=F) +
  ggplot2::scale_color_manual(values = c("#2aa832", "#fab900", "#ef7910",
                                "#ef7910", "#ec5692", "#d8011e", "#007ec8", "#aaaaaa"),
                     guide=F) +
  ggplot2::geom_hline(yintercept = rep(seq(500, 2000, by = 500), 2), size = 2, colour = "white")

Figure 4: Bar charts can also show distributions of ordinal variables

Note. U: universally suitable; PG: parental guidance recommended; 12: suitable for children from 12 years of age; 12A: suitable for children from 12 years of age accompanied by adult; 15: suitable for 15-year-olds and older; 18: only suitable for adults.

Bar charts

Sometimes it makes more sense to flip them horizontally
Grid lines can help comparing things in all kinds of plots

Code

df |>
  dplyr::distinct(title, genre, .keep_all = T) |>
  dplyr::mutate(genre = factor(genre) |>
           forcats::fct_infreq() |>
           forcats::fct_rev()) |>
  ggplot2::ggplot(aes(x = genre)) +
  ggplot2::geom_bar(fill = "#3d755b88", colour = "#3d755b") +
  ggplot2::coord_flip() +
  ggplot2::labs(x = "Genre", y = "Count") +
  ggplot2::theme(panel.grid.major.x = element_line(size=0.1, colour = "#00000044"),
        panel.grid.minor.x = element_line(size=0.1, colour = "#00000022"))

Figure 5: An example of a horizontal bar chart with grid lines

Summary plots

Unlike frequency plots, their primary aim is to summarise the data in term of key statistics
They are often used to compare variables across groups
Some of them can be used to gauge differences between groups and relationships between variables
They are not a substitute for data analysis!

Box plot

AKA box-and-whiskers plots

Code

df |>
  dplyr::distinct(title, .keep_all = T) |>
  ggplot2::ggplot(aes(x = rating)) +
  ggplot2::geom_boxplot(outlier.fill = "#e20000", outlier.shape = 21, width = 0.2) +
  ggplot2::annotate("line", x = c(6.4, 6.4), y = c(-0.1, 0.1), colour = "#007ec8", size = 1.5) +
  ggplot2::labs(x = "Mean viewer rating", y = "") +
  ggplot2::coord_cartesian(ylim = c(-0.3, 0.3)) +
  ggplot2::scale_x_continuous(breaks = 0:11) +
  ggplot2::theme(axis.ticks.y = element_blank(),
        axis.text.y = element_blank(), axis.line.y = element_blank())

Figure 6: A box plot gives a more detailed info about a variable’s distribution and basic descriptive statistics

Box plot

AKA box-and-whiskers plots

Code

df |>
  dplyr::distinct(title, .keep_all = T) |>
  ggplot2::ggplot(aes(x = rating)) +
  ggplot2::geom_boxplot(outlier.fill = "#e20000", outlier.shape = 21, width = 0.2) +
  ggplot2::labs(x = "Mean viewer rating", y = "") +
  ggplot2::annotate("text", x = 6.4, y = -0.18, label="Median", size = 7, colour="#007ec8") +
  ggplot2::annotate("text", x = 2.4, y = 0.12, label="Outliers", size = 7, colour = "#e20000") +
  ggplot2::annotate("text", x = 6.5, y = 0.23, label="IQR", size = 6, colour="black") +
  ggplot2::annotate("line", x = c(5.8, 7.1), y = c(0.15, 0.15), colour = "black") +
  ggplot2::annotate("line", x = c(5.8, 5.8), y = c(0.12, 0.15), colour = "black") +
  ggplot2::annotate("line", x = c(7.1, 7.1), y = c(0.12, 0.15), colour = "black") +
  ggplot2::annotate("line", x = c(6.4, 6.4), y = c(-0.1, 0.1), colour = "#007ec8", size = 1.5) +
  ggplot2::coord_cartesian(ylim = c(-0.3, 0.3)) +
  ggplot2::scale_x_continuous(breaks = 0:11) +
  ggplot2::theme(axis.ticks.y = element_blank(),
        axis.text.y = element_blank(), axis.line.y = element_blank())

Figure 7: A box plot gives a more detailed info about a variable’s distribution and basic descriptive statistics

Grouped box plot

Code

df |>
  dplyr::distinct(title, continent, .keep_all = T) |>
  ggplot2::ggplot(aes(x = continent, y = rating)) +
  ggplot2::geom_boxplot(outlier.fill = "#e20000", outlier.shape = 21, varwidth = T) +
  ggplot2::labs(x = "Continent", y = "Mean viewer rating") +
  ggplot2::theme(panel.grid.major.y = element_line(colour = "#00000033"),
        panel.grid.minor.y = element_line(colour = "#00000010"))

Figure 8: Boxplots are useful to compare distributions of a variable between groups

Note. Width of boxes proportional to number of observation per category of the Continent variable

Violin plot

Code

df |>
  dplyr::distinct(title, .keep_all = T) |>
  dplyr::mutate(cert = forcats::fct_explicit_na(cert)) |>
  ggplot2::ggplot(aes(x = cert, y = rating, fill = cert)) +
  ggplot2::geom_violin(draw_quantiles = T, trim = F) +
  ggplot2::geom_boxplot(width = 0.1, outlier.size = 2, fill = "white") +
  ggplot2::labs(x = "BBFC Certificate", y = "Mean viewer rating") +
  ggplot2::scale_fill_manual(
    values = c(
      "#2aa832", "#fab900", "#ef7910",
      "#ef7910", "#ec5692", "#d8011e", "#007ec8", "#aaaaaa"
    ),
    guide = F
  ) +
  ggplot2::theme(
    panel.grid.major.y = element_line(colour = "#00000033"),
    panel.grid.minor.y = element_line(colour = "#00000010")
  )

Figure 9: Violin plots with inserted box plots showing mean viewer rating by different levels of BBFC certificate

Errorbar plot

Errorbar plots are great for showing means and spread/inferential statistics
Some of them can be used to gauge statistical differences between groups
Error bars can show several things (e.g, standard deviations, standard errors, their multiples)
Plot should clearly indicate what they represent
Pay attention to what the error bars mean
Interpretation of plots changes based on what the bars show!

Errorbar plot

Code

df |>
  dplyr::distinct(title, .keep_all = T) |>
  dplyr::mutate(cert = forcats::fct_explicit_na(cert)) |>
  ggplot2::ggplot(aes(x = cert, y = budget/1000000, fill = cert)) + 
  ggplot2::stat_summary(fun.data = mean_se, geom = "errorbar", width=0.1, fun.args = 2) +
  ggplot2::stat_summary(fun.y = mean, geom = "point", pch=23, size = 4) + 
  ggplot2::labs(x = "BBFC Certificate", y = "Budget in millions of USD") +
  ggplot2::scale_fill_manual(values = c("#2aa832", "#fab900", "#ef7910",
                               "#ef7910", "#ec5692", "#d8011e", "#007ec8", "#aaaaaa"),
                    guide=F) +
  ggplot2::theme(panel.grid.major.y = element_line(colour = "#00000033"),
        panel.grid.minor.y = element_line(colour = "#00000010"))

Figure 10: Errorbar plot showing mean estimated budget of movies by level of BBFC certificate

Note. Error bars represent ±2 SE from the mean.

Errorbar plot

Code

df |>
  dplyr::distinct(title, .keep_all = T) |>
  dplyr::mutate(cert = forcats::fct_explicit_na(cert)) |>
  ggplot2::ggplot(aes(x = cert, y = budget/1000000, fill = cert)) + 
  ggplot2::stat_summary(fun.data = function (x, mult = 1) {
    x <- stats::na.omit(x)
    sd <- stats::sd(x)
    mean <- mean(x)
    ggplot2:::new_data_frame(list(y = mean, ymin = mean - sd, ymax = mean + 
                                    sd), n = 1)},
    geom = "errorbar", width=0.1) +
  ggplot2::stat_summary(fun.y = mean, geom = "point", pch=23, size = 4) + 
  ggplot2::labs(x = "BBFC Certificate", y = "Budget in millions of USD") +
  ggplot2::scale_fill_manual(values = c("#2aa832", "#fab900", "#ef7910", 
                               "#ef7910", "#ec5692", "#d8011e", "#007ec8", "#aaaaaa"),
                    guide=F) +
  ggplot2::scale_y_continuous(breaks = seq(0, 160, by = 20)) +
  ggplot2::theme(panel.grid.major.y = element_line(colour = "#00000033"),
        panel.grid.minor.y = element_line(colour = "#00000010"))

Figure 11: Errorbar plot showing mean estimated budget of movies by level of BBFC certificate

Note. Error bars represent ±1 SD from the mean.

Scatter plot

Best way to show relationships between two continuous variables.

Code

df |>
  dplyr::distinct(title, .keep_all = T) |>
  ggplot2::ggplot(aes(x = budget/1000000, y = opening_week/1000000)) + 
  ggplot2::geom_point(colour = "orangered", size = 2, alpha = .2,
             position = position_jitter(width = 1, height = 1)) +
  ggplot2::labs(x = "Budget in millions of USD", y = "Opening week grossing\n(millions of USD)")

Figure 12: The relationship between a film’s budget and it’s opening week box office performance

Line plot

Great for highlighting repeated measures and within-subject structure

Code

df |>
  dplyr::distinct(title, continent, .keep_all = T) |>
  ggplot2::ggplot(aes(x = ordered(year), y = runtime, group=1)) + 
  ggplot2::stat_summary(fun.data = "mean_se", geom = "errorbar", width = 0, lty = 1) +
  ggplot2::stat_summary(fun = mean, geom = "line") + 
  ggplot2::stat_summary(fun = mean, geom = "point", size = 4, colour="steelblue") + 
  ggplot2::labs(x = "Year of release", y = "Runtime in minutes") +
  ggplot2::coord_cartesian(ylim=c(105, 115)) +
  ggplot2::scale_y_continuous(breaks = 105:115)

Figure 13: Average film runtime over time in the second decade of the 21^st century

Note. Error bars represent ±1 SE from the mean.

Lot of info!

Code

df |>
  dplyr::distinct(title, continent, .keep_all = T) |>
  ggplot2::ggplot(aes(x = ordered(year), y = n_ratings/100000,
             group = continent, fill = continent, shape = continent)) + 
  ggplot2::stat_summary(fun.data = "mean_se", geom = "errorbar", width = 0, lty = 1) +
  ggplot2::stat_summary(fun.y = mean, geom = "line") + 
  ggplot2::stat_summary(fun.y = mean, geom = "point", size = 3) + 
  ggplot2::labs(x = "Year of release", y = "Number of IMDB ratings\n(in 100k)") +
  ggplot2::scale_shape_manual(values=21:25, name="Continent") +
  ggplot2::scale_fill_brewer(palette = "Set1", name="Continent") +
  ggplot2::theme(legend.position = c(.77, 0.74)) +
  ggplot2::coord_cartesian(ylim = c(0, 4.1))

Figure 14: Mean number of IMDB viewer rating of films by continent over time

Note. Error bars represent ±1 SE from the mean.

Sometimes less is more!

Plots and tables should supplement body text, not repeat what’s already there
There’s no need to show the same thing in a table AND in a plot at the same time!
Always make sure font size and size of graphics are big enough to be easily legible
For more detailed APA guidelines, see the APA website
- They also provide sample tables and figures. (But remember, not bar charts for summary stats! Not ever!)