---
title: "Drawing graphs"
editor: 
  markdown: 
    wrap: 72
---

## 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

```{r graphs-R-1}
library(tidyverse)
```

## Reading data into R

-   Use `read_tsv` ("tab-separated values"), like `read_csv`.
-   Data in `ais.txt`:

```{r graphs-R-2}
my_url <- "http://ritsokiguess.site/datafiles/ais.txt"
athletes <- read_tsv(my_url)
```

## The data (some)

\small

```{r}
#| echo: false

wid <- getOption("width")
options(width = 60)
```


```{r graphs-R-3}
athletes
```


```{r}
#| echo: false

options(width = wid)
```

\normalsize

## Types of graph {.smaller}

Depends on number and type of variables:

| Categorical | Quantitative | Graph                                                       |
|-------------:|-------------:|:-------------------------------------------|
|           1 |            0 | bar chart                                                   |
|           0 |            1 | histogram                                                   |
|           2 |            0 | grouped bar charts                                          |
|           1 |            1 | side-by-side boxplots                                       |
|           0 |            2 | scatterplot                                                 |
|           2 |            1 | grouped boxplots                                            |
|           1 |            2 | scatterplot with points identified by group (eg. by colour) |

With more (categorical) variables, might want *separate plots by
groups*. This is called `facetting` in R.

## `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

```{r graphs-R-4, fig.height=3.9}
ggplot(athletes, aes(x = Sport)) + geom_bar()
```

## Histogram of body mass index

```{r graphs-R-5, fig.height=3.9}
ggplot(athletes, aes(x = BMI)) + geom_histogram(bins = 10)
```

## Which sports are played by males and females?

Grouped bar chart:

```{r graphs-R-6, fig.height=3.15}
ggplot(athletes, aes(x = Sport, fill = Sex)) +
  geom_bar(position = "dodge")
```

## BMI by gender

```{r graphs-R-7, fig.height=4}
ggplot(athletes, aes(x = Sex, y = BMI)) + geom_boxplot() 
```

## Height vs. weight

Scatterplot:

```{r graphs-R-8, fig.height=3.4}
ggplot(athletes, aes(x = Ht, y = Wt)) + geom_point()
```

## With regression line

```{r graphs-R-9, fig.height=3.6}
ggplot(athletes, aes(x = Ht, y = Wt)) +
  geom_point() + geom_smooth(method = "lm")
```

## BMI by sport and gender

```{r graphs-R-10, fig.height=3.6}
ggplot(athletes, aes(x = Sport, y = BMI, fill = Sex)) +
  geom_boxplot()
```

## Or...

A variation that uses `colour` instead of `fill`:

```{r}
#| fig-height: 5
ggplot(athletes, aes(x = Sport, y = BMI, colour = Sex)) +
  geom_boxplot()
```

## Height and weight by gender

```{r}
#| fig-height: 5
ggplot(athletes, aes(x = Ht, y = Wt, colour = Sex)) +
  geom_point()
```

## Height by weight by gender for each sport, with facets

```{r graphs-R-12, fig.height=3.6}
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:

```{r graphs-R-13, fig.height=4.8}
ggplot(athletes, aes(x = Ht, y = Wt, colour = Sex)) +
  geom_point() + facet_wrap(~Sport, scales = "free")
```

## Another view of height vs weight

```{r}
#| fig-height: 4.5
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:

```{r}
#| fig-height: 4 
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:

```{r}
#| fig-height: 4
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

```{r set-seed, echo=F}
set.seed(457299)
```

```{r inference-4a-R-11, fig.height=4.5}
d <- tibble(x=rnorm(200))
ggplot(d, aes(x=x)) + geom_histogram(bins=10)
```

## The normal quantile plot

```{r inference-4a-R-12, fig.height=4.5}
ggplot(d,aes(sample=x))+stat_qq()+stat_qq_line()
```

## Normal data, small sample

```{r inference-4a-R-13, echo=F}
set.seed(457299)
```

-   Not so convincingly normal, but not obviously skewed:

```{r normal-small, fig.height=4.5}
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:

```{r inference-4a-R-14, fig.height=4.5}
ggplot(d, aes(sample=x)) + stat_qq() + stat_qq_line()
```

## Chi-squared data, *df* = 10

Somewhat skewed to right:

```{r inference-4a-R-15, fig.height=4.5}
d <- tibble(x=rchisq(100, 10))
ggplot(d,aes(x=x)) + geom_histogram(bins=10)
```

## The normal quantile plot

Somewhat opening-up curve:

```{r inference-4a-R-16, fig.height=4.5}
ggplot(d,aes(sample=x))+stat_qq()+stat_qq_line()
```

## Chi-squared data, df = 3

Definitely skewed to right:

```{r chisq-small-df, fig.height=4.5}
d <- tibble(x=rchisq(100, 3))
ggplot(d, aes(x=x)) + geom_histogram(bins=10)
```

## The normal quantile plot

Clear upward-opening curve:

```{r inference-4a-R-17, fig.height=4.5}
ggplot(d,aes(sample=x))+stat_qq()+stat_qq_line()
```

## t-distributed data, df = 3

Long tails (or a very sharp peak):

```{r t-small, fig.height=4.5}
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.

```{r inference-4a-R-18, fig.height=4.5}
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:

|                | High points |              |
|----------------|-------------|--------------|
| **Low points** | **Too low** | **Too high** |
| **Too low**    | Skewed left | Long tails   |
| **Too high**   | Short tails | Skewed right |