Numerical Summaries

Summarizing data

A graph is a summary of data that is a picture
but how do we get summaries of data that are numbers?
- a summary or two (eg. mean, median, SD) of just one column
- a count of observations in each category of a categorical variable
- summaries by group (defined by a categorical variable)
- a summary of all of several columns.
To do this, meet pipe operator %>%. This takes input data frame, does something to it, and outputs result. (Learn: Ctrl-Shift-M.)

cont’d

Output from a pipe can be used as input to something else, so can have a sequence of pipes.
Summaries include: mean, median, min, max, sd, IQR, quantile (for obtaining quartiles or any percentile), n (for counting observations).
Use our Australian athletes data again.
to begin, as usual:

library(tidyverse)

── Attaching core tidyverse packages ──────────────────────── tidyverse 2.0.0 ──
✔ dplyr     1.2.1     ✔ readr     2.2.0
✔ forcats   1.0.1     ✔ stringr   1.6.0
✔ ggplot2   4.0.3     ✔ tibble    3.3.1
✔ lubridate 1.9.5     ✔ tidyr     1.3.2
✔ purrr     1.2.2     
── Conflicts ────────────────────────────────────────── tidyverse_conflicts() ──
✖ dplyr::filter() masks stats::filter()
✖ dplyr::lag()    masks stats::lag()
ℹ Use the conflicted package (<http://conflicted.r-lib.org/>) to force all conflicts to become errors

The athletes, again

Rows: 202
Columns: 13
$ Sex     <chr> "female", "female", "female", "female", "female", "female", "f…
$ Sport   <chr> "Netball", "Netball", "Netball", "Netball", "Netball", "Netbal…
$ RCC     <dbl> 4.56, 4.15, 4.16, 4.32, 4.06, 4.12, 4.17, 3.80, 3.96, 4.44, 4.…
$ WCC     <dbl> 13.3, 6.0, 7.6, 6.4, 5.8, 6.1, 5.0, 6.6, 5.5, 9.7, 10.6, 6.3, …
$ Hc      <dbl> 42.2, 38.0, 37.5, 37.7, 38.7, 36.6, 37.4, 36.5, 36.3, 41.4, 37…
$ Hg      <dbl> 13.6, 12.7, 12.3, 12.3, 12.8, 11.8, 12.7, 12.4, 12.4, 14.1, 12…
$ Ferr    <dbl> 20, 59, 22, 30, 78, 21, 109, 102, 71, 64, 68, 78, 107, 39, 58,…
$ BMI     <dbl> 19.16, 21.15, 21.40, 21.03, 21.77, 21.38, 21.47, 24.45, 22.63,…
$ SSF     <dbl> 49.0, 110.2, 89.0, 98.3, 122.1, 90.4, 106.9, 156.6, 101.1, 126…
$ `%Bfat` <dbl> 11.29, 25.26, 19.39, 19.63, 23.11, 16.86, 21.32, 26.57, 17.93,…
$ LBM     <dbl> 53.14, 47.09, 53.44, 48.78, 56.05, 56.45, 53.11, 54.41, 55.97,…
$ Ht      <dbl> 176.8, 172.6, 176.0, 169.9, 183.0, 178.2, 177.3, 174.1, 173.6,…
$ Wt      <dbl> 59.90, 63.00, 66.30, 60.70, 72.90, 67.90, 67.50, 74.10, 68.20,…

Summarizing one column

Mean height:

athletes %>% summarize(mean_ht = mean(Ht))

# A tibble: 1 × 1
  mean_ht
    <dbl>
1    180.

or to get mean and SD of BMI:

athletes %>% summarize(mean_bmi = mean(BMI), 
                       sd_bmi = sd(BMI))

# A tibble: 1 × 2
  mean_bmi sd_bmi
     <dbl>  <dbl>
1     23.0   2.86

A warning

This doesn’t work:

mean(BMI)

Error:
! object 'BMI' not found

because R needs to know what dataframe BMI lives in.

Quartiles

quantile calculates percentiles (“fractiles”); quartiles are 25th and 75th percentiles:

athletes %>% summarize( Q1_wt = quantile(Wt, 0.25),
                        Q3_wt = quantile(Wt, 0.75))

# A tibble: 1 × 2
  Q1_wt Q3_wt
  <dbl> <dbl>
1  66.5  84.1

Creating new columns

These weights are in kilograms. Maybe we want to summarize the weights in pounds.
Convert kg to lb by multiplying by 2.2.
Create new column and summarize that:

athletes %>% mutate(wt_lb = Wt * 2.2) %>%
  summarize(Q1_lb=quantile(wt_lb, 0.25),
            Q3_lb=quantile(wt_lb, 0.75))

# A tibble: 1 × 2
  Q1_lb Q3_lb
  <dbl> <dbl>
1  146.  185.

Counting how many

for example, number of athletes in each sport:

athletes %>% count(Sport)

# A tibble: 10 × 2
   Sport       n
   <chr>   <int>
 1 BBall      25
 2 Field      19
 3 Gym         4
 4 Netball    23
 5 Row        37
 6 Swim       22
 7 T400m      29
 8 TSprnt     15
 9 Tennis     11
10 WPolo      17

Summaries by group

Might want separate summaries for each “group”, eg. mean and SD of height for males and females. Strategy is group_by (to define the groups) and then summarize:

athletes %>% 
  group_by(Sex) %>% 
  summarize(mean_ht = mean(Ht), sd_ht = sd(Ht))

# A tibble: 2 × 3
  Sex    mean_ht sd_ht
  <chr>    <dbl> <dbl>
1 female    175.  8.24
2 male      186.  7.90

Counting how many, variation 2:

athletes %>% group_by(Sport) %>%
  summarize(count = n())

# A tibble: 10 × 2
   Sport   count
   <chr>   <int>
 1 BBall      25
 2 Field      19
 3 Gym         4
 4 Netball    23
 5 Row        37
 6 Swim       22
 7 T400m      29
 8 TSprnt     15
 9 Tennis     11
10 WPolo      17

Count plus stats

If you want number of observations per group plus some stats, you need to go the n() way:

athletes %>% 
  group_by(Sex) %>%
  summarize(n = n(), mean_ht = mean(Ht), sd_ht = sd(Ht))

# A tibble: 2 × 4
  Sex        n mean_ht sd_ht
  <chr>  <int>   <dbl> <dbl>
1 female   100    175.  8.24
2 male     102    186.  7.90

Summarizing several columns 1/2

Standard deviation of each (numeric) column:

athletes %>% 
  summarize(across(where(is.numeric), 
                   \(x) sd(x)))

# A tibble: 1 × 11
    RCC   WCC    Hc    Hg  Ferr   BMI   SSF `%Bfat`   LBM    Ht    Wt
  <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>   <dbl> <dbl> <dbl> <dbl>
1 0.458  1.80  3.66  1.36  47.5  2.86  32.6    6.19  13.1  9.73  13.9

Summarizing several columns 2/2

Median of all columns whose name starts with H:

athletes %>% 
  summarize(across(starts_with("H"), 
                   \(x) median(x)))

# A tibble: 1 × 3
     Hc    Hg    Ht
  <dbl> <dbl> <dbl>
1  43.5  14.7  180.

Same thing by group

athletes %>% 
  group_by(Sex) %>% 
  summarize(across(starts_with("H"), 
                   \(x) median(x)))

# A tibble: 2 × 4
  Sex       Hc    Hg    Ht
  <chr>  <dbl> <dbl> <dbl>
1 female  40.6  13.5  175 
2 male    45.5  15.5  186.

… another one, getting two summaries

athletes %>% 
  group_by(Sex) %>% 
  summarize(across(ends_with("C"), 
                   list(med = \(x) median(x), 
                        iqr = \(x) IQR(x))))

# A tibble: 2 × 7
  Sex    RCC_med RCC_iqr WCC_med WCC_iqr Hc_med Hc_iqr
  <chr>    <dbl>   <dbl>   <dbl>   <dbl>  <dbl>  <dbl>
1 female    4.38   0.370     6.7    2.15   40.6   4.03
2 male      5.01   0.315     7.1    2.35   45.5   2.57