Hands-on_Ex4-2 Visualising Uncertainty

10.1 Learning Outcome

10.2 Visualizing the uncertainty of point estimates

• A point estimate is a single number, such as a mean.

• Uncertainty 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

pacman::p_load(tidyverse, plotly, crosstalk, DT, ggdist, gganimate, ggplot2, dplyr)

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

10.2.1 Visualizing the uncertainty of point estimates: ggplot2 methods

The code chunk below performs the followings:

• group the observation by RACE,

• computes the count of observations, mean, standard deviation and standard error of Maths by RACE, and

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

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

Note: For the mathematical explanation, please refer to Slide 20 of Lesson 4.

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

10.2.2 Visualizing the uncertainty of point estimates: ggplot2 methods

The code chunk below is used to reveal the standard error of mean maths score by race.

ggplot(my_sum) +
  geom_errorbar(
    aes(x=RACE, 
        ymin=mean-se, 
        ymax=mean+se), 
    width=0.2, 
    colour="black", 
    alpha=0.9, 
    size=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")

10.2.3 Visualizing the uncertainty of point estimates: ggplot2 methods

my_sum_sorted <- my_sum %>% 
  arrange(desc(mean)) %>%
  mutate(RACE = forcats::fct_reorder(RACE, -mean))


ggplot(my_sum_sorted) +
  geom_errorbar(
    aes(x=RACE, 
        ymin=mean-se, 
        ymax=mean+se), 
    width=0.2, 
    colour="black", 
    alpha=0.9, 
    size=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")