Number of variables involved

• Univariate data analysis: distribution of single variable

• Bivariate data analysis: relationship between two variables

• Multivariate data analysis: relationship between many variables at once, usually focusing on the relationship between two while conditioning for others

Types of variables

• Numerical variables can be classified as continuous or discrete based on whether or not the variable can take on an infinite number of values or only non-negative whole numbers, respectively.
  • height is continuous
  • number of siblings is discrete

• If the variable is categorical, we can determine if it is ordinal based on whether or not the levels have a natural ordering.
  • hair color is unordered
  • year in school is ordinal

Describing numerical distributions

• shape:

  • skewness: right-skewed, left-skewed, symmetric
  • modality: unimodal, bimodal, multimodal, uniform

• center: mean (mean), median (median), mode (not always useful)

• spread: range (range), standard deviation (sd), inter-quartile range (IQR)

• outliers: observations outside of the usual pattern

Starwars data

starwars

## # A tibble: 87 x 14
##    name  height  mass hair_color skin_color eye_color birth_year sex   gender
##    <chr>  <int> <dbl> <chr>      <chr>      <chr>          <dbl> <chr> <chr> 
##  1 Luke…    172    77 other      fair       blue            19   male  mascu…
##  2 C-3PO    167    75 none       gold       yellow         112   none  mascu…
##  3 R2-D2     96    32 none       white, bl… red             33   none  mascu…
##  4 Dart…    202   136 none       white      yellow          41.9 male  mascu…
##  5 Leia…    150    49 brown      light      brown           19   fema… femin…
##  6 Owen…    178   120 brown      light      blue            52   male  mascu…
##  7 Beru…    165    75 brown      light      blue            47   fema… femin…
##  8 R5-D4     97    32 none       white, red red             NA   none  mascu…
##  9 Bigg…    183    84 black      light      brown           24   male  mascu…
## 10 Obi-…    182    77 other      fair       blue-gray       57   male  mascu…
## # … with 77 more rows, and 5 more variables: homeworld <chr>, species <chr>,
## #   films <list>, vehicles <list>, starships <list>

Histograms

ggplot(data = starwars, mapping = aes(x = height)) +
  geom_histogram(binwidth = 10)

Density plots

ggplot(data = starwars, mapping = aes(x = height)) +
  geom_density()

Side-by-side box plots

ggplot(data = starwars, mapping = aes(y = height, x = hair_color)) +
  geom_boxplot()

Bar plots

ggplot(data = starwars, mapping = aes(x = hair_color)) +
  geom_bar()

Segmented bar plots, counts

ggplot(data = starwars, mapping = aes(x = hair_color, fill = eye_color2)) +
  geom_bar()

Segmented bar plots, proportions

ggplot(data = starwars, mapping = aes(x = hair_color, fill = eye_color2)) +
         geom_bar(position = "fill") +
         labs(y = "proportion")

Which bar plot is more appropriate?

What is data visualization?

Anything that converts data sources into a visual representation

• charts
• plots
• maps
• tables
• etc.

Data: datasaurus_dozen

Below is an excerpt from the datasaurus_dozen dataset:

## # A tibble: 142 x 8
##    away_x away_y bullseye_x bullseye_y circle_x circle_y dino_x dino_y
##     <dbl>  <dbl>      <dbl>      <dbl>    <dbl>    <dbl>  <dbl>  <dbl>
##  1   32.3   61.4       51.2       83.3     56.0     79.3   55.4   97.2
##  2   53.4   26.2       59.0       85.5     50.0     79.0   51.5   96.0
##  3   63.9   30.8       51.9       85.8     51.3     82.4   46.2   94.5
##  4   70.3   82.5       48.2       85.0     51.2     79.2   42.8   91.4
##  5   34.1   45.7       41.7       84.0     44.4     78.2   40.8   88.3
##  6   67.7   37.1       37.9       82.6     45.0     77.9   38.7   84.9
##  7   53.3   97.5       39.5       80.8     48.6     78.8   35.6   79.9
##  8   63.5   25.1       39.6       82.7     42.1     76.9   33.1   77.6
##  9   68.0   81.0       34.8       80.0     41.0     76.4   29.0   74.5
## 10   67.4   29.7       27.6       72.8     34.6     72.7   26.2   71.4
## # … with 132 more rows

Summary statistics

datasaurus_dozen %>%
  group_by(dataset) %>%
  summarise(r = cor(x, y))

## # A tibble: 13 x 2
##    dataset          r
##    <chr>        <dbl>
##  1 away       -0.0641
##  2 bullseye   -0.0686
##  3 circle     -0.0683
##  4 dino       -0.0645
##  5 dots       -0.0603
##  6 h_lines    -0.0617
##  7 high_lines -0.0685
##  8 slant_down -0.0690
##  9 slant_up   -0.0686
## 10 star       -0.0630
## 11 v_lines    -0.0694
## 12 wide_lines -0.0666
## 13 x_shape    -0.0656

Anscombe's quartet

library(Tmisc)
quartet

##    set  x     y
## 1    I 10  8.04
## 2    I  8  6.95
## 3    I 13  7.58
## 4    I  9  8.81
## 5    I 11  8.33
## 6    I 14  9.96
## 7    I  6  7.24
## 8    I  4  4.26
## 9    I 12 10.84
## 10   I  7  4.82
## 11   I  5  5.68
## 12  II 10  9.14
## 13  II  8  8.14
## 14  II 13  8.74
## 15  II  9  8.77
## 16  II 11  9.26
## 17  II 14  8.10
## 18  II  6  6.13
## 19  II  4  3.10
## 20  II 12  9.13
## 21  II  7  7.26
## 22  II  5  4.74

##    set  x     y
## 23 III 10  7.46
## 24 III  8  6.77
## 25 III 13 12.74
## 26 III  9  7.11
## 27 III 11  7.81
## 28 III 14  8.84
## 29 III  6  6.08
## 30 III  4  5.39
## 31 III 12  8.15
## 32 III  7  6.42
## 33 III  5  5.73
## 34  IV  8  6.58
## 35  IV  8  5.76
## 36  IV  8  7.71
## 37  IV  8  8.84
## 38  IV  8  8.47
## 39  IV  8  7.04
## 40  IV  8  5.25
## 41  IV 19 12.50
## 42  IV  8  5.56
## 43  IV  8  7.91
## 44  IV  8  6.89

Summarising Anscombe's quartet

quartet %>%
  group_by(set) %>%
  summarise(
    mean_x = mean(x), mean_y = mean(y),
    sd_x = sd(x), sd_y = sd(y),
    r = cor(x, y)
  )

## # A tibble: 4 x 6
##   set   mean_x mean_y  sd_x  sd_y     r
##   <fct>  <dbl>  <dbl> <dbl> <dbl> <dbl>
## 1 I          9   7.50  3.32  2.03 0.816
## 2 II         9   7.50  3.32  2.03 0.816
## 3 III        9   7.5   3.32  2.03 0.816
## 4 IV         9   7.50  3.32  2.03 0.817

Visualizing Anscombe's quartet

ggplot(quartet, aes(x = x, y = y)) +
  geom_point() +
  facet_wrap(~ set, ncol = 4)

Do you see anything out of the ordinary?

ggplot(student_survey, aes(x = first_kiss)) +
  geom_histogram(binwidth = 1) +
  labs(title = "How old were you when you had your first kiss?")

Reporting lower vs. higher values

ggplot(student_survey, aes(x = fb_visits_per_day)) +
  geom_dotplot(binwidth = 5, dotsize = 0.4) +
  labs(title = "How many times do you go on Facebook per day?")

Keep it simple

Use color to draw attention

Tell a story