19  Exercises: When in doubt, plot it out

TipHallo Medical Statistics

Pre-requicite for these exercises was covered within the session and is therefore not repeated here. The exercises build on this material.

19.1 Exercises: “Let’s first see what the data are telling us”

You are given a dataset containing demographic measurements from !Kung San individuals, including age, height, weight, and sex.

The research team wants to explore a simple question:

How do height and weight vary with age, and do these patterns differ between males and females?

Before drawing conclusions, the team wants to first understand the data visually. In particular, they want to examine the distributions of height and weight, compare males and females, and explore relationships between the continuous variables.

The Professor asks you to start by asking:

Which visualization is most appropriate for each question?

19.1.1 A: Preparing to start plotting

Before we can plot anything, we need our data and we need to know which state and format it’s in. This sections shows a common workflow to do this.

Exercise 1A:

Import the Height dataset into R — see Section 17.14 for more info.

Click for the solution 
height_data <- medisr::height_data

Exercise 2A:

View the dataset.

  1. How many observations do we have?
  2. How many variables?
  3. What type are they?
Click for the solution 
View(height_data) <- medisr::height_data
  1. 544
  2. 4
  3. all numeric (dbl and int)

this is easier to see if you make the dataset a tibble

height_data |>
    tibble::as_tibble()
# A tibble: 544 × 4
   height weight   age  male
    <dbl>  <dbl> <dbl> <int>
 1   152.   47.8    63     1
 2   140.   36.5    63     0
 3   137.   31.9    65     0
 4   157.   53.0    41     1
 5   145.   41.3    51     0
 6   164.   63.0    35     1
 7   149.   38.2    32     0
 8   169.   55.5    27     1
 9   148.   34.9    19     0
10   165.   54.5    54     1
# ℹ 534 more rows

Exercise 3A:

Are we happy with going strait to plotting or do we need to wrangle the dataset a bit with dplyr first?

Click for the solution male is obviously not continuous but rather a yes/no factor. So we should consider this later before comparing males and females.

19.1.2 B: Exploratory data analysis with plotting

It is extremely useful (and often necessary) to plot your data before you start doing any statistics or conclusions. This section covers a typical workflow.

Exercise 1B:

The variable male is coded as 0 and 1. Before plotting, convert it into a factor with meaningful labels:

  • 0 should represent "Female"
  • 1 should represent "Male"
  • Print the resulting variable to check that the transformation worked.
Click for the solution 
height_data <- height_data |>
  dplyr::mutate(
    male = factor(
      male,
      levels = c(0, 1),
      labels = c("Female", "Male")
    )
  )

height_data  |>
  dplyr::pull(male)
  [1] Male   Female Female Male   Female Male   Female Male   Female
 [10] Male   Female Male   Female Female Female Male   Male   Female
 [19] Male   Female Female Male   Female Male   Female Male   Female
 [28] Female Male   Female Male   Male   Male   Female Female Female
 [37] Female Female Female Male   Male   Male   Male   Female Female
 [46] Female Male   Female Female Male   Female Male   Male   Male  
 [55] Female Female Male   Female Female Female Female Male   Female
 [64] Male   Female Female Female Male   Male   Female Male   Female
 [73] Male   Female Female Male   Female Male   Male   Female Female
 [82] Female Female Male   Male   Female Male   Male   Female Female
 [91] Male   Female Male   Male   Female Male   Female Female Male  
[100] Female Male   Female Male   Female Female Male   Male   Female
[109] Female Male   Male   Male   Female Female Male   Male   Male  
[118] Female Male   Female Male   Male   Male   Male   Female Female
[127] Male   Male   Male   Female Female Male   Male   Male   Female
[136] Male   Female Female Male   Male   Female Male   Female Male  
[145] Female Female Female Female Male   Male   Female Female Male  
[154] Male   Female Female Female Male   Male   Female Male   Male  
[163] Female Female Female Male   Female Male   Female Female Female
[172] Female Female Female Male   Female Female Male   Male   Female
[181] Male   Female Male   Male   Male   Female Female Male   Male  
[190] Female Male   Female Female Female Female Female Female Male  
[199] Female Male   Male   Female Male   Male   Female Male   Female
[208] Male   Female Male   Female Female Female Male   Male   Female
[217] Male   Male   Female Female Male   Male   Male   Male   Male  
[226] Female Male   Male   Female Female Female Female Female Male  
[235] Female Male   Female Male   Female Female Female Female Female
[244] Male   Female Male   Male   Female Female Female Female Male  
[253] Male   Female Male   Female Male   Male   Female Male   Female
[262] Male   Female Female Female Female Female Male   Male   Female
[271] Male   Male   Female Female Male   Female Male   Female Female
[280] Female Female Female Female Male   Male   Male   Female Male  
[289] Male   Female Female Female Male   Female Male   Female Female
[298] Male   Female Female Female Female Male   Female Male   Female
[307] Female Female Female Male   Female Male   Male   Male   Female
[316] Female Male   Male   Male   Female Male   Female Female Male  
[325] Male   Female Male   Female Female Female Female Female Male  
[334] Female Male   Female Male   Male   Female Male   Female Male  
[343] Female Female Female Male   Female Female Male   Male   Male  
[352] Male   Male   Female Male   Male   Female Female Male   Female
[361] Male   Female Female Male   Female Female Female Male   Male  
[370] Female Female Male   Female Female Male   Male   Male   Female
[379] Female Male   Female Female Male   Male   Female Female Female
[388] Female Male   Female Male   Male   Female Male   Male   Female
[397] Male   Female Male   Female Male   Male   Male   Female Male  
[406] Male   Female Male   Male   Female Male   Male   Female Male  
[415] Female Female Female Male   Female Female Male   Male   Female
[424] Male   Female Male   Male   Male   Male   Male   Female Male  
[433] Male   Male   Male   Male   Male   Male   Female Male   Female
[442] Male   Female Female Female Male   Male   Female Male   Male  
[451] Male   Female Female Male   Female Female Male   Male   Male  
[460] Male   Male   Female Female Female Female Male   Female Male  
[469] Female Female Female Female Male   Female Female Male   Male  
[478] Female Male   Female Female Male   Female Male   Male   Female
[487] Male   Male   Male   Female Male   Female Male   Female Female
[496] Female Female Male   Male   Male   Male   Male   Female Male  
[505] Female Male   Female Female Male   Male   Female Female Male  
[514] Female Female Female Female Female Female Female Male   Male  
[523] Female Male   Female Male   Female Female Male   Female Female
[532] Female Male   Female Female Male   Female Female Male   Male  
[541] Male   Female Male   Male  
Levels: Female Male

Exercise 2B:

Create a plot that proofes to yourself that the median age of males and females are similar within the dataset.

  • What will you put on the x-axis?
  • What will you put on the y-axis?
  • Any color coding?
  • Which geom_?

First draw it so that the two groups have similar age in the population. Consider the fact that this is a demographic study with the entire population of the Kalahari !Kung San people (so we have a wide range of ages).

Second implement the plot in R.

Click for the solution 
height_data |>
  ggplot(
    aes(
      x = male,
      y = age,
      color = male
    )
  ) +
  geom_boxplot()

Exercise 3B:

Investigate whether the relationship between height and weight appears to be linear.

Create a scatter plot with:

  • What will you put on the x-axis?
  • What will you put on the y-axis?
  • Any color coding?
  • Which geom_?

Then answer:

  • Does weight increase approximately linearly with height?
  • Does the shape of the relationship look similar for males and females?
  • Is there evidence that one sex tends to weigh more at the same height?
Click for the solution 
height_data |>
  ggplot(
    aes(
      x = height,
      y = weight,
      color = male
    )
  ) +
  geom_point() +
  geom_smooth()
`geom_smooth()` using method = 'loess' and formula = 'y ~ x'

19.1.3 C: Fitting a hypothesis with a plot type

Finally, plots often accompany hypothesis. We want to show the reader of our plot that it supports a specific conclusion. Here, you get experience fitting plot types with hypotheses.

Exercise 1C:

A researcher wants to investigate the following hypothesis:

Hypothesis: There is more variability in male height than in female height.

Which visualization would be most appropriate?

Explain why you chose this visualization and what features of the graph you would look at to evaluate the hypothesis.

Now implement it using ggplot2.

Click for the solution

Code depends on your plot of choice 👀

Example:

height_data |>
  ggplot(
    aes(
      x = height,
      color = male
    )
  ) +
  geom_density()

Exercise 2C:

Consider the hypothesis:

Hypothesis: Males have higher body weight than females.

Which visualization would be most appropriate?

Explain your reasoning and implement the plot using ggplot2.

Click for the solution

Did you choose box plot? 👀

Example:

height_data |>
  ggplot(
    aes(
      x = male,
      y = weight,
      color = male
    )
  ) +
  geom_boxplot()

Exercise 3C:

Consider the hypothesis:

Hypothesis: Females increase their height earlier in development than males.

Which visualization would be most appropriate?

Explain your reasoning and implement the plot using ggplot2.

Click for the solution

example:

height_data |>
  ggplot(
    aes(
      x = age,
      y = height,
      color = male
    )
  ) +
  geom_point() +
  geom_smooth() +
  xlim(c(0,20)) # this line helps a lot by zooming in at the age of interest!
`geom_smooth()` using method = 'loess' and formula = 'y ~ x'
Warning: Removed 331 rows containing non-finite outside the scale range
(`stat_smooth()`).
Warning: Removed 331 rows containing missing values or values outside the scale
range (`geom_point()`).