Chapter 5 - Exploratory Data Analysis (EDA)

Last updated: 2020-11-21

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options(scipen=10000)
library(tidyverse)
library(flair)
library(nycflights13)
library(palmerpenguins)
library(gt)
library(skimr)
library(emo)
library(tidyquant)
library(lubridate)
library(magrittr)
theme_set(theme_tq())

Patterns

Variation: Best way to understand the pattern in a variable is to visualise the distribution of the variables values.
- Categorical: Bar chart
- Continuous: Histogram
- In both:
  - tall bars == common values of the variable
  - short bars == less common values of the variable
  - no bars == absense of that value in your data

Investigate Categories

ggplot(data = penguins) +
  geom_bar(aes(x = species))

ggplot(data = penguins) +
  geom_bar(aes(x = sex))

ggplot(data = penguins) +
  geom_bar(aes(x = island))

Investigate Continuous Data

ggplot(data = penguins) +
  geom_histogram(aes(x = bill_length_mm), 
                 binwidth = 0.6)

penguins %>% 
  count(cut_width(bill_length_mm, 0.6))


# A tibble: 42 x 2
   `cut_width(bill_length_mm, 0.6)`     n
   <fct>                            <int>
 1 [32.1,32.7]                          1
 2 (32.7,33.3]                          1
 3 (33.3,33.9]                          1
 4 (33.9,34.5]                          3
 5 (34.5,35.1]                          5
 6 (35.1,35.7]                          6
 7 (35.7,36.3]                         13
 8 (36.3,36.9]                          9
 9 (36.9,37.5]                          8
10 (37.5,38.1]                         15
# ... with 32 more rows

The data looks bimodal - i.e. there are 2 bumps in the distribution. If we recall we have 3 species, so let’s fill in the bars based on the species.

ggplot(data = penguins) +
  geom_histogram(aes(x = bill_length_mm, fill = species),
                 alpha = 0.5,
                 binwidth = 0.6) +
  scale_fill_tq()

penguins %>% 
  group_by(species) %>% 
  count(cut_width(bill_length_mm, 0.6))


# A tibble: 71 x 3
# Groups:   species [3]
   species `cut_width(bill_length_mm, 0.6)`     n
   <fct>   <fct>                            <int>
 1 Adelie  [32.1,32.7]                          1
 2 Adelie  (32.7,33.3]                          1
 3 Adelie  (33.3,33.9]                          1
 4 Adelie  (33.9,34.5]                          3
 5 Adelie  (34.5,35.1]                          5
 6 Adelie  (35.1,35.7]                          6
 7 Adelie  (35.7,36.3]                         13
 8 Adelie  (36.3,36.9]                          9
 9 Adelie  (36.9,37.5]                          8
10 Adelie  (37.5,38.1]                         15
# ... with 61 more rows

When we have overlapping histograms, the suggestion is to use geom_freqpoly() which uses lines instead of bars.

ggplot(data = penguins) +
  geom_freqpoly(aes(x = bill_length_mm, colour = species),
                binwidth = 0.6) +
  scale_fill_tq()

Looking at the plots ask some questions of your data:

Which values are the most common? Why?
Which values are rare? Why? Does that match your expectations?
Can you see any unusual patterns? What might explain them?

Clusters of similar values suggest that subgroups exist in your data. To understand the subgroups, ask:

How are the observations within each cluster similar to each other?
How are the observations in separate clusters different from each other?
How can you explain or describe the clusters?
Why might the appearance of clusters be misleading?

Investigate Unusual Values

Outliers are observations that don’t seem to gel nicely with the rest of the data.

Here the long y-axis indicates some outliers.

ggplot(data = diamonds) +
  # y is a var in the dataset! it measures one of the
  # dimensions of the diamond
  geom_histogram(aes(x = y), 
                 binwidth = 0.5)

To zoom in lets use coord_cartesian() with the ylim variable.

The coord_cartesian() also has an xlim to zoom into the x-axis.

ggplot(data = diamonds) +
  geom_histogram(mapping = aes(x = y), binwidth = 0.5) +
  # limit the y-axis to btw 0-50! Note to self: DON'T CONFUSE with the x-axis
  # which is named `y`!!
  coord_cartesian(ylim = c(0,50)) +
  labs(x = "The variable y in the diamonds dataset")

# zoom into the unusual values
(unusual <- diamonds %>% 
    filter(y < 3 | y > 20) %>% 
    arrange(y)) %>% 
  print(width = Inf) # print the whole dataset so we can see all cols

# A tibble: 9 x 10
  carat cut       color clarity depth table price     x     y     z
  <dbl> <ord>     <ord> <ord>   <dbl> <dbl> <int> <dbl> <dbl> <dbl>
1  1    Very Good H     VS2      63.3    53  5139  0      0    0   
2  1.14 Fair      G     VS1      57.5    67  6381  0      0    0   
3  1.56 Ideal     G     VS2      62.2    54 12800  0      0    0   
4  1.2  Premium   D     VVS1     62.1    59 15686  0      0    0   
5  2.25 Premium   H     SI2      62.8    59 18034  0      0    0   
6  0.71 Good      F     SI2      64.1    60  2130  0      0    0   
7  0.71 Good      F     SI2      64.1    60  2130  0      0    0   
8  0.51 Ideal     E     VS1      61.8    55  2075  5.15  31.8  5.12
9  2    Premium   H     SI2      58.9    57 12210  8.09  58.9  8.06

The y feature in the diamonds dataset measures a dimension (width, height, depth) in millimeters. A dimension of 0 mm is incorrect, and a dimension of ~32mm or ~59mm is also incorrect. Those diamonds will cost an 💪 and a 🦵!

In practice it is best to do analysis with and without your outliers.

No difference with or without, probably safe to remove them
Big difference with vs without, need to investigate why they are there before any action.
In both cases, disclose the action taken in your analysis.

Exercises

Explore the distribution of each of the x, y, and z variables in diamonds. What do you learn? Think about a diamond and how you might decide which dimension is the length, width, and depth.

ggplot(data = diamonds) +
  geom_histogram(aes(x=x),
                 binwidth = 0.5)

filter(diamonds, x == max(x)) %>% 
  print(width = Inf)

# A tibble: 1 x 10
  carat cut   color clarity depth table price     x     y     z
  <dbl> <ord> <ord> <ord>   <dbl> <dbl> <int> <dbl> <dbl> <dbl>
1  5.01 Fair  J     I1       65.5    59 18018  10.7  10.5  6.98

filter(diamonds, x == min(x)) %>% 
  print(width = Inf)

# A tibble: 8 x 10
  carat cut       color clarity depth table price     x     y     z
  <dbl> <ord>     <ord> <ord>   <dbl> <dbl> <int> <dbl> <dbl> <dbl>
1  1.07 Ideal     F     SI2      61.6    56  4954     0  6.62     0
2  1    Very Good H     VS2      63.3    53  5139     0  0        0
3  1.14 Fair      G     VS1      57.5    67  6381     0  0        0
4  1.56 Ideal     G     VS2      62.2    54 12800     0  0        0
5  1.2  Premium   D     VVS1     62.1    59 15686     0  0        0
6  2.25 Premium   H     SI2      62.8    59 18034     0  0        0
7  0.71 Good      F     SI2      64.1    60  2130     0  0        0
8  0.71 Good      F     SI2      64.1    60  2130     0  0        0

diamonds %>% 
  filter(x != 0) %>% 
  filter(x == min(x)) %>% 
  print(width = Inf)

# A tibble: 2 x 10
  carat cut     color clarity depth table price     x     y     z
  <dbl> <ord>   <ord> <ord>   <dbl> <dbl> <int> <dbl> <dbl> <dbl>
1   0.2 Premium F     VS2      62.6    59   367  3.73  3.71  2.33
2   0.2 Premium D     VS2      62.3    60   367  3.73  3.68  2.31

ggplot(data = diamonds) +
  geom_histogram(aes(x = x), binwidth = 0.5) +
  coord_cartesian(xlim = c(0, 1),
                  ylim = c(0, 10))

ggplot(data = diamonds) +
  geom_histogram(aes(x = y),
                 binwidth = 0.5)

filter(diamonds, y == max(y)) %>% 
  print(width = Inf)

# A tibble: 1 x 10
  carat cut     color clarity depth table price     x     y     z
  <dbl> <ord>   <ord> <ord>   <dbl> <dbl> <int> <dbl> <dbl> <dbl>
1     2 Premium H     SI2      58.9    57 12210  8.09  58.9  8.06

filter(diamonds, y == min(y)) %>% 
  print(width = Inf)

# A tibble: 7 x 10
  carat cut       color clarity depth table price     x     y     z
  <dbl> <ord>     <ord> <ord>   <dbl> <dbl> <int> <dbl> <dbl> <dbl>
1  1    Very Good H     VS2      63.3    53  5139     0     0     0
2  1.14 Fair      G     VS1      57.5    67  6381     0     0     0
3  1.56 Ideal     G     VS2      62.2    54 12800     0     0     0
4  1.2  Premium   D     VVS1     62.1    59 15686     0     0     0
5  2.25 Premium   H     SI2      62.8    59 18034     0     0     0
6  0.71 Good      F     SI2      64.1    60  2130     0     0     0
7  0.71 Good      F     SI2      64.1    60  2130     0     0     0

diamonds %>% 
  filter(y != 0) %>% 
  filter(y == min(y)) %>% 
  print(width = Inf)

# A tibble: 1 x 10
  carat cut     color clarity depth table price     x     y     z
  <dbl> <ord>   <ord> <ord>   <dbl> <dbl> <int> <dbl> <dbl> <dbl>
1   0.2 Premium D     VS2      62.3    60   367  3.73  3.68  2.31

diamonds %>% 
  filter(y < 10) %>% 
  filter(y == max(y)) %>% 
  print(width = Inf)

# A tibble: 2 x 10
  carat cut       color clarity depth table price     x     y     z
  <dbl> <ord>     <ord> <ord>   <dbl> <dbl> <int> <dbl> <dbl> <dbl>
1  4.01 Premium   J     I1       62.5    62 15223  10.0  9.94  6.24
2  4    Very Good I     I1       63.3    58 15984  10.0  9.94  6.31

ggplot(data = diamonds) +
  geom_histogram(aes(x = z),
                 binwidth = 0.5)

filter(diamonds, z == max(z)) %>% 
  print(width = Inf)

# A tibble: 1 x 10
  carat cut       color clarity depth table price     x     y     z
  <dbl> <ord>     <ord> <ord>   <dbl> <dbl> <int> <dbl> <dbl> <dbl>
1  0.51 Very Good E     VS1      61.8  54.7  1970  5.12  5.15  31.8

filter(diamonds, z == min(z)) %>% 
  print(width = Inf)

# A tibble: 20 x 10
   carat cut       color clarity depth table price     x     y     z
   <dbl> <ord>     <ord> <ord>   <dbl> <dbl> <int> <dbl> <dbl> <dbl>
 1  1    Premium   G     SI2      59.1    59  3142  6.55  6.48     0
 2  1.01 Premium   H     I1       58.1    59  3167  6.66  6.6      0
 3  1.1  Premium   G     SI2      63      59  3696  6.5   6.47     0
 4  1.01 Premium   F     SI2      59.2    58  3837  6.5   6.47     0
 5  1.5  Good      G     I1       64      61  4731  7.15  7.04     0
 6  1.07 Ideal     F     SI2      61.6    56  4954  0     6.62     0
 7  1    Very Good H     VS2      63.3    53  5139  0     0        0
 8  1.15 Ideal     G     VS2      59.2    56  5564  6.88  6.83     0
 9  1.14 Fair      G     VS1      57.5    67  6381  0     0        0
10  2.18 Premium   H     SI2      59.4    61 12631  8.49  8.45     0
11  1.56 Ideal     G     VS2      62.2    54 12800  0     0        0
12  2.25 Premium   I     SI1      61.3    58 15397  8.52  8.42     0
13  1.2  Premium   D     VVS1     62.1    59 15686  0     0        0
14  2.2  Premium   H     SI1      61.2    59 17265  8.42  8.37     0
15  2.25 Premium   H     SI2      62.8    59 18034  0     0        0
16  2.02 Premium   H     VS2      62.7    53 18207  8.02  7.95     0
17  2.8  Good      G     SI2      63.8    58 18788  8.9   8.85     0
18  0.71 Good      F     SI2      64.1    60  2130  0     0        0
19  0.71 Good      F     SI2      64.1    60  2130  0     0        0
20  1.12 Premium   G     I1       60.4    59  2383  6.71  6.67     0

unusual_z <- diamonds %>% 
  filter(z < 2 | z > 10)

ggplot(data = unusual_z) +
  geom_histogram(aes(x = z), binwidth = 0.5) +
  coord_cartesian(xlim = c(0, 35),
                  ylim = c(0, 25))

diamonds %>% 
  select(x, y, z) %>% 
  filter(x != 0,
         y != 0, 
         z != 0) %>% 
  skim()

Data summary
Name	Piped data
Number of rows	53920
Number of columns	3
_______________________
Column type frequency:
numeric	3
________________________
Group variables	None

Variable type: numeric

skim_variable	complete_rate	mean	sd	p0	p25	p50	p75	p100	hist
x	1	5.73	1.12	3.73	4.71	5.70	6.54	10.74	▇▇▅▁▁
y	1	5.73	1.14	3.68	4.72	5.71	6.54	58.90	▇▁▁▁▁
z	1	3.54	0.70	1.07	2.91	3.53	4.04	31.80	▇▁▁▁▁

So it turns out a diamond has a table, width and depth.

Credit: https://www.diamonds.pro/

x and y could be depth or width - there’s not much difference between the 2 values. The z is likely to be the table since it is smaller.

But looking at the ?diamonds help page x = length, y = width and z = depth, and there is actually a table variable that is a relative measure 🤷, so there goes my “theory” 🤦.

Explore the distribution of price. Do you discover anything unusual or surprising? (Hint: Carefully think about the binwidth and make sure you try a wide range of values.)

ggplot(data = diamonds) +
  geom_histogram(aes(x = price), bins = 20)

ggplot(data = diamonds) +
  geom_histogram(aes(x = price), binwidth = 1000)

ggplot(data = diamonds) +
  geom_histogram(aes(x = price), binwidth = 200)

ggplot(data = diamonds) +
  geom_histogram(aes(x = price), binwidth = 500)

diamonds %>% 
  select(price) %>% 
  skim()

Data summary
Name	Piped data
Number of rows	53940
Number of columns	1
_______________________
Column type frequency:
numeric	1
________________________
Group variables	None

Variable type: numeric

skim_variable	n_missing	complete_rate	mean	sd	p0	p25	p50	p75	p100	hist
price	0	1	3932.8	3989.44	326	950	2401	5324.25	18823	▇▂▁▁▁

diamonds %>% 
  filter(price == 326 |
           price == 18823) %>% 
  gt()

carat	cut	color	clarity	depth	table	price	x	y	z
0.23	Ideal	E	SI2	61.5	55	326	3.95	3.98	2.43
0.21	Premium	E	SI1	59.8	61	326	3.89	3.84	2.31
2.29	Premium	I	VS2	60.8	60	18823	8.50	8.47	5.16

diamonds %>% 
  arrange(-carat) %>% 
  head(10) %>% 
  gt()

carat	cut	color	clarity	depth	table	price	x	y	z
5.01	Fair	J	I1	65.5	59	18018	10.74	10.54	6.98
4.50	Fair	J	I1	65.8	58	18531	10.23	10.16	6.72
4.13	Fair	H	I1	64.8	61	17329	10.00	9.85	6.43
4.01	Premium	I	I1	61.0	61	15223	10.14	10.10	6.17
4.01	Premium	J	I1	62.5	62	15223	10.02	9.94	6.24
4.00	Very Good	I	I1	63.3	58	15984	10.01	9.94	6.31
3.67	Premium	I	I1	62.4	56	16193	9.86	9.81	6.13
3.65	Fair	H	I1	67.1	53	11668	9.53	9.48	6.38
3.51	Premium	J	VS2	62.5	59	18701	9.66	9.63	6.03
3.50	Ideal	H	I1	62.8	57	12587	9.65	9.59	6.03

The prices range from $326 to $18823. The carat of the high priced $18823 diamond is 2.29. There are other diamonds where the carat is bigger, and the cut is also Premium yet the price is lower. So it seems diamond pricing considers many factors, and could also be determined on who is doing the selling.

How many diamonds are 0.99 carat? How many are 1 carat? What do you think is the cause of the difference?

diamonds %>%   
  filter(
         carat == 1 |
         carat == 0.99
        ) %>%  
  count(carat, sort = TRUE)

# A tibble: 2 x 2
  carat     n
  <dbl> <int>
1  1     1558
2  0.99    23

sample_test <- diamonds %>% 
  filter(carat == 1 |
         carat == 0.99) %>% 
  group_by(carat) %>% 
  arrange(carat, price)

sample_test %>%   
  sample_n(20) %>% 
  gt()

cut	color	clarity	depth	table	price	x	y	z
0.99
Good	F	SI2	63.3	54	4052	6.36	6.43	4.05
Premium	F	VS2	62.6	55	5893	6.50	6.35	4.02
Very Good	F	SI2	61.2	56	4852	6.40	6.45	3.93
Fair	I	SI1	60.7	66	3337	6.42	6.34	3.87
Very Good	D	SI1	62.6	57	5671	6.34	6.37	3.98
Ideal	F	SI1	62.8	57	5728	6.30	6.38	3.98
Ideal	H	SI1	61.1	56	5287	6.44	6.47	3.94
Ideal	F	VS1	61.0	55	5947	6.46	6.52	3.96
Very Good	F	SI1	62.5	58	5112	6.36	6.38	3.98
Very Good	G	SI1	62.8	56	4863	6.34	6.36	3.99
Ideal	F	SI1	62.1	58	6038	6.33	6.40	3.95
Fair	I	SI2	68.1	56	2811	6.21	6.06	4.18
Fair	H	VS2	71.6	57	3593	5.94	5.80	4.20
Very Good	J	SI1	60.3	57	4002	6.44	6.49	3.90
Very Good	F	VS2	61.8	57	6094	6.37	6.39	3.94
Ideal	I	SI1	61.8	57	4763	6.40	6.42	3.96
Very Good	E	SI2	61.8	59	4780	6.30	6.33	3.90
Premium	F	SI2	60.6	61	4075	6.45	6.38	3.89
Very Good	D	SI2	62.5	57	4993	6.30	6.34	3.95
Fair	J	I1	73.6	60	1789	6.01	5.80	4.35
1
Very Good	H	SI1	62.1	58	5247	6.44	6.45	4.00
Very Good	D	SI1	60.1	60	4697	6.47	6.55	3.91
Premium	H	SI1	62.7	60	4469	6.30	6.24	3.93
Ideal	E	SI1	61.9	56	5458	6.37	6.45	3.97
Premium	E	VS2	63.0	58	7168	6.25	6.22	3.93
Good	H	VS1	61.8	61	5219	6.40	6.31	3.93
Very Good	D	IF	63.3	59	16073	6.37	6.33	4.02
Good	D	SI2	64.0	54	3304	6.29	6.24	4.01
Premium	H	VS2	61.5	61	5000	6.45	6.40	3.95
Fair	F	SI1	64.8	59	5292	6.29	6.24	4.06
Ideal	E	SI2	62.0	57	4623	6.37	6.41	3.96
Premium	D	SI1	61.5	60	5488	6.38	6.34	3.91
Premium	G	VS1	60.6	59	6115	6.48	6.42	3.91
Very Good	I	SI1	58.5	61	4649	6.51	6.55	3.82
Premium	D	SI2	61.6	58	4626	6.45	6.37	3.95
Premium	H	VS2	62.6	59	5320	6.37	6.31	3.97
Premium	H	SI2	62.8	60	3080	6.46	6.34	4.02
Ideal	D	SI1	63.0	56	4592	6.33	6.28	3.97
Premium	F	SI1	59.7	60	4939	6.51	6.48	3.88
Ideal	G	VS2	58.9	60	6235	6.53	6.58	3.86

sample_test %>% 
  select(cut, price) %>% 
  skim()

Data summary
Name	Piped data
Number of rows	1581
Number of columns	3
_______________________
Column type frequency:
factor	1
numeric	1
________________________
Group variables	carat

Variable type: factor

skim_variable	carat	n_missing	complete_rate	ordered	n_unique	top_counts
cut	0.99	0	1	TRUE	5	Ver: 8, Fai: 7, Ide: 5, Pre: 2
cut	1.00	0	1	TRUE	5	Pre: 462, Ver: 389, Goo: 333, Ide: 208

Variable type: numeric

skim_variable	carat	n_missing	complete_rate	mean	sd	p0	p25	p50	p75	p100	hist
price	0.99	0	1	4406.17	1318.99	1789	3465	4780	5479	6094	▂▅▅▇▇
price	1.00	0	1	5241.59	1603.94	1681	4155	4864	6073	16469	▇▇▁▁▁

The one carat diamonds are gigher in price and hugely so in the upper range.

Compare and contrast coord_cartesian() vs xlim() or ylim() when zooming in on a histogram. What happens if you leave binwidth unset? What happens if you try and zoom so only half a bar shows?
```
ggplot(data = diamonds) +
  geom_histogram(mapping = aes(x = y), binwidth = 0.5) +
  # limit the y-axis to btw 0-50! 
  # Note to self: DON'T CONFUSE with the x-axis
  # which is named `y`!!
  coord_cartesian(ylim = c(0,50)) +
  labs(x = "The variable y in the diamonds dataset")
```
```
ggplot(data = diamonds) +
  geom_histogram(mapping = aes(x = y), binwidth = 0.5) +
  ylim(c(0,50)) +
  labs(x = "The variable y in the diamonds dataset")
```
```
ggplot(data = diamonds) +
  geom_histogram(mapping = aes(x = y)) +
  ylim(c(0,50)) +
  labs(x = "The variable y in the diamonds dataset")    
```
Documentation reads: “This is a shortcut for supplying the limits argument to the individual scales. Note that, by default, any values outside the limits will be replaced with NA.” So ylim() and xlim() replace values outside the limit with NULL values resulting in the histogram being quite different to what we have when we use coord_cartesian().

If we don’t supply a binwidth ggplot defaults the number of bins to display to 30, and hence implicitly picks a binwidth for us.

Leveraging Missing Values

When you have weird values for variables, e.g. the ~59 mm for y, you may be tempted to drop these values and carry on. Often though a dataset is not nice and neat with all it’s weird values in a few observations! Usually the weird values are spread over multiple observations!

diamonds %>% 
  mutate(row_num = row_number()) %>% 
  filter(x==0 | y==0 | z==0) %>% 
  gt()

carat	cut	color	clarity	depth	table	price	x	y	row_num
1.00	Premium	G	SI2	59.1	59	3142	6.55	6.48	2208
1.01	Premium	H	I1	58.1	59	3167	6.66	6.60	2315
1.10	Premium	G	SI2	63.0	59	3696	6.50	6.47	4792
1.01	Premium	F	SI2	59.2	58	3837	6.50	6.47	5472
1.50	Good	G	I1	64.0	61	4731	7.15	7.04	10168
1.07	Ideal	F	SI2	61.6	56	4954	0.00	6.62	11183
1.00	Very Good	H	VS2	63.3	53	5139	0.00	0.00	11964
1.15	Ideal	G	VS2	59.2	56	5564	6.88	6.83	13602
1.14	Fair	G	VS1	57.5	67	6381	0.00	0.00	15952
2.18	Premium	H	SI2	59.4	61	12631	8.49	8.45	24395
1.56	Ideal	G	VS2	62.2	54	12800	0.00	0.00	24521
2.25	Premium	I	SI1	61.3	58	15397	8.52	8.42	26124
1.20	Premium	D	VVS1	62.1	59	15686	0.00	0.00	26244
2.20	Premium	H	SI1	61.2	59	17265	8.42	8.37	27113
2.25	Premium	H	SI2	62.8	59	18034	0.00	0.00	27430
2.02	Premium	H	VS2	62.7	53	18207	8.02	7.95	27504
2.80	Good	G	SI2	63.8	58	18788	8.90	8.85	27740
0.71	Good	F	SI2	64.1	60	2130	0.00	0.00	49557
0.71	Good	F	SI2	64.1	60	2130	0.00	0.00	49558
1.12	Premium	G	I1	60.4	59	2383	6.71	6.67	51507

Throwing away all observations where a variable has weird values can result in a serious shrinking of your dataset.

The authors suggest that instead of throwing away the observations with weird values, rather replace them with missing values. This may sound strange since many of us have probably heard that missing values shouldn’t be used in data science! It’s usually a problem to be fixed!

But in EDA it may provide insight to either force weird values to be NA, or to investigate how missing values differ from non-missing values.

Exercises

What happens to missing values in a histogram? What happens to missing values in a bar chart? Why is there a difference?

Missing values in bar charts are plotted as a category. Missing values in a histogram are dropped.

I guess that it is easy to create one category for missing and lump all the missing variable observations into that count.

For a continuous variable where data is binned however how do you show that on a graph? The limits are continuous values e.g. from 0 - 100, -100 - 100 etc. Where should the count of NAs go on the x-axis, and y-axis given that the range that NA could represent is any number in the range of the continuous values we have for a variable.

What does na.rm = TRUE do in mean() and sum()?

The NAs are removed and then the mean() or sum() is computed on the remaining non-NA values.

c(1,2,NA,3,4,NA,5) %>% 
  mean(na.rm=TRUE)

[1] 3

# (1+2+3+4+5) / 5 = 15 / 5 = 3

c(1,2,NA,3,4,NA,5) %>% 
  sum(na.rm=TRUE)

[1] 15

# (1+2+3+4+5)

Covariation

Covariance is how two or more variables change together in some way. Visualisation is good for noticing these relationships.

Categorical and Continuous

Density Freq Polygons

We previously used a geom_freqpoly() for this, which doesn’t provide much use if groups are unbalanced. If one group is much smaller than the others it’s hard to see differences.

We can display density on the y-axis instead of a count. ..density.. is a count that is standardised so that the area under each curve is 1.

ggplot(penguins, aes(x = body_mass_g)) +
  geom_freqpoly(aes(colour = species), binwidth = 200)

ggplot(penguins, aes(x = body_mass_g, y = ..density..)) +
  geom_freqpoly(aes(colour = species), binwidth = 200)

ggplot(penguins, aes(x = bill_length_mm)) +
  geom_freqpoly(aes(colour = species), binwidth = 5)

ggplot(penguins, aes(x = bill_length_mm, y = ..density..)) +
  geom_freqpoly(aes(colour = species), binwidth = 5)

ggplot(penguins, aes(x = bill_depth_mm)) +
  geom_freqpoly(aes(colour = species), binwidth = 5)

ggplot(penguins, aes(x = bill_depth_mm, y = ..density..)) +
  geom_freqpoly(aes(colour = species), binwidth = 5)

ggplot(penguins, aes(x = flipper_length_mm)) +
  geom_freqpoly(aes(colour = species), binwidth = 5)

ggplot(penguins, aes(x = flipper_length_mm, y = ..density..)) +
  geom_freqpoly(aes(colour = species), binwidth = 5)

Boxplots

Verbatim from the book:

A box that stretches from the 25th percentile of the distribution to the 75th percentile, a distance known as the interquartile range (IQR). In the middle of the box is a line that displays the median, i.e. 50th percentile, of the distribution. These three lines give you a sense of the spread of the distribution and whether or not the distribution is symmetric about the median or skewed to one side.
Visual points that display observations that fall more than 1.5 times the IQR from either edge of the box. These outlying points are unusual so are plotted individually.
A line (or whisker) that extends from each end of the box and goes to the
farthest non-outlier point in the distribution.

Credit: R for Data Science

ggplot(penguins, aes(x = species, y = body_mass_g)) +
  geom_boxplot()

ggplot(penguins, aes(x = body_mass_g, y = species)) +
  geom_boxplot()

ggplot(penguins, aes(x = bill_length_mm, y = species)) +
  geom_boxplot()

ggplot(penguins, aes(x = flipper_length_mm,
                     y = species)) +
  geom_boxplot()

# the reorder does not seem to be working for me
ggplot(penguins, aes(y = bill_depth_mm, 
                     x = reorder(species,
                                 bill_depth_mm,
                                 FUN = median))) +
  geom_boxplot()

Exercises

Use what you’ve learned to improve the visualisation of the departure times of cancelled vs. non-cancelled flights.

nycflights13::flights %>% 
  mutate(cancelled = is.na(dep_time),
         sched_hour = sched_dep_time %/% 100,
         sched_min = sched_dep_time %/% 100,
         sched_dep_time = sched_hour + sched_min / 60) %>% 
  ggplot(aes(x = sched_dep_time, y = cancelled)) +
  geom_boxplot()

What variable in the diamonds dataset is most important for predicting the price of a diamond? How is that variable correlated with cut? Why does the combination of those two relationships lead to lower quality diamonds being more expensive?

ggplot(diamonds, aes(x = carat, y = price)) +
  geom_point()

ggplot(diamonds, aes(x = reorder(cut, price,
                                 median), y = price)) +
  geom_boxplot()

ggplot(diamonds, aes(x = reorder(color, price,
                                 median), y = price)) +
  geom_boxplot()

ggplot(diamonds, aes(x = reorder(clarity,
                                 price, median),
                     y = price)) +
  geom_boxplot()

ggplot(diamonds, aes(x = reorder(cut, carat,
                                 median), 
                     y = carat)) +
  geom_boxplot()

ggplot(diamonds, aes(x = reorder(color, carat,
                                 median), y = carat)) +
  geom_boxplot()

ggplot(diamonds, aes(x = reorder(clarity, carat,
                                 median), y = carat)) +
  geom_boxplot()

cor(diamonds$price, diamonds$carat)

[1] 0.9215913

They say that there are 4 characteristics of diamonds that come into play when considering the quality - Carat Weight, Cut, Colour and Clarity. It looks like carat, is most correlated with the price, and there are quite a few low quality for the Cut of the diamonds that have a big carat weight.

Install the ggstance package, and create a horizontal boxplot. How does this compare to using coord_flip()?

There is no longer a need to use the ggstance 📦 as this functionality is provided in ggplot2 since version 3.3.0.

One problem with boxplots is that they were developed in an era of much smaller datasets and tend to display a prohibitively large number of “outlying values”. One approach to remedy this problem is the letter value plot. Install the lvplot package, and try using geom_lv() to display the distribution of price vs cut. What do you learn? How do you interpret the plots?

library(lvplot)
ggplot(diamonds, aes(reorder(cut,
                             price, median), price)) +
  geom_boxplot() +
  labs(x = "Cut",
       y = "Price")

ggplot(diamonds, aes(reorder(cut, price,
                             median), price)) +
  geom_lv(outlier.colour = "darkgreen") +
  labs(x = "Cut", y = "Price")

ggplot(diamonds, aes(reorder(cut, price,
                             median), price)) +
  geom_lv(aes(fill = ..LV..), outlier.colour = "darkgreen",
          k = 6) +
  labs(x = "Cut", y = "Price") +
  scale_fill_lv()

The plots are an extension of the boxplots and allows you to see the distribution better especially for large datasets. More information on the plot can be found here.

Compare and contrast geom_violin() with a facetted geom_histogram(), or a coloured geom_freqpoly(). What are the pros and cons of each method?

ggplot(penguins, aes(x = species, body_mass_g)) +
  geom_violin(aes(colour = species))

ggplot(penguins, aes(x = body_mass_g)) +
  geom_histogram() +
  facet_wrap(~ species,
             ncol = 1,
             scales = "free_y")

ggplot(penguins, aes(x = body_mass_g, y = ..density..)) +
  geom_freqpoly(aes(colour = species), binwidth = 200)

They’re all pretty similar, but I think the geom_freqpoly() and geom_violin() use density and hence is harder to interpret.

If you have a small dataset, it’s sometimes useful to use geom_jitter() to see the relationship between a continuous and categorical variable. The ggbeeswarm package provides a number of methods similar to geom_jitter(). List them and briefly describe what each one does.
```
library(ggbeeswarm)
ggplot(penguins, aes(x = species, body_mass_g)) +
    geom_quasirandom()
```
```
ggplot(penguins, aes(x = species, body_mass_g)) +
    geom_beeswarm()
```
```
ggplot(penguins, aes(x = species, bill_depth_mm)) +
    geom_beeswarm()
```
```
ggplot(diamonds, aes(x = reorder(cut, price,
                                median), y = price)) +
      geom_quasirandom()
```
The ggbeeswarm 📦 produces column scatter plots and has 2 functions, one geom_quasirandom() reduces the overplotting and also helps visualise the density at each point.

The other is geom_beeswarm() and does a point-size offset.

Two Categorical Variables

For two catgories we need to count the number of observations in each combination of the 2 categories.

We can use geom_count() for this, and the size of each dot tells you how many observations fell in that category.

ggplot(penguins) +
  geom_count(aes(x = species, y = island))

penguins %>% 
  count(species, island, sort = TRUE)


# A tibble: 5 x 3
  species   island        n
  <fct>     <fct>     <int>
1 Gentoo    Biscoe      124
2 Chinstrap Dream        68
3 Adelie    Dream        56
4 Adelie    Torgersen    52
5 Adelie    Biscoe       44

ggplot(penguins) +
  geom_count(aes(x = species, y = sex))

penguins %>% 
  count(species, sex, sort = TRUE)


# A tibble: 8 x 3
  species   sex        n
  <fct>     <fct>  <int>
1 Adelie    female    73
2 Adelie    male      73
3 Gentoo    male      61
4 Gentoo    female    58
5 Chinstrap female    34
6 Chinstrap male      34
7 Adelie    <NA>       6
8 Gentoo    <NA>       5

We can see that the largest number of observations were of the Gentoo species, on the island Biscoe.

The male / female splits look roughly equal and is confirmed using a count().

Another way is to use the geom_tile() function but here you must first compute the count, and then use the count as a fill.

penguins %>% 
  count(species, island) %>% 
  ggplot(aes(x = species, y = island)) +
  geom_tile(aes(fill = n ))

penguins %>% 
  count(species, island, sort = TRUE)


# A tibble: 5 x 3
  species   island        n
  <fct>     <fct>     <int>
1 Gentoo    Biscoe      124
2 Chinstrap Dream        68
3 Adelie    Dream        56
4 Adelie    Torgersen    52
5 Adelie    Biscoe       44

penguins %>% 
  count(species, sex) %>% 
  ggplot(aes(x = species, y = sex)) +
  geom_tile(aes(fill = n ))

penguins %>% 
  count(species, sex, sort = TRUE)


# A tibble: 8 x 3
  species   sex        n
  <fct>     <fct>  <int>
1 Adelie    female    73
2 Adelie    male      73
3 Gentoo    male      61
4 Gentoo    female    58
5 Chinstrap female    34
6 Chinstrap male      34
7 Adelie    <NA>       6
8 Gentoo    <NA>       5

We see that the colouring for the tiled graph of species and sex show again that the data is quite balanced in terms of males vs females for each species. The NA values also only appear for Adelie and Gentoo.

Exercises

How could you rescale the count dataset above to more clearly show the distribution of cut within colour, or colour within cut?

Original:

diamonds %>% 
  count(color, cut) %>%  
  ggplot(mapping = aes(x = color, y = cut)) +
    geom_tile(mapping = aes(fill = n))

diamonds %>% 
  add_count(color, cut) %>%  
  group_by(color) %>% 
  mutate(perc = n / sum(n) * 100) %>% 
  ggplot(mapping = aes(x = color, y = cut)) +
    geom_tile(mapping = aes(fill = perc)) +
  scale_fill_gradient(low = "#999999",
                      high = "gold") +
  guides(fill = guide_colourbar(barwidth = 10, 
                                barheight = 0.5))

diamonds %>% 
  add_count(cut, color) %>%  
  group_by(cut) %>% 
  mutate(perc = n / sum(n) * 100) %>% 
  ggplot(mapping = aes(x = cut, y = color)) +
    geom_tile(mapping = aes(fill = perc)) +
  scale_fill_gradient(low = "#F4EDCA",
                      high = "#293352") +
  guides(fill = guide_colourbar(barwidth = 10, 
                                barheight = 0.5))

Maybe use a percentage within each color.

Use geom_tile() together with dplyr to explore how average flight delays vary by destination and month of year. What makes the plot difficult to read? How could you improve it?

flights %>% 
  group_by(dest, month) %>% 
  mutate(avg_delay = mean(arr_delay, na.rm = TRUE)) %>% 
  ggplot(aes(x = month, y = dest)) +
    geom_tile(mapping = aes(fill = avg_delay)) +
    scale_fill_gradient(low = "#F4EDCA",
                        high = "#293352") +
    guides(fill = guide_colourbar(barwidth = 10, 
                                  barheight = 0.5))

flights %>% 
  mutate(dest = fct_lump(dest, 10)) %>% 
  group_by(dest, month) %>% 
  mutate(avg_delay = mean(arr_delay, na.rm = TRUE)) %>% 
  ggplot(aes(x = month, y = dest)) +
    geom_tile(mapping = aes(fill = avg_delay)) +
    scale_fill_gradient(low = "#F4EDCA",
                        high = "#293352") +
    guides(fill = guide_colourbar(barwidth = 10, 
                                  barheight = 0.5))

The missing values for some months is an issue. There are many destinations. It will be better to sort it by the highest number of flights and highest average delay, and then maybe also lump the lower ones into a single category with something like fct_lump() which we will learn about later. For now just see fct_lump(var, n = 8) as lumping together factors that are less frequent. Here we keep the most frequent or top 8 of the variable var. In the example above we kept the 10 most frequent destinations, and lumped the rest into Other.

Why is it slightly better to use aes(x = color, y = cut) rather than aes(x = cut, y = color) in the example above?

diamonds %>% 
  count(color, cut) %>%  
  ggplot(mapping = aes(x = color, y = cut)) +
    geom_tile(mapping = aes(fill = n)) +
    scale_fill_gradient(low = "#F4EDCA",
                            high = "#293352") +
    guides(fill = guide_colourbar(barwidth = 10, 
                                      barheight = 0.5))

diamonds %>% 
  count(cut, color) %>%  
  ggplot(mapping = aes(x = cut, y = color)) +
    geom_tile(mapping = aes(fill = n)) +
    scale_fill_gradient(low = "#F4EDCA",
                            high = "#293352") +
    guides(fill = guide_colourbar(barwidth = 10, 
                                      barheight = 0.5))

For me it is easier to read. I can say in the color D there is approximately 200 observations of the cut Fair, ~ 500 observations of the cut Good etc. I.e. there is more variation in the cut within each color than the other way around if that makes sense.

If I read the color in each cut, there’s not much variation, e.g. for the Fair cut ~200 lie in every color.

Two Continuous Variables

One way we have already seen is the geom_point(). When you have lots of data you can use an alpha value to prevent the overplotting, and see you data more clearly.

ggplot(penguins) +
  geom_point(aes(x = bill_length_mm,
                 y = bill_depth_mm))

ggplot(penguins) +
  geom_point(aes(x = bill_length_mm,
                 y = bill_depth_mm,
                 colour = species))

It seems there is an upward trend but it is hard to make it out.

ggplot(penguins) +
  geom_point(aes(x = bill_length_mm,
                 y = bill_depth_mm,
                 colour = species))

Ah that’s much better, when the data is segmented by species we can see a trend.

With large datasets you can also bin your data and use geom_bin2d() and geom_hex().

Or alternately you can bin one variable to act as though it is categorical e.g. using cut_width(), then we can use one of the visualisations suitable for a categorical and continuous combination.

Exercises

Instead of summarising the conditional distribution with a boxplot, you could use a frequency polygon. What do you need to consider when using cut_width() vs cut_number()? How does that impact a visualisation of the 2d distribution of carat and price?

smaller <- diamonds %>%
  filter(carat < 3)

ggplot(data = smaller, mapping = aes(colour = 
                                       cut_width(carat, 
                                               0.4), 
                                     x = price)) + 
  geom_freqpoly()

ggplot(data = smaller, mapping = aes(colour = 
                                       cut_number(carat, 
                                               6), 
                                     x = price)) + 
  geom_freqpoly()

ggplot(data = diamonds, mapping = aes(colour = 
                                       cut_width(carat, 
                                               0.8), 
                                     x = price)) + 
  geom_freqpoly()

ggplot(data = diamonds, mapping = aes(colour = 
                                       cut_number(carat, 
                                               6), 
                                     x = price)) + 
  geom_freqpoly()

cut_width() we say what we’d like the binwidth of the variable to be, and the number of bins will be calculated. cut_number() we say what we’d like as a bin number, and the binwidth of each bin is calculated.

Visualise the distribution of carat, partitioned by price.

ggplot(diamonds,
       aes(x = carat, y = price)) +
  geom_boxplot(aes(group = cut_number(price, 10)))

How does the price distribution of very large diamonds compare to small diamonds? Is it as you expect, or does it surprise you?

Heavier diamonds cost more than lighter diamonds. This does not surprise me, but as you see diamonds in the range 3-5 all get a big price tag, so there is more to the pricing mechanism than just carat weight and I would guess this is where the 4C’s come in. Heavier diamonds attract a big price tag.

Combine two of the techniques you’ve learned to visualise the combined distribution of cut, carat, and price.

ggplot(diamonds, aes(carat, price)) +
  geom_boxplot(aes(group = cut_number(price, 10))) +
  facet_wrap(~ cut, scales = "free_y")

Two dimensional plots reveal outliers that are not visible in one dimensional plots. For example, some points in the plot below have an unusual combination of x and y values, which makes the points outliers even though their x and y values appear normal when examined separately.
```
ggplot(data = diamonds) +
  geom_point(mapping = aes(x = x, y = y)) 
```
```
ggplot(data = diamonds) +
  geom_point(mapping = aes(x = x, y = y)) +
  coord_cartesian(xlim = c(4, 11), ylim = c(4, 11))
```
```
ggplot(data = diamonds) +
  geom_boxplot(mapping = aes(x = x, y = y, group=cut_number(y, 10))) +
  coord_cartesian(xlim = c(4, 11), ylim = c(4, 11))
```
Why is a scatterplot a better display than a binned plot for this case?

In a binned plot the points are gathered together in a bin and you may not notice that it is an outlier.

Patterns

If you spot a pattern, some Qs:

Could this pattern be due to coincidence (i.e. random chance)?
How can you describe the relationship implied by the pattern?
How strong is the relationship implied by the pattern?
What other variables might affect the relationship?
Does the relationship change if you look at individual subgroups of the data?

# old faithful eruption lengths vs wait time
ggplot(faithful) +
  geom_point(mapping = aes(x = eruptions, y = waiting))

sessionInfo()

R version 3.6.3 (2020-02-29)
Platform: x86_64-w64-mingw32/x64 (64-bit)
Running under: Windows 10 x64 (build 19042)

Matrix products: default

locale:
[1] LC_COLLATE=English_South Africa.1252  LC_CTYPE=English_South Africa.1252   
[3] LC_MONETARY=English_South Africa.1252 LC_NUMERIC=C                         
[5] LC_TIME=English_South Africa.1252    

attached base packages:
[1] stats     graphics  grDevices utils     datasets  methods   base     

other attached packages:
 [1] ggbeeswarm_0.6.0           lvplot_0.2.0              
 [3] magrittr_1.5               tidyquant_1.0.0           
 [5] quantmod_0.4.17            TTR_0.23-6                
 [7] PerformanceAnalytics_2.0.4 xts_0.12-0                
 [9] zoo_1.8-7                  lubridate_1.7.9           
[11] emo_0.0.0.9000             skimr_2.1.1               
[13] gt_0.2.2                   palmerpenguins_0.1.0      
[15] nycflights13_1.0.1         flair_0.0.2               
[17] forcats_0.5.0              stringr_1.4.0             
[19] dplyr_1.0.2                purrr_0.3.4               
[21] readr_1.4.0                tidyr_1.1.2               
[23] tibble_3.0.3               ggplot2_3.3.2             
[25] tidyverse_1.3.0            workflowr_1.6.2           

loaded via a namespace (and not attached):
 [1] fs_1.5.0           RColorBrewer_1.1-2 httr_1.4.2         rprojroot_1.3-2   
 [5] repr_1.1.0         tools_3.6.3        backports_1.1.6    utf8_1.1.4        
 [9] R6_2.4.1           vipor_0.4.5        DBI_1.1.0          colorspace_1.4-1  
[13] withr_2.2.0        tidyselect_1.1.0   curl_4.3           compiler_3.6.3    
[17] git2r_0.26.1       cli_2.1.0          rvest_0.3.6        xml2_1.3.2        
[21] labeling_0.3       sass_0.2.0         scales_1.1.0       checkmate_2.0.0   
[25] quadprog_1.5-8     digest_0.6.27      rmarkdown_2.4      base64enc_0.1-3   
[29] pkgconfig_2.0.3    htmltools_0.5.0    dbplyr_2.0.0       highr_0.8         
[33] rlang_0.4.8        readxl_1.3.1       rstudioapi_0.11    generics_0.0.2    
[37] farver_2.0.3       jsonlite_1.7.1     Rcpp_1.0.4.6       Quandl_2.10.0     
[41] munsell_0.5.0      fansi_0.4.1        lifecycle_0.2.0    stringi_1.5.3     
[45] whisker_0.4        yaml_2.2.1         grid_3.6.3         promises_1.1.0    
[49] crayon_1.3.4       lattice_0.20-38    haven_2.3.1        hms_0.5.3         
[53] knitr_1.28         ps_1.3.2           pillar_1.4.6       reprex_0.3.0      
[57] glue_1.4.2         evaluate_0.14      modelr_0.1.8       vctrs_0.3.2       
[61] httpuv_1.5.2       cellranger_1.1.0   gtable_0.3.0       assertthat_0.2.1  
[65] xfun_0.13          broom_0.7.2        later_1.0.0        beeswarm_0.2.3    
[69] ellipsis_0.3.1

Chapter 5 - Exploratory Data Analysis (EDA)

Vebash Naidoo

16/10/2020

Patterns

Investigate Categories

Investigate Continuous Data

Investigate Unusual Values

Exercises

Leveraging Missing Values

Exercises

Covariation

Categorical and Continuous

Density Freq Polygons

Boxplots

Exercises

Two Categorical Variables

Exercises

Two Continuous Variables

Exercises

Patterns