Design Variables and the Grammar of Graphics

SMM635 - Week 2

Prof. Simone Santoni

Bayes Business School

Today’s Journey

Part 1: Grammar of Graphics

• Framework & Philosophy
• Core Components
• Building Blocks

Part 2: Visual Forms

• Univariate Charts
• Bivariate Charts
  
• Multivariate Charts

Learning Objectives

By the end of today’s session, you will:

1. Understand the grammar of graphics framework
2. Map data to visual variables effectively
   
3. Build complex visualizations from simple components
4. Implement layered graphics approaches
5. Create appropriate charts for different data types

Part 1: Grammar of Graphics

Moving Beyond Chart Types

How Do We Describe a Chart?

How Do We Describe a Chart?

Traditional Approach:

• Pie chart
• Bar chart
• Line chart
• Scatter plot

Note

We can use labels or conceptual categories

Grammar Approach:

• Data
• Aesthetics
• Geometries
• Scales
• Coordinates

Note

We can refer to a chart’s constitutive components

What is Grammar of Graphics (GoG)?

“Grammar makes language expressive. A language consisting of words and no grammar expresses only as many ideas as there are words.” - Leland Wilkinson

What’s the Connection between GoG and ggplot2?

• ggplot2 is an implementation of the Grammar of Graphics in R
• Created by Hadley Wickham based on Leland Wilkinson’s framework
• The “gg” in ggplot2 stands for “Grammar of Graphics”
• Allows users to build plots layer by layer using the grammar components
• Instead of choosing from pre-made chart types, you compose visualizations from fundamental building blocks

The Power of GoG

# Traditional thinking
make_pie_chart(data)
make_bar_chart(data)

# Grammar thinking
ggplot(data) +
  geom_bar() +
  coord_polar()  # Bar chart → Pie chart!

Important

A pie chart is just a stacked bar chart in polar coordinates! 🤯

A Bar Chart

library(ggplot2)

# Create data with five categories
data <- data.frame(
  category = c("A", "B", "C", "D", "E"),
  value = c(23, 45, 31, 52, 38)
)

# Create bar chart
ggplot(data, aes(x = category, y = value)) +
  geom_bar(stat = "identity")

Pie Chart = Bar Chart + Polar Coordinates

# Create data with five categories
data <- data.frame(
  category = c("A", "B", "C", "D", "E"),
  value = c(23, 45, 31, 52, 38)
)

# Create bar chart
ggplot(data, aes(x = "", y = value, fill = category)) +
  geom_bar(stat = "identity") +
  coord_polar(theta = "y", start = 0) +
  theme_void()

Core Components of the GoG

1. DATA: What we want to visualize
2. AESTHETICS: How we map data to visual properties
3. GEOMETRIES: The visual marks we use
4. FACETS: Creating small multiples
5. STATISTICS: How to transform or summarize the raw data
6. COORDINATES: The space we’re working in
7. THEMES: Overall visual appearance

Source: https://r.qcbs.ca/

1. Data: The Foundation

# Data is structured information
sales_data <- data.frame(
  month = c("Jan", "Feb", "Mar", "Apr"),
  revenue = c(45000, 52000, 48000, 61000),
  region = c("North", "North", "South", "South")
)

Tip

Good visualization starts with well-structured data

Tidyverse is your friend!

2. Aesthetics: Visual Mappings

Mapping Data → Visual Properties

Data Variables

• Continuous values
• Categories
• Ordered factors
• Time series

Visual Variables

• Position (x, y)
• Size
• Color
• Shape
• Transparency
• Line type

Visual Variables in Action

ggplot(sample_data, aes(
  x = date,        # Position
  y = sales,       # Position
  color = region,  # Color
  size = profit    # Size
)) +
  geom_point()

3. Geometries: Visual Marks

• Points
• Lines
• Bars
• Areas

ggplot(sample_data, aes(x = date, y = sales)) +
  geom_point()

Best for: Scatter plots, distributions

ggplot(sample_data, aes(x = date, y = sales)) +
  geom_line()

Best for: Trends, time series

ggplot(sample_data, aes(x = region, y = sales)) +
  geom_bar(stat = "identity")

Best for: Comparisons, counts

ggplot(sample_data, aes(x = date, y = sales)) +
  geom_area()

Best for: Proportions over time

4. Facets: Small Multiples

• No Facets
• Facet Wrap
• Facet with Free Scales

ggplot(sample_data, aes(x = date, y = sales, color = region)) +
  geom_point()

Note

All data in a single plot

ggplot(sample_data, aes(x = date, y = sales)) +
  geom_point() +
  facet_wrap(~region)

Note

Creates separate panels for each region

ggplot(sample_data, aes(x = date, y = profit)) +
  geom_point() +
  facet_wrap(~region, scales = "free_y")

Note

Independent y-axis scales per facet

5. Statistics: Transforming Data

• Raw Data
• Smooth Trend
• Summary Statistics

ggplot(sample_data, aes(x = date, y = sales)) +
  geom_point()

Note

No statistical transformation

ggplot(sample_data, aes(x = date, y = sales)) +
  geom_point() +
  geom_smooth(method = "lm")

Note

Adds linear regression line with confidence interval

ggplot(sample_data, aes(x = region, y = sales)) +
  geom_point() +
  stat_summary(fun = mean, geom = "point", color = "red")

Note

Calculates and displays mean values

6. Coordinates: The Canvas

• Cartesian (default)
• Flipped
• Polar

ggplot(sample_data, aes(x = region, y = sales)) +
  geom_bar(stat = "identity") +
  coord_cartesian()

Note

The standard x-y coordinate system

ggplot(sample_data, aes(x = region, y = sales)) +
  geom_bar(stat = "identity") +
  coord_flip()

Note

Swaps x and y axes for horizontal bars

ggplot(sample_data, aes(x = "", y = sales, fill = region)) +
  geom_bar(stat = "identity") +
  coord_polar(theta = "y") + 
  theme_void()

Note

Transforms to polar coordinates (e.g., pie charts)

7. Themes: Overall Visual Appearance

• theme_minimal()
• theme_bw()
• theme_classic()
• Custom Theme

ggplot(sample_data, aes(x = date, y = sales, color = region)) +
  geom_point() +
  theme_minimal()

Note

Clean, minimal design

ggplot(sample_data, aes(x = date, y = sales, color = region)) +
  geom_point() +
  theme_bw()

Note

Black and white with borders

ggplot(sample_data, aes(x = date, y = sales, color = region)) +
  geom_point() +
  theme_classic()

Note

Classic look with axis lines only

ggplot(sample_data, aes(x = date, y = sales, color = region)) +
  geom_point() +
  theme_minimal() +
  theme(panel.grid.major = element_line(color = "gray80"),
        panel.grid.minor = element_blank(),
        legend.position = "bottom")

Building Complex from Simple

Part 1: Foundation

flowchart TD
    START((" ")) --> A["DATA"] --> B["AESTHETICS"] --> C["GEOMETRY"]

    style START fill:#90EE90,stroke:#333,stroke-width:1px
    style A fill:#e1f5ff
    style B fill:#e1f5ff
    style C fill:#e1f5ff

Part 2: Refinement

flowchart TD
    D["FACETS"] --> E["STATISTICS"] --> F["COORDINATES"] --> G["THEME"] --> END((" "))

    style D fill:#e1f5ff
    style E fill:#e1f5ff
    style F fill:#e1f5ff
    style G fill:#e1f5ff
    style END fill:#FF6B6B,stroke:#333,stroke-width:1px

Example: Layer by Layer

# 1. Data + Aesthetics
ggplot(data, aes(x, y)) +

  # 2. Geometry
  geom_point() +

  # 3. Facets
  facet_wrap(~category) +

  # 4. Statistics
  geom_smooth() +

  # 5. Coordinates
  coord_cartesian() +

  # 6. Theme
  theme_minimal()

Layering: The Power of Composition

ggplot(economics, aes(date, unemploy)) +
  geom_area(alpha = 0.3) +           # Layer 1: Area
  geom_line(size = 1.2) +            # Layer 2: Line
  geom_smooth(se = FALSE, col = "red") # Layer 3: Trend

Note

Each layer adds information without obscuring previous layers

Part 2: Visual Forms

From Simple to Complex

Univariate Charts

Exploring Single Variables

Continuous Data

• Histograms
• Density plots
• Box plots
• Violin plots

Categorical Data

• Bar charts
• Pie charts
• Waffle charts
• Dot plots

Univariate: Continuous Data

• Histogram
• Density
• Box Plot

ggplot(data, aes(x = value)) +
  geom_histogram(bins = 30)

Histograms divide data into bins and count observations in each bin.

• Best for: Understanding the distribution shape and identifying patterns
• Shows: Frequency, central tendency, spread, and skewness
• Key parameter: Number of bins affects granularity

ggplot(data, aes(x = value)) +
  geom_density(fill = "skyblue", alpha = 0.5)

Density plots show a smoothed version of the distribution.

• Best for: Comparing multiple distributions, identifying modes
• Shows: Probability density across the range of values
• Advantage: Smooth curve makes patterns easier to see

ggplot(data, aes(y = value)) +
  geom_boxplot()

Box plots display the five-number summary: min, Q1, median, Q3, max.

• Best for: Identifying outliers and comparing distributions
• Shows: Central tendency, spread, and asymmetry
• Key insight: Box contains middle 50% of data

Univariate: Categorical Data

• Bar Chart
• Pie Chart
• Cleveland Dot Plot

ggplot(data, aes(x = category)) +
  geom_bar()

Bar charts use bar length to encode category counts or values.

• Best for: Comparing categories, showing rankings
• Shows: Frequency or magnitude for each category
• Advantage: Easy to compare values, natural visual ordering

ggplot(data, aes(x = "", fill = category)) +
  geom_bar() +
  coord_polar("y")

Pie charts show parts of a whole as slices of a circle.

• Best for: Showing proportions when there are few categories (2-5)
• Shows: Relative proportions and percentages
• Limitation: Difficult to compare similar-sized slices

ggplot(data, aes(x = value, y = category)) +
  geom_point()

Cleveland dot plots use position to encode values with minimal ink.

• Best for: Precise value comparisons, when space is limited
• Shows: Exact values for each category
• Advantage: More accurate than bars, less cluttered

Bivariate Charts

Exploring Relationships Between Two Variables

X Variable	Y Variable	Best Chart Types
Continuous	Continuous	Scatter plot, Line chart
Continuous	Categorical	Box plot, Violin plot
Categorical	Categorical	Heatmap, Grouped bars
Time	Continuous	Line chart, Area chart

Bivariate: Continuous × Continuous

• Scatter Plot
• With Trend
• 2D Density

ggplot(data, aes(x = height, y = weight)) +
  geom_point()

Scatter plots display individual data points in 2D space.

• Best for: Exploring relationships, identifying correlations, spotting outliers
• Shows: Direction, strength, and form of relationship between two variables
• Key insight: Patterns reveal linear, non-linear, or no correlation

ggplot(data, aes(x = height, y = weight)) +
  geom_point() +
  geom_smooth(method = "lm")

Scatter plot with trend line adds a fitted model to show the relationship.

• Best for: Confirming correlation patterns, making predictions
• Shows: Overall trend and strength of linear relationship
• Options: Linear (lm), loess (local smoothing), or other methods

ggplot(data, aes(x = height, y = weight)) +
  geom_density_2d_filled()

2D density plots show concentration of points as contours or filled regions.

• Best for: Large datasets where overplotting obscures patterns
• Shows: Areas of high and low data concentration
• Advantage: Reveals patterns in dense data clouds

Bivariate: Categorical × Continuous

• Grouped Box Plot
• Violin Plot
• Strip Chart

ggplot(data, aes(x = category, y = value)) +
  geom_boxplot()

Grouped box plots compare distributions across multiple categories.

• Best for: Comparing central tendency and spread across groups
• Shows: Median, quartiles, and outliers for each category
• Advantage: Compact representation of multiple distributions side-by-side

ggplot(data, aes(x = category, y = value)) +
  geom_violin()

Violin plots combine box plots with kernel density estimation.

• Best for: Revealing distribution shapes and multimodality
• Shows: Full distribution shape for each category
• Advantage: More informative than box plots for complex distributions

ggplot(data, aes(x = category, y = value)) +
  geom_jitter(width = 0.2)

Strip charts (jittered) show all individual data points.

• Best for: Small to medium datasets, showing actual observations
• Shows: Individual values and sample size per category
• Advantage: Transparency - shows the actual data, not summaries

Multivariate Charts

Beyond Two Dimensions

Strategies for encoding multiple variables:

1. Color/Fill: 3rd dimension
2. Size: 4th dimension
   
3. Shape: 5th dimension (categorical only)
4. Faceting: Create small multiples
5. Animation: Time as dimension

Multivariate Example: The Economics Dataset

Multivariate Example: The Economics Dataset

Note

Dataset Variables:

• date: Month of data collection
• pce: Personal consumption expenditures (billions USD)
• pop: Total population (thousands)
• psavert: Personal savings rate (%)
• uempmed: Median duration of unemployment (weeks)
• unemploy: Number of unemployed (thousands)

Multivariate Example

Multivariate Example

Best Practices for Multivariate

1. Start simple: Add dimensions gradually
2. Prioritize: Most important variables get best encodings
3. Test perception: Can viewers decode all dimensions?
4. Consider alternatives: Sometimes multiple simple charts > one complex chart
5. Interactive solutions: Tooltips, filtering, zooming

Putting It All Together

A Practical Workflow

Tip

1. Understand your data
   • Types of variables
   • Relationships to explore
2. Choose appropriate forms
   • Match chart to data type
   • Consider your message
3. Apply the grammar
   • Map variables to aesthetics
   • Layer geometries
   • Refine with scales

Key Takeaways

• 📊 The Grammar of Graphics provides a systematic framework for creating any visualization

• 🔧 Complex visualizations are built from simple, reusable components

• 🎨 Visual variables (position, size, color, etc.) are tools for encoding information

• 📈 Choose chart types based on data types and relationships

• 🔄 Iteration and layering lead to rich, informative graphics

Next Week

Topic 3: Exploratory Data Analysis

• EDA workflow and visualization
• Distribution visualization techniques
  
• Correlation and relationship exploration
• Time series exploration
• Case Study: Nomis Solutions

Homework

• Practice creating layered visualizations
• Experiment with different coordinate systems
• Read: Wickham’s “Layered Grammar of Graphics”

Questions?

Let’s explore the grammar together!

📧 Simone.Santoni.1@city.ac.uk

🌐 Course website: https://simonesantoni.github.io/data-viz-smm635

💬 Office hours: Wednesdays 3-5 PM