2  Module 2 — Data Visualization

Pedagogical note: This module is designed for two audiences at once: - Learners new to statistics (focus on intuition, what to plot, and why) - Learners with statistics background (focus on correctness, assumptions, and best practice)

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2.1 Learning Outcomes

By the end of this module, learners will be able to:

• Choose the right plot for the right question.
• Create common plots using base R and ggplot2.
• Understand the statistical meaning behind plots (distribution, comparison, relationship).
• Build publication-quality and complex visualizations using ggplot2.
• Visualize outputs from PCA, clustering, and machine learning models.

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2.2 1. Why visualization matters (intuition first)

Visualization helps answer three fundamental questions:

1. What does my data look like? (distribution)
2. How do groups compare? (comparison)
3. How are variables related? (relationships)

A good visualization: - Matches the data type (categorical vs numeric) - Matches the question being asked - Avoids distortion and unnecessary decoration

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2.3 2. Base R plotting — foundations

Base R plotting is: - Immediate - Explicit - Very useful for quick diagnostics

2.3.1 2.1 Histogram — distributions (numeric)

When to use: - To understand the distribution of a single numeric variable - To check skewness, modality, outliers

hist(iris$Sepal.Length,
     main = "Histogram of Sepal Length",
     xlab = "Sepal Length",
     col = "lightblue",
     border = "white")

Statistical meaning: area represents frequency; shape approximates the probability distribution.

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2.3.2 2.2 Bar plot — counts or summaries (categorical)

When to use: - Comparing counts across categories

counts <- table(iris$Species)
barplot(counts,
        main = "Count of Species",
        col = "tan")

Do not use bar plots for raw numeric distributions (use histograms instead).

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2.3.3 2.3 Boxplot — distribution comparison

When to use: - Comparing distributions across groups - Identifying outliers

boxplot(Sepal.Length ~ Species,
        data = iris,
        main = "Sepal Length by Species",
        col = "lightgray")

Statistical interpretation: - Median, IQR, and outliers (1.5×IQR rule)

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2.3.4 2.4 Scatter plot — relationships

When to use: - Relationship between two numeric variables

plot(iris$Petal.Length, iris$Petal.Width,
     main = "Petal Length vs Width",
     xlab = "Petal Length",
     ylab = "Petal Width")

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2.3.5 2.5 Pie charts — proportions (use sparingly)

When to use: - Simple proportion comparisons (few categories)

pie(counts, main = "Species Proportion")

⚠️ Teaching warning: Pie charts make precise comparisons difficult. Prefer bar charts.

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2.4 3. Introduction to ggplot2 — Grammar of Graphics

Core idea: build plots by mapping data → aesthetics → geometric objects.

library(ggplot2)

Warning: package 'ggplot2' was built under R version 4.3.3

Structure:

ggplot(data, aes(x, y)) +
  geom_*() +
  theme_*()

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2.5 4. Common plots in ggplot2 (side-by-side with base R)

2.5.1 4.1 Histogram

ggplot(iris, aes(Sepal.Length)) +
  geom_histogram(bins = 20, fill = "steelblue", color = "white") +
  theme_minimal()

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2.5.2 4.2 Bar plot

ggplot(iris, aes(Species)) +
  geom_bar(fill = "tan") +
  theme_minimal()

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2.5.3 4.3 Boxplot

ggplot(iris, aes(Species, Sepal.Length)) +
  geom_boxplot(fill = "lightgray") +
  theme_minimal()

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2.5.4 4.4 Scatter plot with grouping

ggplot(iris, aes(Petal.Length, Petal.Width, color = Species)) +
  geom_point(size = 3) +
  theme_minimal()

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2.6 5. Statistical layers (for advanced learners)

2.6.1 5.1 Trend lines

ggplot(iris, aes(Petal.Length, Petal.Width)) +
  geom_point() +
  geom_smooth(method = "lm", se = TRUE) +
  theme_minimal()

`geom_smooth()` using formula = 'y ~ x'

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2.6.2 5.2 Density plots

ggplot(iris, aes(Sepal.Length, fill = Species)) +
  geom_density(alpha = 0.5) +
  theme_minimal()

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2.7 6. Complex visualizations with ggplot2

2.7.1 6.1 Faceting (small multiples)

ggplot(iris, aes(Sepal.Length)) +
  geom_histogram(bins = 20, fill = "steelblue") +
  facet_wrap(~Species) +
  theme_minimal()

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2.8 7. Choosing the right plot — summary table

Question	Variable types	Recommended plot
Distribution	Numeric	Histogram, Density
Compare groups	Numeric + Categorical	Boxplot, Violin
Counts	Categorical	Bar plot
Proportions	Categorical	Bar (preferred), Pie
Relationship	Numeric + Numeric	Scatter plot
High-dimensional	Numeric (many)	PCA scatter

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2.9 8. Exercises & self-checks

# Sanity checks
stopifnot(is.numeric(iris$Sepal.Length))
stopifnot(length(unique(iris$Species)) == 3)

# Student task ideas:
# 1. Create one plot per question type using iris
# 2. Convert a base plot to ggplot2
# 3. Justify plot choice in one sentence

# - Start with **base R** to build intuition
# - Move to **ggplot2** for flexibility and publication quality
# - Always ask: *What question does this plot answer?*
# - Emphasize interpretation over aesthetics

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