Describing Data Graphically with R

---

layout: true
  
<div class="my-footer">
<span>
<a href="https://psychmethods.github.io/coursenotes/" target="_blank">Methods in Psychological Research</a>
</span>
</div>

---

# Describing Data

---

## Hans Rosling

---

# Summarize

- Transform a pile of numbers into a summary
- Descriptive Statistics
    - Distribution of a variable is a table/graph showing the categories/values of outcomes and their frequency/percentage of occurrence
    - Exploratory Data Analysis (Tukey, 1977)
]
.pull-right[

![](data:image/png;base64,#../img/numberpile.png)
]

---

# Exploratory Data Analysis
.pull-left[
- Tukey (1977)
    - EDA
    - Graphical Data Analysis
    - Numbers as summaries
    - Emphasized Robust Statistics
]
--
.pull-right[
![](data:image/png;base64,#../img/tukey.png)
]

---

# Descriptive Statistics
- Examples
    - Tables
    - Graphs
    - Summary Statistics

---

# Tables

- Woodbridge (1845)
    
<img src="data:image/png;base64,#../img/woodbridge1845.png" width="100%" style="display: block; margin: auto;" />

---

# Graphs

-  Minard (1869)
    
<img src="data:image/png;base64,#../img/minard.png" width="70%" style="display: block; margin: auto;" />

---

# Examples

- Summary Statistics
    - Measures of Central Tendency
    - Measures of Spread
    
<img src="data:image/png;base64,#../img/centralbears.jpg" width="30%" style="display: block; margin: auto;" />

---

# Categorical Variable Displays (Nominal, Ordinal)

- Frequency Distribution Graphs
  - Bar Chart  (appropriate for nominal and ordinal data)
  - Pie Chart (best for nominal data with few categories)
--

- Quantitative Variables
  - Histograms
  - Stem plots
--

- Time Plots
  - (can be used for any level, often interval or ratio)

---

# Frequency distribution graph

.pull-left[
- Bar Chart
    - Graphs of variables with categories of outcomes on the x axis; and the frequency or percent of each category on the Y axis.
    - Appropriate for nominal and ordinal data
 
]
.pull-right[

<img src="data:image/png;base64,#../img/oresme.jpg" width="35%" style="display: block; margin: auto;" />
.footnote[Nicole Oresme (Bishop of Lisieus) circa 1350]
]

---

# Bar Graph/Chart

.pull-left.small[

``` r
# Bar chart
library(HistData)
Minard_troops_demo <- Minard.troops

Minard_troops_demo$group <- paste("Group",Minard_troops_demo$group)

counts <- table(Minard_troops_demo$group)
```
]

--
.pull-right.small[

``` r
barplot(counts, main="Bar Chart of Troops",
        xlab="Group", ylab="Observations",
        col="lightblue")
```

<img src="data:image/png;base64,#descriptive_files/figure-html/unnamed-chunk-8-1.png" width="90%" style="display: block; margin: auto;" />
]

- Note: This example uses nominal data (Troop Group) and how many data points we have for each group.
- Bar charts are suitable for nominal and ordinal data as they show frequency for discrete categories.
---

# Stacked Bar Chart (Total Troops)

.pull-left.small[

``` r
df <- data.frame(
  group = c("Group 1", 
            "Group 2", 
            "Group 3"),
  max = c(340000,60000,22000),
  min = c(4000,28000,6000))

head(df)
```

```
##     group    max   min
## 1 Group 1 340000  4000
## 2 Group 2  60000 28000
## 3 Group 3  22000  6000
```
]
.pull-right.small[

``` r
library(ggplot2)
bp <- ggplot(df, aes(x="",
                     y=max/1000, # to rescale
                     fill = group))+ 
  geom_bar(width = 1,stat = "identity")
bp
```

<img src="data:image/png;base64,#descriptive_files/figure-html/unnamed-chunk-11-1.png" width="90%" style="display: block; margin: auto;" />
]

- Stacked bar charts can show the relationship between two categorical variables.

---

# Pie Chart
.pull-left[
- Graphs of variables with categories of outcomes as frequency or percent of each category in the pie.
- Best for nominal data with few categories
]

.pull-right[
<img src="data:image/png;base64,#../img/pieplay.jpg" width="90%" height="40%" style="display: block; margin: auto;" />
.footnote["A pie chart showing each state in the United States, part of Playfair's translation of A Statistical Account of the United States of America by D. F. Donnant."
]]

---

# Pie chart

``` r
slices <- c(10,12,
            4,16, 8)
lbls <- c("US", "UK",
          "Australia",
          "Germany",
          "France")
```
]
.pull-right-wide[

``` r
pie(slices, labels = lbls,
    main="Pie Chart of Countries")
```

<img src="data:image/png;base64,#descriptive_files/figure-html/unnamed-chunk-14-1.png" width="90%" style="display: block; margin: auto;" />
]
---

# Example 2

.small.pull-left[

``` r
mytable <- table(iris$Species)
lbls <- paste(names(mytable), "\n", mytable, sep="")
pie(mytable, labels = lbls,
		main="Pie Chart of Species\n (with sample sizes)")
```

<img src="data:image/png;base64,#descriptive_files/figure-html/example2-1.png" width="90%" style="display: block; margin: auto;" />
]

.pull-right[
<img src="data:image/png;base64,#descriptive_files/figure-html/unnamed-chunk-15-1.png" width="65%" style="display: block; margin: auto;" />
]

- Pie charts are best for nominal data with few categories, showing part-to-whole relationships.

---

# Convert Bar Chart into Pie Chart

.small.pull-left[

``` r
pie <- bp + coord_polar("y", start=0)
pie
```

``` r
pie + scale_fill_manual(values=c("#999999", "#E69F00", "#56B4E9"))
```

<img src="data:image/png;base64,#descriptive_files/figure-html/polar-2.png" width="90%" style="display: block; margin: auto;" />
]
.pull-right[
<img src="data:image/png;base64,#descriptive_files/figure-html/unnamed-chunk-16-1.png" width="65%" style="display: block; margin: auto;" /><img src="data:image/png;base64,#descriptive_files/figure-html/unnamed-chunk-16-2.png" width="65%" style="display: block; margin: auto;" />
]

[Additional Resources](http://www.sthda.com/english/wiki/ggplot2-pie-chart-quick-start-guide-r-software-and-data-visualization)

---

# Quantitative Variables

- Interval or Ratio Scales
    - Histograms
    - Stem plots
    - Time plots

---

# Histogram 
- A histogram is a graphical representation of the distribution of numerical data.
    - Approximates a probability distribution
    - First described by  Pearson in 1895.
    
---

# Histogram

``` r
library(MASS) # load library
variable<-cats$Bwt
hist(variable)
```

<img src="data:image/png;base64,#descriptive_files/figure-html/unnamed-chunk-17-1.png" width="90%" style="display: block; margin: auto;" />
]

``` r
 #Convert to Imperial
variable<-variable*2.2

hist(variable)
```

<img src="data:image/png;base64,#descriptive_files/figure-html/unnamed-chunk-18-1.png" width="90%" style="display: block; margin: auto;" />
]

- Histograms are appropriate for interval and ratio data, showing the distribution of continuous variables.

---

# Boxplot (Ordinal predictor, Ratio outcome)

.pull-left[
- Boxplots can show the distribution of a ratio variable across categories of an ordinal variable.
]
.pull-right.small[

``` r
boxplot(mpg ~ cyl, data=mtcars,
        main="MPG by Number of Cylinders",
        xlab="Number of Cylinders (Ordinal)",
        ylab="Miles Per Gallon (Ratio)")
```

<img src="data:image/png;base64,#descriptive_files/figure-html/unnamed-chunk-19-1.png" width="90%" style="display: block; margin: auto;" />
]

---

# Stemplot

.pull-left-narrow[
- Sometimes called a stem and leaf diagram
- A way to display data that splits the data into a stem and leaf.
- The stem is the first digit of the number and the leaf is the second digit
- Stem and leaf plots are useful for displaying the distribution of interval or ratio data, especially for smaller datasets.
]
--
.pull-right-wide.small[
- Eruption duration is a ratio variable
- Each leaf represents the ones digit
- Each stem represents the tens digit

``` r
# Stem and Leaf plot
stem(faithful$eruptions,scale=1)
```

```
## 
##   The decimal point is 1 digit(s) to the left of the |
## 
##   16 | 070355555588
##   18 | 000022233333335577777777888822335777888
##   20 | 00002223378800035778
##   22 | 0002335578023578
##   24 | 00228
##   26 | 23
##   28 | 080
##   30 | 7
##   32 | 2337
##   34 | 250077
##   36 | 0000823577
##   38 | 2333335582225577
##   40 | 0000003357788888002233555577778
##   42 | 03335555778800233333555577778
##   44 | 02222335557780000000023333357778888
##   46 | 0000233357700000023578
##   48 | 00000022335800333
##   50 | 0370
```
]

---

# Time Plots

<img src="data:image/png;base64,#../img/minard.png" width="30%" style="display: block; margin: auto;" />
--

- Edward Tufte has said that Minard's plot: 
    > "may well be the best statistical graphic ever drawn"
    
- It packs a ton of information into one dense figure.

---

# Time Plots

---

- The plot contains seven variables, each mapped to a different aesthetic:

| Information                           | Aesthetic       | Level of Measurement |
|---------------------------------------|----------------------------------------|
| Size of Napoleon's Grande Armée       | Width of path   | Ratio             |
| Longitude of the army's position      | x-axis          | Ratio             |
| Latitude of the army's position       | y-axis          | Ratio             |
| Direction of the army's movement      | Color of path   | Nominal           |
| Date of points along retreat path     | Text below plot | ???????  (What do you think?)         |
| Temperature during the army's retreat | Line below plot | ??????? (What do you think?)  |
| Geographic features                   | Map background  | ???????  (What do you think?)            |

---

# Recreation in R

- This plot has been recreated in R by:
    - [Andrew Heiss](https://www.andrewheiss.com/blog/2017/08/10/exploring-minards-1812-plot-with-ggplot2/)
    - [Michael Friendly](http://www.datavis.ca/gallery/re-minard.php)
    - [Hadley Wickham](https://www.tandfonline.com/doi/suppl/10.1198/jcgs.2009.07098?scroll=top)

---

# Side by Side

.pull-left[
<img src="data:image/png;base64,#../img/minard.png" width="90%" style="display: block; margin: auto;" />
]

.pull-right[
<img src="data:image/png;base64,#descriptive_files/figure-html/unnamed-chunk-24-1.png" width="90%" style="display: block; margin: auto;" />
]

---

``` r
library(tidyverse)
library(lubridate)
library(ggplot2)
library(ggmap)
library(ggrepel)
library(gridExtra)
library(psych)
#Download Directly
download=FALSE # set to true to download
if(download){
 cities <- read.table("https://raw.githubusercontent.com/andrewheiss/fancy-minard/master/input/minard/cities.txt",
                      header = TRUE, stringsAsFactors = FALSE)
 
 troops <- read.table("https://raw.githubusercontent.com/andrewheiss/fancy-minard/master/input/minard/troops.txt",
                      header = TRUE, stringsAsFactors = FALSE)
 temps <- read.table("https://raw.githubusercontent.com/andrewheiss/fancy-minard/master/input/minard/temps.txt",
                     header = TRUE, stringsAsFactors = FALSE)
}else{

#Load from local
cities <- read.table("dat/cities.txt",
                     header = TRUE, stringsAsFactors = FALSE)
troops <- read.table("dat/troops.txt",
                     header = TRUE, stringsAsFactors = FALSE)
temps <- read.table("dat/temps.txt",
                    header = TRUE, stringsAsFactors = FALSE)
}

describe(cities)
```

```
##       vars  n  mean   sd median trimmed  mad  min  max range
## long     1 20 30.79 4.08  30.30   30.77 4.74 24.0 37.6  13.6
## lat      2 20 54.87 0.55  54.95   54.89 0.74 53.9 55.8   1.9
## city*    3 20 10.50 5.92  10.50   10.50 7.41  1.0 20.0  19.0
##        skew kurtosis   se
## long   0.17    -1.31 0.91
## lat   -0.20    -1.18 0.12
## city*  0.00    -1.38 1.32
```

``` r
describe(troops)
```

```
##            vars  n     mean        sd  median  trimmed      mad
## long          1 51    28.97      4.39    28.3    28.56     5.49
## lat           2 51    54.93      0.51    54.9    54.91     0.74
## survivors     3 51 91217.65 101718.61 40000.0 72880.49 50408.40
## direction*    4 51     1.51      0.50     2.0     1.51     0.00
## group         5 51     1.43      0.70     1.0     1.29     0.00
##               min      max    range  skew kurtosis       se
## long         24.0     37.7     13.7  0.64    -0.88     0.61
## lat          54.1     55.8      1.7  0.13    -1.29     0.07
## survivors  4000.0 340000.0 336000.0  1.31     0.48 14243.45
## direction*    1.0      2.0      1.0 -0.04    -2.04     0.07
## group         1.0      3.0      2.0  1.27     0.15     0.10
```

``` r
describe(temps)
```

```
##        vars n   mean    sd median trimmed   mad   min  max range
## long      1 9  30.63  4.30   29.2   30.63  4.15  25.3 37.6  12.3
## temp      2 9 -15.67 11.10  -20.0  -15.67 13.34 -30.0  0.0  30.0
## month*    3 9   1.89  0.78    2.0    1.89  1.48   1.0  3.0   2.0
## day       4 9  14.56  9.46   14.0   14.56 11.86   1.0 28.0  27.0
## date*     5 9   5.00  2.74    5.0    5.00  2.97   1.0  9.0   8.0
##        skew kurtosis   se
## long   0.34    -1.56 1.43
## temp   0.26    -1.66 3.70
## month* 0.15    -1.54 0.26
## day    0.06    -1.72 3.15
## date*  0.00    -1.60 0.91
```

``` r
temps$date <- as.Date(strptime(temps$date,"%d%b%Y"))
temps.nice <- temps %>%
  mutate(nice.label = paste0(temp, "°, ", month, ". ", day))

march.1812.plot.simple <- ggplot() +
  geom_path(data = troops, aes(x = long, y = lat, group = group, 
                               color = direction, size = survivors),
            lineend = "round") +
  geom_point(data = cities, aes(x = long, y = lat),
             color = "#DC5B44") +
  geom_text_repel(data = cities, aes(x = long, y = lat, label = city),
                  color = "#DC5B44") +
  scale_size(range = c(0.5, 10)) + 
  scale_colour_manual(values = c("#DFC17E", "#252523")) +
  guides(color = FALSE, size = FALSE) +
  theme_nothing()

march.1812.plot.simple
```

``` r
# Change the x-axis limits to match the simple map
temps.1812.plot <- ggplot(data = temps.nice, aes(x = long, y = temp)) +
  geom_line() +
  geom_label(aes(label = nice.label),
             size = 2.5) + 
  labs(x = NULL, y = "° Celsius") +
  scale_x_continuous(limits = ggplot_build(march.1812.plot.simple)$layout$panel_ranges[[1]]$x.range) +
  scale_y_continuous(position = "right") +
  coord_cartesian(ylim = c(-35, 5)) +  # Add some space above/below
  theme_bw() +
  theme(panel.grid.major.x = element_blank(),
        panel.grid.minor.x = element_blank(),
        panel.grid.minor.y = element_blank(),
        axis.text.x = element_blank(), axis.ticks = element_blank(),
        panel.border = element_blank())

temps.1812.plot
```

``` r
# Combine the two plots
both.1812.plot.simple <- gtable_rbind(ggplotGrob(march.1812.plot.simple),
                               ggplotGrob(temps.1812.plot))

both.1812.plot.simple
```

```
## TableGrob (32 x 13) "layout": 44 grobs
##     z         cells             name
## 1   0 ( 1-16, 1-13)       background
## 2   5 ( 8- 8, 6- 6)           spacer
## 3   7 ( 9- 9, 6- 6)           axis-l
## 4   3 (10-10, 6- 6)           spacer
## 5   6 ( 8- 8, 7- 7)           axis-t
## 6   1 ( 9- 9, 7- 7)            panel
## 7   9 (10-10, 7- 7)           axis-b
## 8   4 ( 8- 8, 8- 8)           spacer
## 9   8 ( 9- 9, 8- 8)           axis-r
## 10  2 (10-10, 8- 8)           spacer
## 11 10 ( 7- 7, 7- 7)           xlab-t
## 12 11 (11-11, 7- 7)           xlab-b
## 13 12 ( 9- 9, 5- 5)           ylab-l
## 14 13 ( 9- 9, 9- 9)           ylab-r
## 15 14 ( 9- 9,11-11)  guide-box-right
## 16 15 ( 9- 9, 3- 3)   guide-box-left
## 17 16 (13-13, 7- 7) guide-box-bottom
## 18 17 ( 5- 5, 7- 7)    guide-box-top
## 19 18 ( 9- 9, 7- 7) guide-box-inside
## 20 19 ( 4- 4, 7- 7)         subtitle
## 21 20 ( 3- 3, 7- 7)            title
## 22 21 (14-14, 7- 7)          caption
## 23  0 (17-32, 1-13)       background
## 24  5 (24-24, 6- 6)           spacer
## 25  7 (25-25, 6- 6)           axis-l
## 26  3 (26-26, 6- 6)           spacer
## 27  6 (24-24, 7- 7)           axis-t
## 28  1 (25-25, 7- 7)            panel
## 29  9 (26-26, 7- 7)           axis-b
## 30  4 (24-24, 8- 8)           spacer
## 31  8 (25-25, 8- 8)           axis-r
## 32  2 (26-26, 8- 8)           spacer
## 33 10 (23-23, 7- 7)           xlab-t
## 34 11 (27-27, 7- 7)           xlab-b
## 35 12 (25-25, 5- 5)           ylab-l
## 36 13 (25-25, 9- 9)           ylab-r
## 37 14 (25-25,11-11)  guide-box-right
## 38 15 (25-25, 3- 3)   guide-box-left
## 39 16 (29-29, 7- 7) guide-box-bottom
## 40 17 (21-21, 7- 7)    guide-box-top
## 41 18 (25-25, 7- 7) guide-box-inside
## 42 19 (20-20, 7- 7)         subtitle
## 43 20 (19-19, 7- 7)            title
## 44 21 (30-30, 7- 7)          caption
##                                            grob
## 1       zeroGrob[plot.background..zeroGrob.694]
## 2                                zeroGrob[NULL]
## 3           absoluteGrob[GRID.absoluteGrob.688]
## 4                                zeroGrob[NULL]
## 5                                zeroGrob[NULL]
## 6                      gTree[panel-1.gTree.686]
## 7           absoluteGrob[GRID.absoluteGrob.687]
## 8                                zeroGrob[NULL]
## 9                                zeroGrob[NULL]
## 10                               zeroGrob[NULL]
## 11                               zeroGrob[NULL]
## 12  zeroGrob[axis.title.x.bottom..zeroGrob.689]
## 13    zeroGrob[axis.title.y.left..zeroGrob.690]
## 14                               zeroGrob[NULL]
## 15                               zeroGrob[NULL]
## 16                               zeroGrob[NULL]
## 17                               zeroGrob[NULL]
## 18                               zeroGrob[NULL]
## 19                               zeroGrob[NULL]
## 20        zeroGrob[plot.subtitle..zeroGrob.692]
## 21           zeroGrob[plot.title..zeroGrob.691]
## 22         zeroGrob[plot.caption..zeroGrob.693]
## 23              rect[plot.background..rect.748]
## 24                               zeroGrob[NULL]
## 25                               zeroGrob[NULL]
## 26                               zeroGrob[NULL]
## 27                               zeroGrob[NULL]
## 28                     gTree[panel-1.gTree.736]
## 29          absoluteGrob[GRID.absoluteGrob.737]
## 30                               zeroGrob[NULL]
## 31          absoluteGrob[GRID.absoluteGrob.740]
## 32                               zeroGrob[NULL]
## 33                               zeroGrob[NULL]
## 34                               zeroGrob[NULL]
## 35                               zeroGrob[NULL]
## 36 titleGrob[axis.title.y.right..titleGrob.743]
## 37                               zeroGrob[NULL]
## 38                               zeroGrob[NULL]
## 39                               zeroGrob[NULL]
## 40                               zeroGrob[NULL]
## 41                               zeroGrob[NULL]
## 42        zeroGrob[plot.subtitle..zeroGrob.745]
## 43           zeroGrob[plot.title..zeroGrob.744]
## 44         zeroGrob[plot.caption..zeroGrob.746]
```

``` r
# Adjust panels
panels <- both.1812.plot.simple$layout$t[grep("panel", both.1812.plot.simple$layout$name)]

# Because this plot doesn't use coord_equal, 
# since it's not a map, we can use whatever relative numbers we want, like a 3:1 ratio
both.1812.plot.simple$heights[panels] <- unit(c(3, 1), "null")

grid::grid.newpage()
grid::grid.draw(both.1812.plot.simple)
```

<img src="data:image/png;base64,#descriptive_files/figure-html/unnamed-chunk-25-3.png" width="90%" style="display: block; margin: auto;" />
]
---

# More Accessible Resources

- [R Graph Gallery](https://r-graph-gallery.com/)
- [Learning Statistics with R](https://learningstatisticswithr.com/)
- .hand-pink[[Data Science for Psychologists](https://datascience4psych.github.io/DataScience4Psych/)]

---

# Wrapping Up...