Hands-on Exercise 4c: Visualising Uncertainty

Author

PHAM Hung Son

Published

February 2, 2026

Modified

February 2, 2026

1 Learning Outcome

Visualising uncertainty is relatively new in statistical graphics. In this chapter, you will gain hands-on experience on creating statistical graphics for visualising uncertainty. By the end of this chapter you will be able:

  • to plot statistics error bars by using ggplot2,

  • to plot interactive error bars by combining ggplot2, plotly and DT,

  • to create advanced by using ggdist, and

  • to create hypothetical outcome plots (HOPs) by using ungeviz package.

2 Getting started

2.1 Installing and loading the required libraries

For the purpose of this exercise, the following R packages will be used, they are:

  • tidyverse, a family of R packages for data science process,

  • plotly for creating interactive plot,

  • gganimate for creating animation plot,

  • DT for displaying interactive html table,

  • crosstalk for for implementing cross-widget interactions (currently, linked brushing and filtering), and

  • ggdist for visualising distribution and uncertainty.

pacman::p_load(plotly, crosstalk, DT, ggdist, ggridges, colorspace, gganimate, tidyverse)

2.2 Importing data

For the purpose of this exercise, Exam_data.csv will be used.

exam <- read_csv("data/Exam_data.csv")

3 Visualizing the uncertainty of point estimates: ggplot2 methods

A point estimate is a single number, such as a mean. Uncertainty, on the other hand, is expressed as standard error, confidence interval, or credible interval.

Important

Don’t confuse the uncertainty of a point estimate with the variation in the sample

In this section, you will learn how to plot error bars of maths scores by race by using data provided in exam tibble data frame.

Firstly, code chunk below will be used to derive the necessary summary statistics.

my_sum <- exam %>%
  group_by(RACE) %>%
  summarise(
    n=n(),
    mean=mean(MATHS),
    sd=sd(MATHS)
    ) %>%
  mutate(se=sd/sqrt(n-1))
Tip

  • group_by() of dplyr package is used to group the observation by RACE,

  • summarise() is used to compute the count of observations, mean, standard deviation

  • mutate() is used to derive standard error of Maths by RACE, and

  • the output is save as a tibble data table called my_sum.

Next, the code chunk below will be used to display my_sum tibble data frame in an html table format.

knitr::kable(head(my_sum), format = 'html')
RACE n mean sd se
Chinese 193 76.50777 15.69040 1.132357
Indian 12 60.66667 23.35237 7.041005
Malay 108 57.44444 21.13478 2.043177
Others 9 69.66667 10.72381 3.791438

3.1 Plotting standard error bars of point estimates

Now we are ready to plot the standard error bars of mean maths score by race as shown below.

ggplot(my_sum) +
  geom_errorbar(
    aes(x=RACE, 
        ymin=mean-se, 
        ymax=mean+se), 
    width=0.2, 
    colour="black", 
    alpha=0.9, 
    linewidth=0.5) +
  geom_point(aes
           (x=RACE, 
            y=mean), 
           stat="identity", 
           color="red",
           size = 1.5,
           alpha=1) +
  ggtitle("Standard error of mean maths score by Race")

Tip

  • The error bars are computed by using the formula mean+/-se.

  • For geom_point(), it is important to indicate stat=“identity”.

3.2 Plotting confidence interval of point estimates

Instead of plotting the standard error bar of point estimates, we can also plot the confidence intervals of mean maths score by race.

ggplot(my_sum) +
  geom_errorbar(
    aes(x=reorder(RACE, -mean), 
        ymin=mean-1.96*se, 
        ymax=mean+1.96*se), 
    width=0.2, 
    colour="black", 
    alpha=0.9, 
    linewidth=0.5) +
  geom_point(aes
           (x=RACE, 
            y=mean), 
           stat="identity", 
           color="red",
           size = 1.5,
           alpha=1) +
  labs(x = "Maths score",
       title = "95% confidence interval of mean maths score by race")

Tip

  • The confidence intervals are computed by using the formula mean+/-1.96*se.

  • The error bars is sorted by using the average maths scores.

  • labs() argument of ggplot2 is used to change the x-axis label.

3.3 Visualizing the uncertainty of point estimates with interactive error bars

In this section, you will learn how to plot interactive error bars for the 99% confidence interval of mean maths score by race as shown in the figure below.

shared_df = SharedData$new(my_sum)

bscols(widths = c(4,8),
       ggplotly((ggplot(shared_df) +
                   geom_errorbar(aes(
                     x=reorder(RACE, -mean),
                     ymin=mean-2.58*se, 
                     ymax=mean+2.58*se), 
                     width=0.2, 
                     colour="black", 
                     alpha=0.9, 
                     size=0.5) +
                   geom_point(aes(
                     x=RACE, 
                     y=mean, 
                     text = paste("Race:", `RACE`, 
                                  "<br>N:", `n`,
                                  "<br>Avg. Scores:", round(mean, digits = 2),
                                  "<br>95% CI:[", 
                                  round((mean-2.58*se), digits = 2), ",",
                                  round((mean+2.58*se), digits = 2),"]")),
                     stat="identity", 
                     color="red", 
                     size = 1.5, 
                     alpha=1) + 
                   xlab("Race") + 
                   ylab("Average Scores") + 
                   theme_minimal() + 
                   theme(axis.text.x = element_text(
                     angle = 45, vjust = 0.5, hjust=1)) +
                   ggtitle("99% Confidence interval of average /<br>maths scores by race")), 
                tooltip = "text"), 
       DT::datatable(shared_df, 
                     rownames = FALSE, 
                     class="compact", 
                     width="100%", 
                     options = list(pageLength = 10,
                                    scrollX=T), 
                     colnames = c("No. of pupils", 
                                  "Avg Scores",
                                  "Std Dev",
                                  "Std Error")) %>%
         formatRound(columns=c('mean', 'sd', 'se'),
                     digits=2))

4 Visualising Uncertainty: ggdist package

  • ggdist is an R package that provides a flexible set of ggplot2 geoms and stats designed especially for visualising distributions and uncertainty.

  • It is designed for both frequentist and Bayesian uncertainty visualization, taking the view that uncertainty visualization can be unified through the perspective of distribution visualization:

    • for frequentist models, one visualises confidence distributions or bootstrap distributions (see vignette(“freq-uncertainty-vis”));

    • for Bayesian models, one visualises probability distributions (see the tidybayes package, which builds on top of ggdist).

4.1 Visualizing the uncertainty of point estimates: ggdist methods

In the code chunk below, stat_pointinterval() of ggdist is used to build a visual for displaying distribution of maths scores by race.

exam %>%
  ggplot(aes(x = RACE, 
             y = MATHS)) +
  stat_pointinterval() +
  labs(
    title = "Visualising confidence intervals of mean math score",
    subtitle = "Mean Point + Multiple-interval plot")

This function comes with many arguments, for example, in the code chunk below the following arguments are used:

  • .width = 0.95

  • .point = median

  • .interval = qi

exam %>%
  ggplot(aes(x = RACE, y = MATHS)) +
  stat_pointinterval(.width = 0.95,
  .point = median,
  .interval = qi) +
  labs(
    title = "Visualising confidence intervals of median math score",
    subtitle = "Median Point + Multiple-interval plot")

4.2 Visualizing the uncertainty of point estimates: ggdist methods

exam %>%
  ggplot(aes(x = RACE, 
             y = MATHS)) +
  stat_pointinterval(
    show.legend = FALSE) +   
  labs(
    title = "Visualising confidence intervals of mean math score",
    subtitle = "Mean Point + Multiple-interval plot")

4.3 Visualizing the uncertainty of point estimates: ggdist methods

In the code chunk below, stat_gradientinterval() of ggdist is used to build a visual for displaying distribution of maths scores by race.

exam %>%
  ggplot(aes(x = RACE, 
             y = MATHS)) +
  stat_gradientinterval(   
    fill = "skyblue",      
    show.legend = TRUE     
  ) +                        
  labs(
    title = "Visualising confidence intervals of mean math score",
    subtitle = "Gradient + interval plot")

5 Visualising Uncertainty with Hypothetical Outcome Plots (HOPs)

library(ungeviz)
ggplot(data = exam, 
       (aes(x = factor(RACE), 
            y = MATHS))) +
  geom_point(position = position_jitter(
    height = 0.3, 
    width = 0.05), 
    size = 0.4, 
    color = "#0072B2", 
    alpha = 1/2) +
  geom_hpline(data = sampler(25, 
                             group = RACE), 
              height = 0.6, 
              color = "#D55E00") +
  theme_bw() + 
  transition_states(.draw, 1, 3)

6 Reference