Visualising data

.title[
# Visualising data
]
.subtitle[
## Introduction to Data Science
]
.author[
### University of Edinburgh
]
.date[
### 2024/2025
]

---

## The story so far...

- **Data** are observations or measurements (unprocessed or processed) of various data types: numbers, characters, factors, dates, etc.

- A **dataset** is a structured collection of data associated with a unique body of work.

- Majority of datasets are structured in a 'tidy' tabular/rectangular form where:
  - Each row is an **observation**
  - Each column is a **variable**

---

## The story so far...

It may be necessary to clean and **wrangle** the dataset in preparation for analysis by...
- Extracting: `select()` and `filter()`
- Ordering: `arrange()`
- Transforming: `mutate()`
- Combine: `left_join()`, `right_join()` and `full_join()`
- Arrangement: `pivot_wide()` and `pivot_long()`

Then the cleaned data is **summarised** for investigation and communication via...

- Grouping: `group_by()`
- Tabulation: `count()`
- Summarising: `summarise()`
  - `sum()`, `n()`
  - `mean()`, `var()`, `sd()`, `cor()`
  - `median()`, `min()`, `max()`, `quantile()`, `IQR()`

---

# Exploratory data analysis

---

## What is EDA?

- Exploratory data analysis (EDA) is the first step in **understanding** the main features and structures of a data set.
 
- Many statistical tools and techniques are used when performing EDA, but crucially they are **simple** to allow the data __speak__ for itself.
 
- Tools that a data scientist may use are:
 - Data transformation/wrangling
 - Calculation of simple summary statistics (mean, median, variance, correlation, etc.)
 - Tabulation
 - Graphical or visual representations
 - etc.

> *"Although we often hear that data speak for themselves, their voices can be soft and sly." --- Mosteller et al. (1983)*

---

## Common statistics

`$$\bar{x} = \frac{1}{n}\sum_{i=1}^n x_i$$`

* **Median** &#9632;: The mid-point that splits the data in a lower 50% and an upper 50%.

* **Mode** &#9632;: The most frequent/likely value.
]

]

.pull-left[
* **Standard deviation**: How far, on average, the data is from the mean. `$s = \sqrt{\frac{1}{n-1}\sum_{i=1}^n (x_i-\bar{x})^2}$`

![](w04-L07_files/figure-html/spread1-1.png)

]

* **Inter-quartile range**: The width of the middle 50% of the data.
`$IQR = Q_3 - Q_1\phantom{s = \sqrt{\frac{1}{n-1}\sum_{i=1}^n (x_i-\bar{x})^2}}$`

![](w04-L07_files/figure-html/spread2-1.png)
]
]

.pull-left[
* **Correlation**: The degree of _linear_ dependence between two variables.
]
.pull-right[
`$r = \frac{\sum_{i=1}^n (x_i - \bar{x})(y_i - \bar{y})}{\sqrt{\sum_{i=1}^n (x_i - \bar{x})^2}\sqrt{\sum_{i=1}^n (y_i - \bar{y})^2}}$`
]

![](w04-L07_files/figure-html/unnamed-chunk-1-1.png)

]
]

---

## Simulated example

* File `simulated_datasets.csv` contains two sets of data, labelled `"A"` and `"B"`
* Each data set consists 1000 samples of two numerical variables, `x` and `y`.

``` r
data <- read_csv("data/simulated_datasets.csv")
```

``` r
data %>% filter(set == "A") %>% head(n = 3)
```

```
## # A tibble: 3 × 4
## set id x y
## <chr> <dbl> <dbl> <dbl>
## 1 A 1 52.6 32.7
## 2 A 2 52.5 38.8
## 3 A 3 52.4 33.0
```
]
.pull-right[

``` r
data %>% filter(set == "B") %>% head(n = 3)
```

```
## # A tibble: 3 × 4
## set id x y
## <chr> <dbl> <dbl> <dbl>
## 1 B 1 52.4 32.7
## 2 B 2 55.4 35.2
## 3 B 3 56.0 35.2
```
]

]

``` r
data %>% 
  group_by(set) %>%
  summarise(
    avg_x = mean(x), sd_x = sd(x), med_x = median(x),
    min_x = min(x),  max_x = max(x), IQR_x = IQR(x),
    
    avg_y = mean(y), sd_y = sd(y),   med_y = median(y),
    min_y = min(y),  max_y = max(y), IQR_y = IQR(y),
    
    cor_xy = cor(x, y)
  )
```

```
## # A tibble: 2 × 14
## set avg_x sd_x med_x min_x max_x IQR_x avg_y sd_y med_y min_y max_y IQR_y cor_xy
## <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 A 52.4 3.32 52.4 43.9 60.9 5.96 32.7 2.39 32.7 26.6 38.8 4.27 -0.000537
## 2 B 52.4 3.32 52.4 43.9 60.9 5.96 32.7 2.39 32.7 26.6 38.8 4.27 -0.000657
```

]

``` r
ggplot(data, 
 mapping = aes(x = x, 
 fill = set)) + 
 geom_histogram(bins = 30) + 
 facet_wrap(~set)
```
]
.pull-right[
![](w04-L07_files/figure-html/hist_image-1.png)
]

]

``` r
ggplot(data, 
 mapping = aes(x = x, 
 y = y, 
 col = set)) + 
 geom_point() + 
 facet_wrap(~set)
```
]
.pull-right[
![](w04-L07_files/figure-html/scatter_image-1.png)
]

]

---

# Data visualization

---

## Data visualization

> *"The simple graph has brought more information to the data analyst's mind than any other device." --- John Tukey*

- Data visualization is the creation and study of the visual representation of data.

- The purpose is to literally *see* what your data seems to say.

- Human brains are very good at identifying complex patterns ...
  - ... and similarly they can easily be fooled!
  
- Visualising the data can help identify unusual shapes and structures that are not intuitive and difficult to examine numerically.

---

## Example: RANDU

- Pseudo-random number generators are algorithms that generate a sequence of numbers that satisfy important statistical properties of randomness.

- **Randu** was a popular algorithm for generating random numbers in 1960s & 1970s.

- Numbers are generated via the recursion:
`$$V_{j+1} = (65539~ V_j) \mod 2^{31}$$`
- Typically, these numbers are scaled to the `$[0, 1]$` interval: `$X_j = V_j / 2^{31}$`.

- **Question**: What are the desired properties you want from (uniform) random numbers?

---

## Example: RANDU plots

.pull-left[
![](w04-L07_files/figure-html/randu_hist-1.png)
]
.pull-right[
![](w04-L07_files/figure-html/randu_scatter-1.png)
]

---

## Example: RANDU

* But, if we create a 3D scatter plot with three consecutive RANDU values and rotate ...

* Use visualisations to **explore** the data. You may need more than one perspective.

---

## Example: Facebook visits

.pull-left[
![](w04-L07_files/figure-html/unnamed-chunk-3-1.png)
]
.pull-right[
- What insights does this plot give about:
 - how frequent participants are viewing Facebook?
 - how the participants are answering the question?
]

- You may need to iterate between visualisation and data transform.

---

## The good, the bad and the ugly 🤠

* Not all data visualisations are designed equally in their informativeness.

* Be cautions of data visualisations that are designed to mislead! 👿

---

## The Four respects:

1. **Respect the people**
  - Who are the target audience?
  - Respect users perception and cognitive capabilities.
  - Is your visualisation inclusive?
2. **Respect the data**
  - Let the data speak for itself!
  - Use an appropriate visualisation style for the data type.
  - Don't "massage" the data for a particular narrative.
  - Use an informative title and axis labels.
3. **Respect the mathematics**
  - Use of appropriateness geometric attribute (eg, length vs area)
  - Is the geometry of the visualisation correct?
  - Scale and range of the axes.
4. **Respect the computers**
  - Don't overtax the computer

---

# ggplot2

---

## ggplot2 `$\in$` tidyverse

.pull-left[
<img src="img/ggplot2-part-of-tidyverse.png" width="80%" />
] 
.pull-right[ 
- **ggplot2** is tidyverse's data visualization package 
- `gg` in "ggplot2" stands for *Grammar of Graphics* from the book by Leland Wilkinson

<img src="img/grammar-of-graphics.png" width="100%" />
]

---

## Structure of creating a plot

- `ggplot()` is the main function in ggplot2
- Construct plots by _adding_ (`+`) layers -- **Not** the `%>%` pipe!
- Structure of the code for plots can be summarized as:

``` r
ggplot(data = [dataset],                                         # Data
       mapping = aes(x = [x-variable], y = [y-variable])) +      # Aesthetics
   geom_[*]() +                                                  # Geometries
   other options                                                 # ...
```

- Many types of geometries:
  - `geom_points()`, `geom_histogram()`, `geom_line()`, `geom_boxplot()`, etc.

- [ggplot2 cheat sheet](https://www.rstudio.com/resources/cheatsheets/)

---

## Example: Palmer Penguins

Measurements for penguin species, island in Palmer Archipelago, size (flipper length, body mass, bill dimensions), and sex.

``` r
library(palmerpenguins)
penguins
```

```
## # A tibble: 344 × 8
## species island bill_length_mm bill_depth_mm flipper_length_mm body_mass_g
## <fct> <fct> <dbl> <dbl> <int> <int>
## 1 Adelie Torgersen 39.1 18.7 181 3750
## 2 Adelie Torgersen 39.5 17.4 186 3800
## 3 Adelie Torgersen 40.3 18 195 3250
## 4 Adelie Torgersen NA NA NA NA
## 5 Adelie Torgersen 36.7 19.3 193 3450
## 6 Adelie Torgersen 39.3 20.6 190 3650
## 7 Adelie Torgersen 38.9 17.8 181 3625
## 8 Adelie Torgersen 39.2 19.6 195 4675
## 9 Adelie Torgersen 34.1 18.1 193 3475
## 10 Adelie Torgersen 42 20.2 190 4250
## # ℹ 334 more rows
## # ℹ 2 more variables: sex <fct>, year <int>
```
]
]

---

## Example: Penguins dataset

---

## Coding narative

.midi[
> **Start with the `penguins` data frame,**
> map bill depth to the x-axis
> and map bill length to the y-axis. 
> Represent each observation with a point
> and map species to the colour of each point.
> Title the plot "Penguin bill depth & length", 
> label the x and y axes as "Bill depth (mm)" and "Bill length (mm)", respectively,
> and label the legend "Species".
]

``` r
*ggplot(data = penguins)
```
]
.pull-right[
<img src="w04-L07_files/figure-html/unnamed-chunk-11-1.png" width="80%" />
]

---

## Coding narative

.midi[
> Start with the `penguins` data frame,
> **map bill depth to the x-axis**
> and map bill length to the y-axis. 
> Represent each observation with a point
> and map species to the colour of each point.
> Title the plot "Penguin bill depth & length", 
> label the x and y axes as "Bill depth (mm)" and "Bill length (mm)", respectively,
> and label the legend "Species".
]

``` r
ggplot(data = penguins,
* mapping = aes(x = bill_depth_mm))
```
]
.pull-right[
<img src="w04-L07_files/figure-html/unnamed-chunk-12-1.png" width="80%" />
]

---

## Coding narative

.midi[
> Start with the `penguins` data frame,
> map bill depth to the x-axis
> **and map bill length to the y-axis.** 
> Represent each observation with a point
> and map species to the colour of each point.
> Title the plot "Penguin bill depth & length", 
> label the x and y axes as "Bill depth (mm)" and "Bill length (mm)", respectively,
> and label the legend "Species".
]

``` r
ggplot(data = penguins,
 mapping = aes(x = bill_depth_mm,
* y = bill_length_mm))
```
]
.pull-right[
<img src="w04-L07_files/figure-html/unnamed-chunk-13-1.png" width="80%" />
]

---

## Coding narative

.midi[
> Start with the `penguins` data frame,
> map bill depth to the x-axis
> and map bill length to the y-axis. 
> **Represent each observation with a point**
> and map species to the colour of each point.
> Title the plot "Penguin bill depth & length", 
> label the x and y axes as "Bill depth (mm)" and "Bill length (mm)", respectively,
> and label the legend "Species".
]

``` r
ggplot(data = penguins,
 mapping = aes(x = bill_depth_mm,
 y = bill_length_mm)) + 
* geom_point()
```
]
.pull-right[
<img src="w04-L07_files/figure-html/unnamed-chunk-14-1.png" width="80%" />
]

---

## Coding narative

.midi[
> Start with the `penguins` data frame,
> map bill depth to the x-axis
> and map bill length to the y-axis. 
> Represent each observation with a point
> **and map species to the colour of each point.**
> Title the plot "Penguin bill depth & length", 
> label the x and y axes as "Bill depth (mm)" and "Bill length (mm)", respectively,
> and label the legend "Species".
]

``` r
ggplot(data = penguins,
 mapping = aes(x = bill_depth_mm,
 y = bill_length_mm,
* colour = species)) +
 geom_point()
```
]
.pull-right[
<img src="w04-L07_files/figure-html/unnamed-chunk-15-1.png" width="80%" />
]

---

## Coding narative

.midi[
> Start with the `penguins` data frame,
> map bill depth to the x-axis
> and map bill length to the y-axis. 
> Represent each observation with a point
> and map species to the colour of each point.
> **Title the plot "Penguin bill depth & length", **
> label the x and y axes as "Bill depth (mm)" and "Bill length (mm)", respectively,
> and label the legend "Species".
]

``` r
ggplot(data = penguins,
 mapping = aes(x = bill_depth_mm,
 y = bill_length_mm,
 colour = species)) +
 geom_point() +
* labs(title = "Penguin bill depth & length")
```
]
.pull-right[
<img src="w04-L07_files/figure-html/unnamed-chunk-16-1.png" width="80%" />
]

---

## Coding narative

.midi[
> Start with the `penguins` data frame,
> map bill depth to the x-axis
> and map bill length to the y-axis. 
> Represent each observation with a point
> and map species to the colour of each point.
> Title the plot "Penguin bill depth & length", 
> **label the x and y axes as "Bill depth (mm)" and "Bill length (mm)", respectively,**
> and label the legend "Species".
]

``` r
ggplot(data = penguins,
 mapping = aes(x = bill_depth_mm,
 y = bill_length_mm,
 colour = species)) +
 geom_point() +
 labs(title = "Penguin bill depth & length",
* x = "Bill depth (mm)",
* y = "Bill length (mm)")
```
]
.pull-right[
<img src="w04-L07_files/figure-html/unnamed-chunk-17-1.png" width="80%" />
]

---

## Coding narative

.midi[
> Start with the `penguins` data frame,
> map bill depth to the x-axis
> and map bill length to the y-axis. 
> Represent each observation with a point
> and map species to the colour of each point.
> Title the plot "Penguin bill depth & length", 
> label the x and y axes as "Bill depth (mm)" and "Bill length (mm)", respectively,
> **and label the legend "Species".**
]

``` r
ggplot(data = penguins,
 mapping = aes(x = bill_depth_mm,
 y = bill_length_mm,
 colour = species)) +
 geom_point() +
 labs(title = "Penguin bill depth & length",
 x = "Bill depth (mm)", 
 y = "Bill length (mm)",
* colour = "Species")
```
]
.pull-right[
<img src="w04-L07_files/figure-html/unnamed-chunk-18-1.png" width="80%" />
]

---

.panelset[
.panel[.panel-name[Plot]
<img src="w04-L07_files/figure-html/unnamed-chunk-19-1.png" width="45%" style="display: block; margin: auto;" />
]
.panel[.panel-name[Code]

``` r
ggplot(data = penguins, 
       mapping = aes(x = bill_depth_mm, y = bill_length_mm,
                     colour = species)) +
  geom_point() +
  labs(title = "Penguin bill depth & length",
       x = "Bill depth (mm)", 
       y = "Bill length (mm)",
       colour = "Species")
```

]
]

---

# And iterate ...

* Editing the aesthetic options: Point colour, size, shape, etc.

* Incorporate more variables from the data set.

* Specify the limits of the co-ordinate axes to zoom in or out.

* Include additional descriptive information: sub-title, caption, data source citation, etc.

* Add other graphical information: line/curve of best fit, arrows, estimation intervals, etc.

* Faceting/panelling multiple plots into a grid.

* Changing the colour pallet that is more accessible for colour blindness.

* ...

**However**, more is not necessarily good - Remember the 4 respects.