Outline

The tidyverse is a collection of R packages designed for data science.

• readr
• dplyr
• tidyr
• ggplot2 (Next week)
• others …

library(readr)
library(dplyr)

## 
## Attaching package: 'dplyr'

## The following objects are masked from 'package:stats':
## 
##     filter, lag

## The following objects are masked from 'package:base':
## 
##     intersect, setdiff, setequal, union

library(tidyr)
library(ggplot2)
## alternatively, you can do library(tidyverse) to include all of them

library(tidyverse)

## ── Attaching packages ─────────────────────────────────────────────────────── tidyverse 1.2.1 ──

## ✔ tibble  2.1.3     ✔ stringr 1.4.0
## ✔ purrr   0.3.2     ✔ forcats 0.4.0

## ── Conflicts ────────────────────────────────────────────────────────── tidyverse_conflicts() ──
## ✖ dplyr::filter() masks stats::filter()
## ✖ dplyr::lag()    masks stats::lag()

Read in data (readr)

• data source: sleepstudy.csv (also available in R lme4 package)

• Original way to read in data

asleepfile <- "https:///Caleb-Huo.github.io/teaching/data/sleep/sleepstudy.csv"
data0 <- read.csv(asleepfile)

• Use read_csv
  • Much faster than read.csv, especially for large datasets

data1 <- read_csv(asleepfile)

## Parsed with column specification:
## cols(
##   Reaction = col_double(),
##   Days = col_double(),
##   Subject = col_double()
## )

Inspect the data

• read.csv
  • You may want to use head, otherwise it will print out everyting

head(data0)

##   Reaction Days Subject
## 1 249.5600    0     308
## 2 258.7047    1     308
## 3 250.8006    2     308
## 4 321.4398    3     308
## 5 356.8519    4     308
## 6 414.6901    5     308

class(data0)

## [1] "data.frame"

• read_csv
  • smartly print out the first few rows

data1

## # A tibble: 180 x 3
##    Reaction  Days Subject
##       <dbl> <dbl>   <dbl>
##  1     250.     0     308
##  2     259.     1     308
##  3     251.     2     308
##  4     321.     3     308
##  5     357.     4     308
##  6     415.     5     308
##  7     382.     6     308
##  8     290.     7     308
##  9     431.     8     308
## 10     466.     9     308
## # … with 170 more rows

class(data1)

## [1] "spec_tbl_df" "tbl_df"      "tbl"         "data.frame"

read_delim

• Similar to read_csv, we can use read_delim, which is more general
  • read_csv assumes the delimiter is “,”
  • for read_delim, you need to specify the delimiter
    • “,”: comma delimited (usually for .csv)
    • “\t”: tab delimited (usually for .txt)
    • " ": space delimited

data2 <- read_delim("sleepstudy.csv", delim=",")

## Parsed with column specification:
## cols(
##   Reaction = col_double(),
##   Days = col_double(),
##   Subject = col_double()
## )

Play with data1

data1_sub <- data1[1:3,]
data1_sub$Reaction

## [1] 249.5600 258.7047 250.8006

as.matrix(data1_sub)

##      Reaction Days Subject
## [1,] 249.5600    0     308
## [2,] 258.7047    1     308
## [3,] 250.8006    2     308

as.data.frame(data1_sub)

##   Reaction Days Subject
## 1 249.5600    0     308
## 2 258.7047    1     308
## 3 250.8006    2     308

dplyr

• %>%: pipe
• select(): select columns
• filter(): filter rows by logical variable
• slice(): subset rows by index
• arrange(): re-order or arrange rows
• mutate(): create new columns
• mutate_at(): directly change original data
• rename(): rename
• summarise(): summarise values
• group_by(): allows for group operations in the “split-apply-combine” concept
• merge data.frame
  • inner_join()
  • left_join()
  • right_join()
  • full_join()
  • anti_join()

select

select(data1, Days, Subject)

## # A tibble: 180 x 2
##     Days Subject
##    <dbl>   <dbl>
##  1     0     308
##  2     1     308
##  3     2     308
##  4     3     308
##  5     4     308
##  6     5     308
##  7     6     308
##  8     7     308
##  9     8     308
## 10     9     308
## # … with 170 more rows

• Use pipe

data1 %>% select(Days, Subject)

## # A tibble: 180 x 2
##     Days Subject
##    <dbl>   <dbl>
##  1     0     308
##  2     1     308
##  3     2     308
##  4     3     308
##  5     4     308
##  6     5     308
##  7     6     308
##  8     7     308
##  9     8     308
## 10     9     308
## # … with 170 more rows

pipe

• %>%
• data1 %>% select(Days, Subject)
  • the result before %>% will be piped into the first argument of the function behind %>%
• data1 %>% select(., Days, Subject)
• shortcut:
  • cmd + shift + M: MAC
  • ctrl + shift + M: Windows

exp(1)

## [1] 2.718282

1 %>% exp()

## [1] 2.718282

1 %>% exp() %>% log ## () can be omitted if the data is the only argument

## [1] 1

• Do not select

data1 %>% select(-Reaction)

## # A tibble: 180 x 2
##     Days Subject
##    <dbl>   <dbl>
##  1     0     308
##  2     1     308
##  3     2     308
##  4     3     308
##  5     4     308
##  6     5     308
##  7     6     308
##  8     7     308
##  9     8     308
## 10     9     308
## # … with 170 more rows

filter

data1 %>% 
  select(Days, Subject) %>%
  filter(Subject == 308)

## # A tibble: 10 x 2
##     Days Subject
##    <dbl>   <dbl>
##  1     0     308
##  2     1     308
##  3     2     308
##  4     3     308
##  5     4     308
##  6     5     308
##  7     6     308
##  8     7     308
##  9     8     308
## 10     9     308

data1 %>% 
  filter(Reaction >= 300) %>%
  select(Days, Subject) %>%
  filter(Subject == 308)

## # A tibble: 6 x 2
##    Days Subject
##   <dbl>   <dbl>
## 1     3     308
## 2     4     308
## 3     5     308
## 4     6     308
## 5     8     308
## 6     9     308

• multiple filtering criteria

data1 %>% 
  filter(Reaction >= 300, Subject == 308) 

## # A tibble: 6 x 3
##   Reaction  Days Subject
##      <dbl> <dbl>   <dbl>
## 1     321.     3     308
## 2     357.     4     308
## 3     415.     5     308
## 4     382.     6     308
## 5     431.     8     308
## 6     466.     9     308

data1 %>% 
  filter(Reaction >= 300 & Subject == 308) 

## # A tibble: 6 x 3
##   Reaction  Days Subject
##      <dbl> <dbl>   <dbl>
## 1     321.     3     308
## 2     357.     4     308
## 3     415.     5     308
## 4     382.     6     308
## 5     431.     8     308
## 6     466.     9     308

pull

(data1 %>% 
  filter(Reaction >= 300, Subject == 308))$Reaction

## [1] 321.4398 356.8519 414.6901 382.2038 430.5853 466.3535

data1 %>% 
  filter(Reaction >= 300, Subject == 308) %>%
  pull(Reaction)

## [1] 321.4398 356.8519 414.6901 382.2038 430.5853 466.3535

slice

which(data1$Reaction >= 300 & data1$Subject == 308)

## [1]  4  5  6  7  9 10

with(data1, which(Reaction >= 300 & Subject == 308)) ## works for data.frame

## [1]  4  5  6  7  9 10

data1 %>% 
  slice(which(Reaction >= 300 & Subject == 308)) 

## # A tibble: 6 x 3
##   Reaction  Days Subject
##      <dbl> <dbl>   <dbl>
## 1     321.     3     308
## 2     357.     4     308
## 3     415.     5     308
## 4     382.     6     308
## 5     431.     8     308
## 6     466.     9     308

data1 %>% 
  slice(1:8) 

## # A tibble: 8 x 3
##   Reaction  Days Subject
##      <dbl> <dbl>   <dbl>
## 1     250.     0     308
## 2     259.     1     308
## 3     251.     2     308
## 4     321.     3     308
## 5     357.     4     308
## 6     415.     5     308
## 7     382.     6     308
## 8     290.     7     308

data1 %>% 
  head(n=8) 

## # A tibble: 8 x 3
##   Reaction  Days Subject
##      <dbl> <dbl>   <dbl>
## 1     250.     0     308
## 2     259.     1     308
## 3     251.     2     308
## 4     321.     3     308
## 5     357.     4     308
## 6     415.     5     308
## 7     382.     6     308
## 8     290.     7     308

arrange

• arrange() is similar to sort() and order()
• assending order by default

data1 %>% arrange(Reaction) %>% head

## # A tibble: 6 x 3
##   Reaction  Days Subject
##      <dbl> <dbl>   <dbl>
## 1     194.     1     310
## 2     199.     0     310
## 3     203.     2     309
## 4     205.     3     309
## 5     205.     1     309
## 6     208.     4     309

data1 %>% 
  arrange(Days, Reaction) %>% 
  head

## # A tibble: 6 x 3
##   Reaction  Days Subject
##      <dbl> <dbl>   <dbl>
## 1     199.     0     310
## 2     222.     0     352
## 3     223.     0     309
## 4     225.     0     370
## 5     235.     0     332
## 6     236.     0     349

data1 %>% 
  arrange(Days, Reaction) %>% 
  head %>%
  colSums ## pipe also work for other functions

## Reaction     Days  Subject 
## 1339.693    0.000 2022.000

data1 %>% 
  arrange(desc(Days), Reaction) %>% 
  head

## # A tibble: 6 x 3
##   Reaction  Days Subject
##      <dbl> <dbl>   <dbl>
## 1     237.     9     335
## 2     237.     9     309
## 3     248.     9     310
## 4     254.     9     332
## 5     348.     9     351
## 6     352.     9     349

mutate

data1 %>% 
  mutate(Reaction_binary = Reaction<250) %>%
  head

## # A tibble: 6 x 4
##   Reaction  Days Subject Reaction_binary
##      <dbl> <dbl>   <dbl> <lgl>          
## 1     250.     0     308 TRUE           
## 2     259.     1     308 FALSE          
## 3     251.     2     308 FALSE          
## 4     321.     3     308 FALSE          
## 5     357.     4     308 FALSE          
## 6     415.     5     308 FALSE

data1 %>% 
  mutate(Reaction_binary = Reaction<250,
        Reaction_sec = Reaction/1000) %>% 
  head

## # A tibble: 6 x 5
##   Reaction  Days Subject Reaction_binary Reaction_sec
##      <dbl> <dbl>   <dbl> <lgl>                  <dbl>
## 1     250.     0     308 TRUE                   0.250
## 2     259.     1     308 FALSE                  0.259
## 3     251.     2     308 FALSE                  0.251
## 4     321.     3     308 FALSE                  0.321
## 5     357.     4     308 FALSE                  0.357
## 6     415.     5     308 FALSE                  0.415

mutate at (apply a function to one or several columns)

data1 %>% 
  head

## # A tibble: 6 x 3
##   Reaction  Days Subject
##      <dbl> <dbl>   <dbl>
## 1     250.     0     308
## 2     259.     1     308
## 3     251.     2     308
## 4     321.     3     308
## 5     357.     4     308
## 6     415.     5     308

data1 %>% 
  head %>%
  mutate_at(c("Reaction", "Subject"), log)

## # A tibble: 6 x 3
##   Reaction  Days Subject
##      <dbl> <dbl>   <dbl>
## 1     5.52     0    5.73
## 2     5.56     1    5.73
## 3     5.52     2    5.73
## 4     5.77     3    5.73
## 5     5.88     4    5.73
## 6     6.03     5    5.73

rename

data1 %>% 
  rename(ID = Subject)

## # A tibble: 180 x 3
##    Reaction  Days    ID
##       <dbl> <dbl> <dbl>
##  1     250.     0   308
##  2     259.     1   308
##  3     251.     2   308
##  4     321.     3   308
##  5     357.     4   308
##  6     415.     5   308
##  7     382.     6   308
##  8     290.     7   308
##  9     431.     8   308
## 10     466.     9   308
## # … with 170 more rows

summarise

data1 %>% 
    summarise(avg_reaction = mean(Reaction), 
              min_reaction = min(Reaction),
              max_reaction = max(Reaction),
              total = n())

## # A tibble: 1 x 4
##   avg_reaction min_reaction max_reaction total
##          <dbl>        <dbl>        <dbl> <int>
## 1         299.         194.         466.   180

adata <- data1 %>% 
    summarise(avg_reaction = mean(Reaction), 
              min_reaction = min(Reaction),
              max_reaction = max(Reaction),
              total = n())

group_by

• seems to be more powerful than tapply

tt <- data1 %>% 
      group_by(Subject) %>%
      summarise(avg_reaction = mean(Reaction), 
              min_reaction = min(Reaction),
              max_reaction = max(Reaction),
              total = n())
tt %>% head

## # A tibble: 6 x 5
##   Subject avg_reaction min_reaction max_reaction total
##     <dbl>        <dbl>        <dbl>        <dbl> <int>
## 1     308         342.         250.         466.    10
## 2     309         215.         203.         237.    10
## 3     310         231.         194.         261.    10
## 4     330         303.         280.         354.    10
## 5     331         309.         285          372.    10
## 6     332         307.         235.         454.    10

tt %>% ungroup() %>% head ## sometimes, we want to do ungroup

## # A tibble: 6 x 5
##   Subject avg_reaction min_reaction max_reaction total
##     <dbl>        <dbl>        <dbl>        <dbl> <int>
## 1     308         342.         250.         466.    10
## 2     309         215.         203.         237.    10
## 3     310         231.         194.         261.    10
## 4     330         303.         280.         354.    10
## 5     331         309.         285          372.    10
## 6     332         307.         235.         454.    10

select (2)

• Select a range

tt %>% 
  head %>% 
  select(avg_reaction:max_reaction)

## # A tibble: 6 x 3
##   avg_reaction min_reaction max_reaction
##          <dbl>        <dbl>        <dbl>
## 1         342.         250.         466.
## 2         215.         203.         237.
## 3         231.         194.         261.
## 4         303.         280.         354.
## 5         309.         285          372.
## 6         307.         235.         454.

• contains

tt %>% 
  head %>% 
  select(contains("reaction"))

## # A tibble: 6 x 3
##   avg_reaction min_reaction max_reaction
##          <dbl>        <dbl>        <dbl>
## 1         342.         250.         466.
## 2         215.         203.         237.
## 3         231.         194.         261.
## 4         303.         280.         354.
## 5         309.         285          372.
## 6         307.         235.         454.

more options for select()

• starts_with() = Select columns that start with a character string
• ends_with() = Select columns that end with a character string
• contains() = Select columns that contain a character string
• matches() = Select columns that match a regular expression
• one_of() = Select columns names that are from a group of names

merge data.frame

the data for merge

superheroes <- "
    name, alignment, gender,         publisher
 Magneto,       bad,   male,            Marvel
   Storm,      good, female,            Marvel
Mystique,       bad, female,            Marvel
  Batman,      good,   male,                DC
   Joker,       bad,   male,                DC
Catwoman,       bad, female,                DC
 Hellboy,      good,   male, Dark Horse Comics
"
superheroes <- read_csv(superheroes, skip = 1)

publishers <- "
  publisher, yr_founded
         DC,       1934
     Marvel,       1939
      Image,       1992
"
publishers <- read_csv(publishers, skip = 1)

inner_join

• inner_join(x, y): Return all rows from x where there are matching values in y, and all columns from x and y.
• If there are multiple matches between x and y, all combination of the matches are returned.

inner_join(superheroes, publishers)

## Joining, by = "publisher"

## # A tibble: 6 x 5
##   name     alignment gender publisher yr_founded
##   <chr>    <chr>     <chr>  <chr>          <dbl>
## 1 Magneto  bad       male   Marvel          1939
## 2 Storm    good      female Marvel          1939
## 3 Mystique bad       female Marvel          1939
## 4 Batman   good      male   DC              1934
## 5 Joker    bad       male   DC              1934
## 6 Catwoman bad       female DC              1934

inner_join(publishers, superheroes)

## Joining, by = "publisher"

## # A tibble: 6 x 5
##   publisher yr_founded name     alignment gender
##   <chr>          <dbl> <chr>    <chr>     <chr> 
## 1 DC              1934 Batman   good      male  
## 2 DC              1934 Joker    bad       male  
## 3 DC              1934 Catwoman bad       female
## 4 Marvel          1939 Magneto  bad       male  
## 5 Marvel          1939 Storm    good      female
## 6 Marvel          1939 Mystique bad       female

left_join

• left_join(x, y): Return all rows from x, and all columns from x and y.
• If there are multiple matches between x and y, all combination of the matches are returned.

left_join(superheroes, publishers)

## Joining, by = "publisher"

## # A tibble: 7 x 5
##   name     alignment gender publisher         yr_founded
##   <chr>    <chr>     <chr>  <chr>                  <dbl>
## 1 Magneto  bad       male   Marvel                  1939
## 2 Storm    good      female Marvel                  1939
## 3 Mystique bad       female Marvel                  1939
## 4 Batman   good      male   DC                      1934
## 5 Joker    bad       male   DC                      1934
## 6 Catwoman bad       female DC                      1934
## 7 Hellboy  good      male   Dark Horse Comics         NA

left_join(publishers, superheroes)

## Joining, by = "publisher"

## # A tibble: 7 x 5
##   publisher yr_founded name     alignment gender
##   <chr>          <dbl> <chr>    <chr>     <chr> 
## 1 DC              1934 Batman   good      male  
## 2 DC              1934 Joker    bad       male  
## 3 DC              1934 Catwoman bad       female
## 4 Marvel          1939 Magneto  bad       male  
## 5 Marvel          1939 Storm    good      female
## 6 Marvel          1939 Mystique bad       female
## 7 Image           1992 <NA>     <NA>      <NA>

right_join

• right_join(x, y): Return all rows from y, and all columns from x and y.
• If there are multiple matches between x and y, all combination of the matches are returned.

right_join(superheroes, publishers)

## Joining, by = "publisher"

## # A tibble: 7 x 5
##   name     alignment gender publisher yr_founded
##   <chr>    <chr>     <chr>  <chr>          <dbl>
## 1 Batman   good      male   DC              1934
## 2 Joker    bad       male   DC              1934
## 3 Catwoman bad       female DC              1934
## 4 Magneto  bad       male   Marvel          1939
## 5 Storm    good      female Marvel          1939
## 6 Mystique bad       female Marvel          1939
## 7 <NA>     <NA>      <NA>   Image           1992

right_join(publishers, superheroes)

## Joining, by = "publisher"

## # A tibble: 7 x 5
##   publisher         yr_founded name     alignment gender
##   <chr>                  <dbl> <chr>    <chr>     <chr> 
## 1 Marvel                  1939 Magneto  bad       male  
## 2 Marvel                  1939 Storm    good      female
## 3 Marvel                  1939 Mystique bad       female
## 4 DC                      1934 Batman   good      male  
## 5 DC                      1934 Joker    bad       male  
## 6 DC                      1934 Catwoman bad       female
## 7 Dark Horse Comics         NA Hellboy  good      male

anti_join

• anti_join(x, y): Return all rows from x where there are not matching values in y, keeping just columns from x.

anti_join(superheroes, publishers)

## Joining, by = "publisher"

## # A tibble: 1 x 4
##   name    alignment gender publisher        
##   <chr>   <chr>     <chr>  <chr>            
## 1 Hellboy good      male   Dark Horse Comics

anti_join(publishers, superheroes)

## Joining, by = "publisher"

## # A tibble: 1 x 2
##   publisher yr_founded
##   <chr>          <dbl>
## 1 Image           1992

full_join

• full_join(x, y): Return all rows and all columns from both x and y.
• Where there are not matching values, returns NA for the one missing.

full_join(superheroes, publishers)

## Joining, by = "publisher"

## # A tibble: 8 x 5
##   name     alignment gender publisher         yr_founded
##   <chr>    <chr>     <chr>  <chr>                  <dbl>
## 1 Magneto  bad       male   Marvel                  1939
## 2 Storm    good      female Marvel                  1939
## 3 Mystique bad       female Marvel                  1939
## 4 Batman   good      male   DC                      1934
## 5 Joker    bad       male   DC                      1934
## 6 Catwoman bad       female DC                      1934
## 7 Hellboy  good      male   Dark Horse Comics         NA
## 8 <NA>     <NA>      <NA>   Image                   1992

full_join(publishers, superheroes)

## Joining, by = "publisher"

## # A tibble: 8 x 5
##   publisher         yr_founded name     alignment gender
##   <chr>                  <dbl> <chr>    <chr>     <chr> 
## 1 DC                      1934 Batman   good      male  
## 2 DC                      1934 Joker    bad       male  
## 3 DC                      1934 Catwoman bad       female
## 4 Marvel                  1939 Magneto  bad       male  
## 5 Marvel                  1939 Storm    good      female
## 6 Marvel                  1939 Mystique bad       female
## 7 Image                   1992 <NA>     <NA>      <NA>  
## 8 Dark Horse Comics         NA Hellboy  good      male

tidyr

• gather
• separate
• spread
• merge

spread

• Function:
  • spread(data, key, value, fill = NA, convert = FALSE)
• Same as:
  • data %>% spread(key, value, fill = NA, convert = FALSE)
• Arguments:
  • data: data frame
  • key: column values to convert to multiple columns
  • value: single column values to convert to multiple columns’ values
  • fill: If there isn’t a value for every combination of the other variables and the key column, this value will be substituted
  • convert: if TRUE will automatically convert values to logical, integer, numeric, complex or factor as appropriate

spread example

data1_wide <- data1 %>% spread(Days, Reaction, fill = NA, convert = FALSE)
head(data1_wide)

## # A tibble: 6 x 11
##   Subject   `0`   `1`   `2`   `3`   `4`   `5`   `6`   `7`   `8`   `9`
##     <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1     308  250.  259.  251.  321.  357.  415.  382.  290.  431.  466.
## 2     309  223.  205.  203.  205.  208.  216.  214.  218.  224.  237.
## 3     310  199.  194.  234.  233.  229.  220.  235.  256.  261.  248.
## 4     330  322.  300.  284.  285.  286.  298.  280.  318.  305.  354.
## 5     331  288.  285   302.  320.  316.  293.  290.  335.  294.  372.
## 6     332  235.  243.  273.  310.  317.  310.  454.  347.  330.  254.

gather

• Function:
  • gather(data, key, value, …, na.rm = FALSE, convert = FALSE)
• Same as:
  • data %>% gather(key, value, …, na.rm = FALSE, convert = FALSE)
• Arguments:
  • data: data frame
  • key: column name representing new variable
  • value: column name representing variable values
  • …: names of columns to gather (or not gather)
  • na.rm: option to remove observations with missing values (represented by NAs)
  • convert: if TRUE will automatically convert values to logical, integer, numeric, complex or factor as appropriate

gather example

data1_long <- data1_wide %>% gather(ddays, rreaction, "0":"9")
head(data1_long)

## # A tibble: 6 x 3
##   Subject ddays rreaction
##     <dbl> <chr>     <dbl>
## 1     308 0          250.
## 2     309 0          223.
## 3     310 0          199.
## 4     330 0          322.
## 5     331 0          288.
## 6     332 0          235.

unite

• Function:
  • unite(data, col, …, sep = " ", remove = TRUE)
• Same as:
  • data %>% unite(col, …, sep = " ", remove = TRUE)
• Arguments:
  • data: data frame
  • col: column name of new “merged” column
  • …: names of columns to merge
  • sep: separator to use between merged values
  • remove: if TRUE, remove input column from output data frame

unite example

data1_unite<- data1 %>% unite(Subject_Days, Subject, Days, sep="_")
head(data1_unite)

## # A tibble: 6 x 2
##   Reaction Subject_Days
##      <dbl> <chr>       
## 1     250. 308_0       
## 2     259. 308_1       
## 3     251. 308_2       
## 4     321. 308_3       
## 5     357. 308_4       
## 6     415. 308_5

separate

• Function:
  • separate(data, col, into, sep = " ", remove = TRUE, convert = FALSE)
• Same as:
  • data %>% separate(col, into, sep = " ", remove = TRUE, convert = FALSE)
• Arguments:
  • data: data frame
  • col: column name representing current variable
  • into: names of variables representing new variables
  • sep: how to separate current variable (char, num, or symbol)
  • remove: if TRUE, remove input column from output data frame
  • convert: if TRUE will automatically convert values to logical, integer, numeric, complex or factor as appropriate

separate example

data1_separate<- data1_unite %>% separate(Subject_Days, c("subjects", "days"), sep="_")
head(data1_separate)

## # A tibble: 6 x 3
##   Reaction subjects days 
##      <dbl> <chr>    <chr>
## 1     250. 308      0    
## 2     259. 308      1    
## 3     251. 308      2    
## 4     321. 308      3    
## 5     357. 308      4    
## 6     415. 308      5

references

• http://genomicsclass.github.io/book/pages/dplyr_tutorial.html
• https://uc-r.github.io/tidyr
• http://stat545.com/bit001_dplyr-cheatsheet.html#inner_joinsuperheroes-publishers
• http://www.stat.cmu.edu/~ryantibs/statcomp-F18/