Drawing graphs

Our data

• To illustrate making graphs, we need some data.
• Data on 202 male and female athletes at the Australian Institute of Sport.
• Variables:
  • categorical: Sex of athlete, sport they play
  • quantitative: height (cm), weight (kg), lean body mass, red and white blood cell counts, haematocrit and haemoglobin (blood), ferritin concentration, body mass index, percent body fat.
• Values separated by tabs (which impacts reading in).

Preliminaries

• Package:

library(tidyverse)

• Use read_tsv (“tab-separated values”), like read_csv.
• Data in ais.txt:

my_url <- "http://datafiles.ritsokiguess.site/ais.txt"
athletes <- read_tsv(my_url)

The data (some)

athletes

ggplot

• R has a standard graphing procedure ggplot, that we use for all our graphs.
• Use in different ways to get precise graph we want.
• Let’s start with bar chart of the sports played by the athletes.

Bar chart

• one categorical variable
• count how many athletes play each Sport
• Sport is x of graph

ggplot(athletes, aes(x = Sport)) + geom_bar()

The bar chart

Histogram of body mass index

• one quantitative variable
• count how many observations fall into intervals (of BMI)
• BMI is x of graph
• histogram needs number of bins. Choose it to show distribution shape clearly.

ggplot(athletes, aes(x = BMI)) + geom_histogram(bins = 10)

The histogram

Which sports are played by males and females?

• two categorical variables Sport and Sex
• grouped bar chart
• one variable is x and other is fill
• put bars side by side:

ggplot(athletes, aes(x = Sport, fill = Sex)) +
  geom_bar(position = "dodge")

Grouped bar chart

BMI by gender

• one quantitative variable and one categorical
• boxplot
• for us, boxplots are vertical
• quantitative is y and categorical x

ggplot(athletes, aes(x = Sex, y = BMI)) + geom_boxplot() 

The boxplot

Height vs. weight

• two quantitative variables
• scatterplot
• “outcome” as y, “explanatory” as x

ggplot(athletes, aes(x = Ht, y = Wt)) + geom_point()

Scatterplot

With regression line

• use geom_smooth to add regression lines or smooth trends

ggplot(athletes, aes(x = Ht, y = Wt)) +
  geom_point() + geom_smooth(method = "lm")

Scatterplot with regression line

BMI by sport and gender

• one quantitative and two categorical
• grouped boxplots
• quantitative as y
• one categorical as x, other as fill
• can use colour instead of fill

ggplot(athletes, aes(x = Sport, y = BMI, fill = Sex)) +
  geom_boxplot()

Grouped boxplot with fill

Grouped boxplot with colour

Height and weight by gender

• two quantitative variables and one categorical
• scatterplot with colours for categories
• x and y as for scatterplot, colour for categories
• points have only an “outside”:

ggplot(athletes, aes(x = Ht, y = Wt, colour = Sex)) +
  geom_point()

Scatterplot with colours

Height by weight by gender for each sport

• four variables, two quantitative, two categorical
• “extra” categorical variable
• use this (Sport) to make facets.

ggplot(athletes, aes(x = Ht, y = Wt, colour = Sex)) +
  geom_point() + facet_wrap(~Sport)

Facetted scatterplots

Filling each facet

Default uses same scale for each facet. To use different scales for each facet, this:

ggplot(athletes, aes(x = Ht, y = Wt, colour = Sex)) +
  geom_point() + facet_wrap(~Sport, scales = "free")

Facetted scatterplots

Another view of height vs weight

• Think of Sex as “extra” categorical variable
• turn into facets

ggplot(athletes, aes(x = Ht, y = Wt)) +
  geom_point() + facet_wrap(~ Sex)

Height vs weight alternative

Normal quantile plot

• For assessing whether a quantitative variable has a normal distribution or not
• Quantitative variable is sample for this.

ggplot(athletes, aes(sample = BMI)) + stat_qq() + 
  stat_qq_line()

The normal quantile plot

Comments

• Data on \(y\)-axis
• on \(x\)-axis, the \(z\)-scores you would expect if normal distribution correct
• if the points follow the line, distribution is normal
• the way in which the points don’t follow line tell you about how the distribution is not normal
• in this case, the highest values are too high (long upper tail).

Facetting again

• to do normal quantiles for each level of a categorical variable, use facets
• male and female athletes’ BMI separately:

ggplot(athletes, aes(sample = BMI)) + stat_qq() + 
  stat_qq_line() + facet_wrap(~ Sex)

The normal quantile plots

Comments

• The distribution of BMI for females is closer to normal, with only the highest few values being too high
• The distribution of BMI values for males might even be right-skewed: not only are the upper values too high, but some of the lowest ones are not low enough.

More normal quantile plots

• How straight does a normal quantile plot have to be?
• There is randomness in real data, so even a normal quantile plot from normal data won’t look perfectly straight.
• With a small sample, can look not very straight even from normal data.
• Looking for systematic departure from a straight line; random wiggles ought not to concern us.
• Look at some examples where we know the answer, so that we can see what to expect.
• Code not shown here; look at lecture notes web page if you want to see it.

Normal data, large sample

The normal quantile plot

Normal data, small sample

The normal quantile plot

Somewhat right-skewed

The normal quantile plot

Very right-skewed

The normal quantile plot

Long tails

The normal quantile plot

Summary

On a normal quantile plot:

• points following line (with some small wiggles): normal.
• kind of deviation from a straight line indicates kind of nonnormality:
  • a few highest point(s) too high and/or lowest too low: outliers
  • else see how points at each end off the line: