2.5.Displaying & Describing Data

Plots and Tables

Bárbara D. Bitarello

2025-09-29

Outline

• Letting data type guide visualizations
• Rules of data visualization - principles of good plots

Cumulative Frequency Distributions

Number of students per grade

school_grade	Frequency_of_Students
1	23
2	20
3	15
4	12
5	10
6	8

The cumulative frequency of a value is the proportion of individuals equal to or less than that value. In this case, equal or less than a given grade.

Sort data, calculate cumulative frequency…

Based on example from: https://statisticsbyjim.com/basics/cumulative-frequency/

Cumulative Frequency Distributions

1. Sort all values
2. Calculate the fraction of values \(\leq\) each value – the cumulative relative frequency

library(dplyr)
df <- df |>
    mutate(Cumul_Freq = cumsum(Frequency_of_Students))
df <- df |>
    mutate(Rel_CFreq = Cumul_Freq/sum(Frequency_of_Students))
df

  school_grade Frequency_of_Students Cumul_Freq Rel_CFreq
1            1                    23         23 0.2613636
2            2                    20         43 0.4886364
3            3                    15         58 0.6590909
4            4                    12         70 0.7954545
5            5                    10         80 0.9090909
6            6                     8         88 1.0000000

Cumulative Frequency Distributions

3. Plot the values on the \(x\) and their cumulative relative frequencies on the \(y\)
4. Connect the values with lines

• Plot
• Code

ggplot(df, aes(x = school_grade))+
  stat_ecdf(geom = "step") +
  theme_bw() #this is just to make the background clear

Cumulative Frequency Distributions

example 2: Temperatures near LaGuardia (1973)

datasets::airquality |> 
  ggplot(aes(x= Temp)) + 
  stat_ecdf(geom = "step") +
  theme_bw() #this is just to make the background clear

ECDF: empirical cumulative distribution function

Cumulative Frequency Distributions

Example 3: Spider running speed

Figure caption: Figure 3.4-1 from the textbook

Cumulative frequency distributions clearly communicate quantiles.

Histograms, density plots, & cumulative frequency plots …

• can reveal the shapes of distributions

• important for understanding data

• and choosing a statistical approach

Distribution shapes

Histograms

Distribution shapes

Cumulative Frequency Distributions

Less common plots for one numerical variable

These are more often used to look at the association between a numerical and a categorical variable:

• Boxplots
• Violin plots
• Strip charts

Two or more variables …

Categorical x Categorical

Contingency Table

From: Whitlock & Schluter, The Analysis of Biological Data

Categorical x Categorical

Grouped bar plot

Figure caption: figure 2.3-1 from Whitlock & Schluter, The Analysis of Biological Data

Categorical x Categorical

Mosaic plot

Figure caption: figure 2.3-2 from Whitlock & Schluter, The Analysis of Biological Data

2+ variables. No upper limit, but too many variables may be confusing

Width indicates the relative proportion of the corresponding value

Numerical x Numerical

Scatter Plot

• Plot
• Code

library(ggplot2)
ggplot(iris,aes(x = Petal.Width, y = Petal.Length)) + 
  geom_point()+
  xlab("Petal Width (cm)") + 
  ylab("Petal Length (cm)")

Numerical x Numerical

Scatter Plot

• Plot
• Code

library(ggplot2)
ggplot(iris, aes(x = Petal.Width, y = Petal.Length)) +
    geom_point() + xlab("Petal Width (cm)") + ylab("Petal Length (cm)") +
    geom_smooth(method = "lm", se = F)

Numerical x Categorical

Multiple Histograms

Numerical x Categorical

Strip Chart

Numerical x Categorical

Boxplot

Numerical x Categorical

Violin Plot

Numerical (2) + Categorical

Multiple Scatterplots with legend

Numerical (2) x Categorical

Multiple scatterplots plotted separately

Visualizations Over Time and Space

Line Graphs Show Data Over Time

For temporal data, note all observations with a data point, and connect each point with a line.

Small multiples line chart

A grid of line charts that uses the same scales and axes

To show spatial data

Maps

Spatial data does not have to be a geographical map

How to make good plots

1. Show the data.
2. Make patterns easy to see.
3. Display magnitudes honestly.
4. Draw graphics clearly.

Mistakes in displaying data:

1. Hiding the data

What is the main problem here?

1. Hide the data.
2. Make patterns hard to see.
3. Display magnitudes dishonestly.
4. Draw graphics unclearly.

👎 Not showing data, just summaries

1. Hide the data.
2. Make patterns hard to see.
3. Display magnitudes dishonestly.
4. Draw graphics unclearly.

This plot hides the variation between positions.

What is the main problem here?

1. Hide the data.
2. Make patterns hard to see.
3. Display magnitudes dishonestly.
4. Draw graphics unclearly.

👎 Not showing data, overplotting

1. Hide the data.
2. Make patterns hard to see.
3. Display magnitudes dishonestly.
4. Draw graphics unclearly.

Over-plotting hides data by placing data points on top of each other.

👍 Showing data by jittering

This plot shows all the observations

👎 How to hide data

• Provide only statistical summaries.
• Over-plotting - too many points.

👍 How to reveal data

• Present all of the data points.
• Allow all points to be seen.

Mistakes in displaying data:

2. Making patterns hard to see

What’s the main problem here?

Nonsensical order hides pattern

Reordering factors makes pattern clear

Tables should follow similar rules

Cause_of_death	Number
Congen. abnor.	222
Heart disease	463
Accidents	6688
All other cause	1653
Other tumor	52
Suicide	1615
Homicide	2093
Chronic res. disease	107
Cerebrov. disease	67
Flu/pneumonia	73
Malig. tumor	745

👎

• Nonsense order hides patterns

• Alphabetical order is usually a bad idea.

Tables should follow similar rules

Cause_of_death	Number
Accidents	6688
Homicide	2093
Suicide	1615
Malig. tumor	745
Heart disease	463
Congen. abnor.	222
Chronic res. disease	107
Flu/pneumonia	73
Cerebrov. disease	67
Other tumor	52
All other cause	1653

👍

• Order to reveal patterns

• List ordinal factors in a meaningful order

• List nominal factors from greatest to least, with “all others” last.

How to hide patterns 👎

• Make one plot and call it good
• Unreasonable scales
• Arrange factors nonsensically

How to reveal patterns 👍

• Explore multiple potential plots
• Use appropriate scales
• Arrange factors meaningfully
• Order ordinal factors meaningfully (e.g., January to December.
• Order nominal factors by count
• If there is a grab bag category, place it after the lowest count

Problem?

Bad Axis-Limits Hide Patterns 👎

In this plot, the large scale hides the pattern (difference between the two groups)

That’s all for today

From: makeameme.org