Lecture 10: Arranging Tables

Brian J. Smith

2026-02-24

Arranging Tables

This lecture is based on Chapter 7 of Visualization Analysis & Design.

“Arrange Tables”

Arranging Tables

The goal of this chapter is to understand the visual encoding design choices for how to arrange tabular data spatially.

Why Arrange?

The arrange design choice covers all aspects of the use of spatial channels for visual encoding.
- Use of space dominates the user’s mental model, so it is the most important choice.
- The three highest ranked effectiveness channels for quantitative and ordered attributes are all related to spatial position:
  - Planar position against a common scale
  - Planar position along an unaligned scale
  - Length
- The highest ranked effectiveness channel for categorical data relates to spatial position.
  - There are no non-spatial channels effective for all attribute types

Arrange by Keys and Values

Attributes can be categorized as key or value attributes:
- Key attributes are independent attributes that can be used as a unique index to lookup items.
  - Can be categorical or ordinal.
- Value attributes are dependent attributes giving the value of a cell.
  - Can be any type.
  - Unique values of categorical or ordinal attributes are known as levels.
    - Avoid overloading the word value.
    - Same term used for factor variables in R.

Arrange by Keys and Values

Design choices relate directly to the semantics of the table attributes, the number of keys and the number of values.
An idiom can show:
- only values with no keys:
  - Scatter plot
- one key and one value:
  - Bar chart
- two keys and one value:
  - Heat map
- many keys and many values:
  - Scatter plot matrix
  - Faceted scatter plot

Express Quantitative Values

Scatter Plot

Two values, no keys

Code

library(dplyr)
library(ggplot2)
data("starwars")

starwars %>% 
  filter(mass < 500) %>% 
  ggplot(aes(x = height, y = mass)) +
  geom_point() +
  ggtitle("Scatter Plot", subtitle = "Star Wars data") +
  theme_classic()

Express Quantitative Values

Scatter Plots

Idiom	Scatterplots
What: Data	Table: two quantitative value attributes
How: Encode	Express values with horizontal and vertical spatial position and point marks
Why: Task	Find trends, outliers, distribution, correlation, locate clusters
Scale	Items: hundreds

Express Quantitative Values

Scatter Plots

Good for finding trends.
- Sometimes a trendline is superimposed.
Color coding can show an additional attribute.
Size coding can show yet another attribute.
- Sometimes called a bubble plot.

Separate, Order, and Align

Categorical Regions

The principle of expressiveness would be violated if we encoded categorical attributes with spatial position.
Instead, we can use spatial region.
- Regions are continuous, bounded areas that are distinct from each other.
- Drawing items with the same level uses spatial proximity to encode their similarity.
  - Adheres to the expressiveness principle.
- Still leaves flexibility for how to encoded information within a region.

Separate, Order, and Align

Categorical Regions

Distributing regions involves three operations:
- Separating into regions.
- Aligning the regions.
- Ordering the regions.
Separating and ordering always happen.
Alignment is optional.
Separating should be done by the categorical attribute.
Ordering and alignment should be done by an ordered attribute.

Separate, Order, Align

With one key, use list alignment.
Results in one region per item.
Arrangement can be horizontal or vertical.

Separate, Order, Align

Bar Chart

One key, one value

Code

starwars %>% 
  filter(mass < 500,
         !is.na(gender)) %>% 
  group_by(gender) %>% 
  summarize(mass = mean(mass)) %>% 
  ggplot(aes(x = gender, y = mass)) +
  geom_col(width = 0.2) +
  coord_cartesian(expand = c(bottom = FALSE)) +
  ggtitle("Bar Chart", subtitle = "Star Wars data") +
  theme_classic()

Separate, Order, Align

Bar Charts

Use a line mark, aligned in a common frame.
Encode a quantitative attribute with spatial position.
Encode a categorical attribute with spatial region.
Ordering can default to alphabetical or be data-driven.

Fig. 7.4. Marks are ordered (a) alphabetically or (b) by weight.

Separate, Order, Align

Bar Charts

Idiom	Bar Charts
What: Data	Table: one quantitative value attribute, one categorical key attribute
How: Encode	Line marks, express values with aligned position, separate values with region
Why: Task	Lookup and compare values
Scale	Key attribute: dozens to hundreds of levels

Separate, Order, Align

Stacked Bar Charts

Code

starwars %>% 
  filter(mass < 500,
         !is.na(gender),
         hair_color %in% c("black", "blond", "brown")) %>% 
  mutate(gender = factor(gender),
         hair_color = factor(hair_color)) %>% 
  group_by(gender, hair_color) %>% 
  summarize(mass = sum(mass)) %>% 
  ggplot(aes(x = gender, y = mass, fill = hair_color)) +
  geom_col() +
  xlab("Gender") +
  ylab("Total Mass") +
  scale_fill_discrete(name = "Hair Color") +
  coord_cartesian(expand = c(bottom = FALSE)) +
  ggtitle("Stacked Bar Chart", subtitle = "Star Wars data") +
  theme_bw()

Separate, Order, Align

Stacked Bar Charts

Idiom	Stacked Bar Charts
What: Data	Multidimensional table: one quantitative value attribute, two categorical key attributes
How: Encode	Bar glyph with length-coded subcomponents of value attribute for each category of secondary key attribute; separate bars by category of primary key attribute
Why: Task	Part-to-whole relationship, lookup values, find trends
Scale	Key attribute (main axis): dozens to hundreds of levels, Key attribute (stacked glyph axis): several to one dozen

Separate, Order, Align

Dot and Line Charts

Dot Chart
- Like a bar chart, but uses point marks (standard use); or, like a scatter plot, but one axis is ordered categories.
- One quantitative attribute using spatial position, one ordered attribute using spatial region.
Line Chart
- A dot chart with lines connecting the dots to show trend.

Separate, Order, Align

Dot and Line Charts

Idiom	Dot Charts
What: Data	Table: one quantitative value attribute, one ordered key attribute
How: Encode	Express value attribute with aligned vertical position and point marks; separate/order into horizontal regions by key attribute

Separate, Order, Align

Dot and Line Charts

Idiom	Line Charts
What: Data	Table: one quantitative value attribute, one ordered key attribute
How: Encode	Dot chart with connection marks between dots
Why: Task	Show trend
Scale	Key attribute: hundreds of levels

Separate, Order, Align

Bar vs. Line Charts

Bar charts encourage discrete comparisons.
Line charts encourage trend assessment.
- Should not be used for categorical (unordered) attributes (top right)

Separate, Order, Align

Matrix Alignment

Distribute one key along rows and another along columns.
Heat maps are the simplest example.
Scatter Plot Matrices (SPLOMs) show all possible pairwise combinations.

Separate, Order, Align

Heat Map

Two keys, one value

Code

hm <- starwars %>% 
  filter(mass < 500,
         !is.na(gender),
         hair_color %in% c("black", "blond", "brown")) %>% 
  mutate(gender = factor(gender),
         hair_color = factor(hair_color)) %>% 
  group_by(gender, hair_color, .drop = FALSE) %>% 
  summarize(n = n()) %>% 
  ggplot(aes(x = gender, y = hair_color, fill = n)) +
  geom_tile() +
  coord_cartesian(expand = FALSE) +
  scale_fill_viridis_b() +
  ggtitle("Heat Map", subtitle = "Star Wars data") +
  theme_classic()

print(hm)

Separate, Order, Align

Heat Maps

Idiom	Heat Maps
What: Data	Table: two categorical key attributes, one quantitative value attribute
How: Encode	2D matrix alignment of area marks, diverging color map
Why: Task	Find clusters, outliers; summarize
Scale	Items: one million; categorical attribute levels: hundreds; quantitative attribute levels: 3 - 11

Separate, Order, Align

Scatter Plot Matrix

Many keys, many values

Code

xx <- starwars %>% 
  filter(mass < 500,
         birth_year < 200) %>% 
  select(height, mass, birth_year)

plot(xx, main = "Scatter Plot Matrix", sub = "Star Wars data",
     pch = 16)

Separate, Order, Align

Scatter Plot Matrix

Idiom	SPLOMs
What: Data	Table
What: Derived	Ordered key attribute; list of original attributes
How: Encode	Scatter Plots in 2D matrix alignment
Why: Task	Find correlations, trends, outliers
Scale	Attributes: one dozen; items: dozens to hundreds

Separate, Order, Align

Faceted Scatter Plot

Many keys, many values

Code

starwars %>% 
  filter(mass < 500,
         !is.na(gender),
         hair_color %in% c("black", "blond", "brown")) %>% 
  mutate(gender = factor(gender),
         hair_color = factor(hair_color)) %>% 
  ggplot(aes(x = height, y = mass)) +
  facet_grid(gender ~ hair_color) +
  geom_point() +
  coord_cartesian(expand = FALSE) +
  ggtitle("Faceted Scatter Plot", subtitle = "Star Wars data") +
  theme_bw()

Spatial Axis Orientation

Spatial axes can be oriented three ways:
- Rectilinear
- Parallel
- Radial

Spatial Axis Orientation

Rectilinear Layouts

The most common layouts in data viz.
All the previous examples.
Limited to two perpendicular axes.
- Or at most, three, although depth is a low-precision channel.

Spatial Axis Orientation

Parallel Layouts

Allow more than three attributes to be encoded with spatial position channel.
Parallel coordinates plots are used to show many attributes.
Use jagged lines that cross each axis exactly once.

Spatial Axis Orientation

Parallel Layouts

Use two spatial dimensions:
- one to show a quantitative value,
- the other to lay out the multiple axes.

Spatial Axis Orientation

Parallel Layouts

Patterns are easily seen between neighboring axes, but not easily for distant axes.
- Ordering axes is a critical decision.
These layouts have a long training time.
- Most users are not familiar with these plots and don’t have intuition about the patterns.
- Often used in conjunction with more familiar idioms, such as scatter plots (i.e., multiple views).

Spatial Axis Orientation

Radial Layouts

Items are distributed around a circle using the angle channel.
Also uses one ore more linear spatial channels.
Might imply one attribute is more important than another.

Spatial Axis Orientation

Radial Layouts

Natural coordinate system is polar coordinates.
- One dimension is an angle.
- The other dimension is a spatial position.
- Mathematically completely equivalent to Cartesian coordinates.

Spatial Axis Orientation

Radial Layouts

While, mathematically, radial layout are equivalent to Cartesian coordinates, perceptually, they are not.
- The angle channel is less accurately perceived than the rectilinear spatial position.
- The angle channel is inherently cyclic.
  - Radial layouts may be more effective for showing periodic patterns.

Spatial Axis Orientation

Radial Layouts

Code

library(patchwork)

cyclic <- data.frame(x = seq(0, 2*pi, length.out = 300)) %>% 
  mutate(y = sin(4*x))

a <- ggplot(cyclic, aes(x = x, y = y)) +
  geom_line() +
  ggtitle("Rectilinear") +
  theme_bw()

b <- a +
  coord_polar() +
  scale_x_continuous(breaks = c(0, pi/2, pi, 3*pi/2, 2*pi),
                     labels = c("0", "π/2", "π", "3π/2", "2π")) +
  ggtitle("Radial")

a + b

Side note, the polar transformation is a key idea behind the Fast Fourier Transform

Spatial Axis Orientation

Radial Bar Charts

Idiom	Radial Bar Charts
What: Data	Table: one quantitative attribute, one categorical attribute
How: Encode	Length coding of line marks; radial layout

Spatial Axis Orientation

Rectilinear vs. Radial Layouts

Spatial Axis Orientation

Pie Charts

Code

pie <- starwars %>% 
  filter(hair_color  %in% c("black", "blond", "brown")) %>% 
  group_by(hair_color) %>% 
  summarize(n = n()) %>% 
  ggplot(aes(x = "", y = n, fill = hair_color)) +
  geom_bar(stat = "identity", width = 1) +
  coord_polar("y", start = 0) +
  xlab(NULL) + 
  ylab(NULL) +
  ggtitle("Pie Chart", subtitle = "Star Wars data") +
  theme_classic() +
  theme(axis.text.x = element_blank())
print(pie)

Spatial Axis Orientation

Pie Charts

Idiom	Pie Charts
What: Data	Table: one quantitative attribute, one categorical attribute
Why: Task	Part-whole relationship
How: Encode	Area marks (wedges) with angle channel; radial layout
Scale	One dozen categories

Spatial Axis Orientation

Polar Area Charts

Code

pa <- starwars %>% 
  filter(hair_color  %in% c("black", "blond", "brown")) %>% 
  group_by(hair_color) %>% 
  summarize(n = n()) %>% 
  ggplot(aes(x = hair_color, y = n, fill = hair_color)) +
  geom_col(width = 1) +
  coord_polar() +
  xlab(NULL) + 
  ylab(NULL) +
  ggtitle("Polar Area Chart", subtitle = "Star Wars data") +
  theme_classic() +
  theme(axis.text.x = element_blank())
print(pa)

Spatial Axis Orientation

Polar Area Charts

Idiom	Polar Area Charts
What: Data	Table: one quantitative attribute, one categorical attribute
Why: Task	Part-whole relationship
How: Encode	Area marks (wedges) with angle channel; radial layout
Scale	One dozen categories

Spatial Axis Orientation

Polar Area Charts

Pie charts require angle and area judgements.
Polar area charts are a more direct equivalent of bar charts.

Questions?

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