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).

Packages for this section

library(tidyverse)

Reading data into R

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

my_url <- "http://ritsokiguess.site/datafiles/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

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

Histogram of body mass index

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

Which sports are played by males and females?

Grouped bar chart:

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

BMI by gender

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

Height vs. weight

Scatterplot:

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

With regression line

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

BMI by sport and gender

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

A variation that uses colour instead of fill:

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

Height and weight by gender

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

Height by weight by gender for each sport, with facets

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

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")

Another view of height vs weight

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

Normal quantile plot

For assessing whether a column has a normal distribution or not:

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

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

Male and female athletes’ BMI separately:

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

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.

Normal data, large sample

d <- tibble(x=rnorm(200))
ggplot(d, aes(x=x)) + geom_histogram(bins=10)

The normal quantile plot

ggplot(d,aes(sample=x))+stat_qq()+stat_qq_line()

Normal data, small sample

• Not so convincingly normal, but not obviously skewed:

d <- tibble(x=rnorm(20))
ggplot(d, aes(x=x)) + geom_histogram(bins=5)

The normal quantile plot

Good, apart from the highest and lowest points being slightly off. I’d call this good:

ggplot(d, aes(sample=x)) + stat_qq() + stat_qq_line()

Chi-squared data, df = 10

Somewhat skewed to right:

d <- tibble(x=rchisq(100, 10))
ggplot(d,aes(x=x)) + geom_histogram(bins=10)

The normal quantile plot

Somewhat opening-up curve:

ggplot(d,aes(sample=x))+stat_qq()+stat_qq_line()

Chi-squared data, df = 3

Definitely skewed to right:

d <- tibble(x=rchisq(100, 3))
ggplot(d, aes(x=x)) + geom_histogram(bins=10)

The normal quantile plot

Clear upward-opening curve:

ggplot(d,aes(sample=x))+stat_qq()+stat_qq_line()

t-distributed data, df = 3

Long tails (or a very sharp peak):

d <- tibble(x=rt(300, 3))
ggplot(d, aes(x=x)) + geom_histogram(bins=15)

The normal quantile plot

Low values too low and high values too high for normal.

ggplot(d,aes(sample=x))+stat_qq()+stat_qq_line()

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: