Psych 447: Coding basics

Joseph Bulbulia; Johannes Karl

To do:

A good, and free introduction to R for Data Science Read chapters: 2-8 (they are short chapters.)

Fundamentals of R

A console runs all your code in R

A source page runs all your code in R.

A working directory is where R will look for raw data and other material.

In R-studio, (for starters) you can can use the file tab to import and save your material.

Similarly, in R-studio, (for starters) you can can use install packages by clicking the Install tab in the package pane (generally lower right pane) to install packagees.

How to use R as calculator

We can use R as a calculator. You can run any mathematical operation you would normally use by entering it into the console:

## Addition
x <- 3 + 2
x

[1] 5


## Subtraction
x <-  3 - 2
x

[1] 1


## Multiplication
x <-  3 * 2
x

[1] 6


## Division
x <-  3 / 2
x

[1] 1.5


## Modulus (Remainder from division)
x <-  3 %% 2
x

[1] 1


## Exponentiation
x = 3 ^ 2
x

[1] 9


## Integer Division (Number of times denominator fits in numerator)
x = 3 %/% 2
x

[1] 1

Inspecting data

In a moment, we’ll teach you how to import data into R. For now, let’s work with a dataset that is already present in your R environment, the iris dataset.

Here are some useful commands for inspecting data

check head of dataset sing `head`

# the top rows and columns of the dataset
head(iris)

  Sepal.Length Sepal.Width Petal.Length Petal.Width Species
1          5.1         3.5          1.4         0.2  setosa
2          4.9         3.0          1.4         0.2  setosa
3          4.7         3.2          1.3         0.2  setosa
4          4.6         3.1          1.5         0.2  setosa
5          5.0         3.6          1.4         0.2  setosa
6          5.4         3.9          1.7         0.4  setosa

check data types using `str`

str(iris)

'data.frame':   150 obs. of  5 variables:
 $ Sepal.Length: num  5.1 4.9 4.7 4.6 5 5.4 4.6 5 4.4 4.9 ...
 $ Sepal.Width : num  3.5 3 3.2 3.1 3.6 3.9 3.4 3.4 2.9 3.1 ...
 $ Petal.Length: num  1.4 1.4 1.3 1.5 1.4 1.7 1.4 1.5 1.4 1.5 ...
 $ Petal.Width : num  0.2 0.2 0.2 0.2 0.2 0.4 0.3 0.2 0.2 0.1 ...
 $ Species     : Factor w/ 3 levels "setosa","versicolor",..: 1 1 1 1 1 1 1 1 1 1 ...

names

#names of the columns
names(iris)

[1] "Sepal.Length" "Sepal.Width"  "Petal.Length"
[4] "Petal.Width"  "Species"

view rownames

# view rownames
rownames(iris)

  [1] "1"   "2"   "3"   "4"   "5"   "6"   "7"   "8"   "9"  
 [10] "10"  "11"  "12"  "13"  "14"  "15"  "16"  "17"  "18" 
 [19] "19"  "20"  "21"  "22"  "23"  "24"  "25"  "26"  "27" 
 [28] "28"  "29"  "30"  "31"  "32"  "33"  "34"  "35"  "36" 
 [37] "37"  "38"  "39"  "40"  "41"  "42"  "43"  "44"  "45" 
 [46] "46"  "47"  "48"  "49"  "50"  "51"  "52"  "53"  "54" 
 [55] "55"  "56"  "57"  "58"  "59"  "60"  "61"  "62"  "63" 
 [64] "64"  "65"  "66"  "67"  "68"  "69"  "70"  "71"  "72" 
 [73] "73"  "74"  "75"  "76"  "77"  "78"  "79"  "80"  "81" 
 [82] "82"  "83"  "84"  "85"  "86"  "87"  "88"  "89"  "90" 
 [91] "91"  "92"  "93"  "94"  "95"  "96"  "97"  "98"  "99" 
[100] "100" "101" "102" "103" "104" "105" "106" "107" "108"
[109] "109" "110" "111" "112" "113" "114" "115" "116" "117"
[118] "118" "119" "120" "121" "122" "123" "124" "125" "126"
[127] "127" "128" "129" "130" "131" "132" "133" "134" "135"
[136] "136" "137" "138" "139" "140" "141" "142" "143" "144"
[145] "145" "146" "147" "148" "149" "150"

head(iris)

  Sepal.Length Sepal.Width Petal.Length Petal.Width Species
1          5.1         3.5          1.4         0.2  setosa
2          4.9         3.0          1.4         0.2  setosa
3          4.7         3.2          1.3         0.2  setosa
4          4.6         3.1          1.5         0.2  setosa
5          5.0         3.6          1.4         0.2  setosa
6          5.4         3.9          1.7         0.4  setosa

table (and use of `$`)

# create a table
table(iris$Species)


    setosa versicolor  virginica 
        50         50         50

change column names

# change column names
# create new dataset for 
irisdat2 <- iris
# chage names of columns
names(irisdat2)[] <- c("s_l", "s_w", "p_l", "p_w", "sp")
#inspect
head(irisdat2)

  s_l s_w p_l p_w     sp
1 5.1 3.5 1.4 0.2 setosa
2 4.9 3.0 1.4 0.2 setosa
3 4.7 3.2 1.3 0.2 setosa
4 4.6 3.1 1.5 0.2 setosa
5 5.0 3.6 1.4 0.2 setosa
6 5.4 3.9 1.7 0.4 setosa

Basic data structures

vectors of numbers ( and use of `c` and `i:x` )

go_vector <- c(1:5)
go_vector

[1] 1 2 3 4 5

vectors of characters

go_vector2 <- c("hello", "world")
go_vector2

[1] "hello" "world"

as.vector(irisdat2$s_l)

  [1] 5.1 4.9 4.7 4.6 5.0 5.4 4.6 5.0 4.4 4.9 5.4 4.8 4.8
 [14] 4.3 5.8 5.7 5.4 5.1 5.7 5.1 5.4 5.1 4.6 5.1 4.8 5.0
 [27] 5.0 5.2 5.2 4.7 4.8 5.4 5.2 5.5 4.9 5.0 5.5 4.9 4.4
 [40] 5.1 5.0 4.5 4.4 5.0 5.1 4.8 5.1 4.6 5.3 5.0 7.0 6.4
 [53] 6.9 5.5 6.5 5.7 6.3 4.9 6.6 5.2 5.0 5.9 6.0 6.1 5.6
 [66] 6.7 5.6 5.8 6.2 5.6 5.9 6.1 6.3 6.1 6.4 6.6 6.8 6.7
 [79] 6.0 5.7 5.5 5.5 5.8 6.0 5.4 6.0 6.7 6.3 5.6 5.5 5.5
 [92] 6.1 5.8 5.0 5.6 5.7 5.7 6.2 5.1 5.7 6.3 5.8 7.1 6.3
[105] 6.5 7.6 4.9 7.3 6.7 7.2 6.5 6.4 6.8 5.7 5.8 6.4 6.5
[118] 7.7 7.7 6.0 6.9 5.6 7.7 6.3 6.7 7.2 6.2 6.1 6.4 7.2
[131] 7.4 7.9 6.4 6.3 6.1 7.7 6.3 6.4 6.0 6.9 6.7 6.9 5.8
[144] 6.8 6.7 6.7 6.3 6.5 6.2 5.9

dataframes (2 dimensional square arrays of vectors)

2 x dimensional “square” array with equal column and row lengths. Can contain data with multiple formats characters, facotors, integers, etc.

yuk <- data.frame(c("the", "enumeration", "of", "the", "constitution"), 6:10)
yuk

  c..the....enumeration....of....the....constitution..
1                                                  the
2                                          enumeration
3                                                   of
4                                                  the
5                                         constitution
  X6.10
1     6
2     7
3     8
4     9
5    10

rename columns of a data frame

names(yuk)[] <- c("short", "best")
yuk

         short best
1          the    6
2  enumeration    7
3           of    8
4          the    9
5 constitution   10

matrix

Same as a dataframe but can only contain one format (e.g. numbers or characters)

yok <- as.matrix(yuk)
yok

     short          best
[1,] "the"          " 6"
[2,] "enumeration"  " 7"
[3,] "of"           " 8"
[4,] "the"          " 9"
[5,] "constitution" "10"

lists

Arrays with constraints on “squareness” or data types.

lok <- list(yok, yuk)
lok

[[1]]
     short          best
[1,] "the"          " 6"
[2,] "enumeration"  " 7"
[3,] "of"           " 8"
[4,] "the"          " 9"
[5,] "constitution" "10"

[[2]]
         short best
1          the    6
2  enumeration    7
3           of    8
4          the    9
5 constitution   10

Classes in R

`numeric` and `integer`

numeric means number

is.numeric(4.2)

[1] TRUE

integer means a number that is not a fraction

is.integer(4.2)

[1] FALSE

Note the default here:

is.integer(4)

[1] FALSE

is.integer(as.integer(4))

[1] TRUE

We’ll need to ensure that certain numbers are integers later on, when we are estimating poisson models and/or doing bayesian data analysis.

characters

Characters are strings:

# this is a character
is.character("chapeau")

[1] TRUE

# this is not
is.character(4)

[1] FALSE

factors

A factor is a category. It can be ordered (e.g. an ordinal scale) or unordered (say a participant in a study, or a wave in a longitidunal study)

str(iris)

'data.frame':   150 obs. of  5 variables:
 $ Sepal.Length: num  5.1 4.9 4.7 4.6 5 5.4 4.6 5 4.4 4.9 ...
 $ Sepal.Width : num  3.5 3 3.2 3.1 3.6 3.9 3.4 3.4 2.9 3.1 ...
 $ Petal.Length: num  1.4 1.4 1.3 1.5 1.4 1.7 1.4 1.5 1.4 1.5 ...
 $ Petal.Width : num  0.2 0.2 0.2 0.2 0.2 0.4 0.3 0.2 0.2 0.1 ...
 $ Species     : Factor w/ 3 levels "setosa","versicolor",..: 1 1 1 1 1 1 1 1 1 1 ...

It’s really important to check that ordered categories are really ordered categories in your dataset.

There was is a famous retraction recently where a group found that religion was associated with immorality, however the countries in the the study had been coded as numbers, not as factors. The study’s effect entirely disappeared once this error was corrected!

Indexing in R

columns

# select second column of "yuk"
yuk[, 2]

[1]  6  7  8  9 10

rows

# select second row of yuk
yuk[2, ]

        short best
2 enumeration    7

rows and columns

#select first row and first column of yuk
yuk[1, 2]

[1] 6

selection by negation

# negate the first column of yuk
yuk[, -1]

[1]  6  7  8  9 10

# negate the second column of yuk
yuk[,-2]

[1] "the"          "enumeration"  "of"          
[4] "the"          "constitution"

Basic data wrangling in R

`c`

# select only the first and second cols of iris
iris_short2 <- iris[ ,c( 1, 2 ) ]
head(iris_short2)

  Sepal.Length Sepal.Width
1          5.1         3.5
2          4.9         3.0
3          4.7         3.2
4          4.6         3.1
5          5.0         3.6
6          5.4         3.9

`-c`

# select all columns but the first and second of iris
iris_short <- iris[ ,-c( 1, 2 ) ]
head(iris_short)

  Petal.Length Petal.Width Species
1          1.4         0.2  setosa
2          1.4         0.2  setosa
3          1.3         0.2  setosa
4          1.5         0.2  setosa
5          1.4         0.2  setosa
6          1.7         0.4  setosa

`cbind`

# for use with dataframes and matrices -- note that srings a are c
yokyuk<-cbind(yok,yuk)
yokyuk

         short best        short best
1          the    6          the    6
2  enumeration    7  enumeration    7
3           of    8           of    8
4          the    9          the    9
5 constitution   10 constitution   10

str(yokyuk)

'data.frame':   5 obs. of  4 variables:
 $ short: chr  "the" "enumeration" "of" "the" ...
 $ best : chr  " 6" " 7" " 8" " 9" ...
 $ short: chr  "the" "enumeration" "of" "the" ...
 $ best : int  6 7 8 9 10

`rbind`

rbind(yuk[,],yok[2:3])

         short best
1          the    6
2  enumeration    7
3           of    8
4          the    9
5 constitution   10
6  enumeration   of

use of `$` and []

#select the fifth row of the column
iris_short$Petal.Width[5]

[1] 0.2

use of `$` and [i:x]

#select the 5th-25th row of the column
iris_short$Petal.Width[5:25]

 [1] 0.2 0.4 0.3 0.2 0.2 0.1 0.2 0.2 0.1 0.1 0.2 0.4 0.4 0.3
[15] 0.3 0.3 0.2 0.4 0.2 0.5 0.2

Indexing for logical operations

definitions

== means “equals to”
!= means “not equals to”
> means “greater than”
< means “less than”
>=means “greater than or equal”
<= means “less than or equal”
! means “not”
& means “and”
| means “or”!
is.na means “is missing” (missing values are coded in R as NA)

evaluation using logical operators

create dataframe

# create data frame
df<-data.frame( x = c(1:10),y = c(11:20) )

evaluate cases

#evaluate cases in y that greater  than 15
df[,"y"] > 15

 [1] FALSE FALSE FALSE FALSE FALSE  TRUE  TRUE  TRUE  TRUE
[10]  TRUE

sum instances

# count these cases
sum(df[,"y"] > 15)

[1] 5

sum instances with a different operator

# count cases greater than or equal to 15
sum(df[,"y"] >= 15)

[1] 6

another methods

# another approach
sum(df$y >= 15)

[1] 6

using the `or` function

# combine operators
sum(df$y >= 15 | df$y <=11)

[1] 7

go meta

# go "meta"
sum(df$y >= 15 | df$y <= 11) == sum(df$x >=5 | df$x <=1 )

[1] TRUE

go meta-meta!

# go meta-meta
sum(sum(df$y >= 15 | df$y <= 11) == sum(df$x >=5 | df$x <=1 ))

[1] 1

use operators to modify data

# using assignment to modify data
df$x[df$x >=5 ] <- NA
df

using `is.na` and `!is.na`

sum(is.na(df$x))

[1] 6

sum(!is.na(df$x))

[1] 4

sum(is.na(df$x)) + sum(!is.na(df$x))

[1] 10

The basic structure of R commands

The four main elements of every R code are:

objects,
functions,
arguments
operators.

Figure 1 provides a simple example, that produces a new object which contains the mean of variable x.

$\label{fig:syntax-figure}The Basic Syntax of R$

Figure 1: The Basic Syntax of R

`mean`

The function mean generates the arithmetic mean of an input object:

# a function to assess the mean of a Sepal.Length
mean(iris$Sepal.Length)

[1] 5.843333

`sd`

The function sd gives us the standard deviation:

# standard deviation of Sepal.Length
sd(iris$Sepal.Length)

[1] 0.8280661

`summary`

# summary of the "Sepal Length" column
summary(iris$Sepal.Length)

   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
  4.300   5.100   5.800   5.843   6.400   7.900

# summary of the Iris data set
summary(iris)

  Sepal.Length    Sepal.Width     Petal.Length  
 Min.   :4.300   Min.   :2.000   Min.   :1.000  
 1st Qu.:5.100   1st Qu.:2.800   1st Qu.:1.600  
 Median :5.800   Median :3.000   Median :4.350  
 Mean   :5.843   Mean   :3.057   Mean   :3.758  
 3rd Qu.:6.400   3rd Qu.:3.300   3rd Qu.:5.100  
 Max.   :7.900   Max.   :4.400   Max.   :6.900  
  Petal.Width          Species  
 Min.   :0.100   setosa    :50  
 1st Qu.:0.300   versicolor:50  
 Median :1.300   virginica :50  
 Mean   :1.199                  
 3rd Qu.:1.800                  
 Max.   :2.500

Coding

The object needs to be specified inside of the function brackets as the x argument, in this case we define x = df .

Last, we assign the result of this function for later us via the <- operator to an object which we decided to call object.

In other words, we create a new object that can be further manipulated and contains information about the mean of a previously created object “x”. This structure represents the foundation of most operations in R.

Instead calling the mean function as above one could manually add all values of x dividing it by the number of x values.

Nevertheless, this would be very cumbersome.

For this reason, functions (pre-assembled lines of code) exist to reduce the amount of coding necessary.

These functions can be bundled into packages. R’s capacity for creating packages is main appeal of R as a statistical tool because community developed functions are available from a central repository called CRAN in the form of packages.

These packages can be installed in R with the command install.packages(“package name”).

It is important that you only need to install a package once on your machine, expect if you want to upgrade the package. Generally speaking you regularly want to upgrade your packages, but keep a permanent note in your code which version of a package you used when it was initially written.

Installing package

install these packages (we’ll be using them later)

install.packages("devtools") # installing packages

install.packages("remotes") # installing packages

install.packages("tidyverse") ## data wrangling and visualisation

install.packages("lme4") # multilevel modelling

install.packages("patchwork") # arranging multiple graphs

library(devtools)
devtools::install_github("strengejacke/sjPlot") # plots and tables

install.packages("papaja")  # writing APA documents

install.packages("table1") # summary tables

extra credit

devtools::install_github("easystats/easystats")

devtools::install_github("strengejacke/ggeffects")

super extra credit

if (!requireNamespace("remotes")) {
  install.packages("remotes")
}
remotes::install_github("paul-buerkner/brms")

devtools::install_github("stan-dev/cmdstanr")

Rolling your own code

Let’s use R to write a function. Recall that a factorial for a number $n$ is the product of all positive inters less than or equal to $n$. Thus the factorial for 5 = \[1 \times 2 \times 3 \times 4 \times 5\]

In R we can write a function:

# create a function to perform the factorial operation 
go_factorial <- function(x) {
  y <- 1
  for (i in 1:x) {
    y <- y * ((1:x)[i])
  }
  print(y)
}

Let’s try it out

# test of the `go_factorial` function
go_factorial(5)

[1] 120

Let’s see if this is the number that R’s factorial function produces:

# R's native factorial function
factorial(5)

[1] 120

We can use R’s == relational operator to evaluate whether the two functions are the same

# are the two functions equivalent for factorial five
go_factorial(5) == factorial(5)

[1] 120
[1] TRUE

We can make more complicated functions:

# function for factorial that throws warnings when the data that are entered are not appropriate. 
go_bayes_factorial <- function (x) {
  # check is the number is negative, positive or zero
  if (x  < 0) {
    print("not even Ashley Bloomfield could make a factorial for a negative number")
  } else if (x == 0) {
    print("the factorial of zero is defined as 1")
  } else {
    for (i in 1:x)
      y <- 1
    for (i in 1:x) {
      y <- y * ((1:x)[i])
    }
    print(y)
  }
}

We’ll come back to functions later. It’s useful to look at an example of a function so that you can see that R is much more than a calcultor. It is a tool to empower you for doing data anlysis in new and creative ways.

Coding etiquette

Keep your code legible and annotate

Why is this bad code?

df1<-data.frame(a=rnorm(10,1,1),b=rnorm(10,4,8),c=rnorm(10,8,1),d=rnorm(10,7,2))

Why is this better code?


# Create a data frame with four columns of randomly generated numbers specifying different means and standard deviations 
df1 <- data.frame(
  a = rnorm( 10, mean = 1, sd = 1 ),
  b = rnorm( 10, mean = 4, sd = 8 ),
  c = rnorm( 10, mean = 8, sd = 1 ),
  d = rnorm( 10, mean = 7, sd = 2 )
)

using R!

data summary

# basic summary
summary(iris)

  Sepal.Length    Sepal.Width     Petal.Length  
 Min.   :4.300   Min.   :2.000   Min.   :1.000  
 1st Qu.:5.100   1st Qu.:2.800   1st Qu.:1.600  
 Median :5.800   Median :3.000   Median :4.350  
 Mean   :5.843   Mean   :3.057   Mean   :3.758  
 3rd Qu.:6.400   3rd Qu.:3.300   3rd Qu.:5.100  
 Max.   :7.900   Max.   :4.400   Max.   :6.900  
  Petal.Width          Species  
 Min.   :0.100   setosa    :50  
 1st Qu.:0.300   versicolor:50  
 Median :1.300   virginica :50  
 Mean   :1.199                  
 3rd Qu.:1.800                  
 Max.   :2.500

table1::table1(~ Sepal.Length   + Sepal.Width   + Petal.Length  + Petal.Width |Species, data = iris  )

	setosa (N=50)	versicolor (N=50)	virginica (N=50)	Overall (N=150)
Sepal.Length
Mean (SD)	5.01 (0.352)	5.94 (0.516)	6.59 (0.636)	5.84 (0.828)
Median [Min, Max]	5.00 [4.30, 5.80]	5.90 [4.90, 7.00]	6.50 [4.90, 7.90]	5.80 [4.30, 7.90]
Sepal.Width
Mean (SD)	3.43 (0.379)	2.77 (0.314)	2.97 (0.322)	3.06 (0.436)
Median [Min, Max]	3.40 [2.30, 4.40]	2.80 [2.00, 3.40]	3.00 [2.20, 3.80]	3.00 [2.00, 4.40]
Petal.Length
Mean (SD)	1.46 (0.174)	4.26 (0.470)	5.55 (0.552)	3.76 (1.77)
Median [Min, Max]	1.50 [1.00, 1.90]	4.35 [3.00, 5.10]	5.55 [4.50, 6.90]	4.35 [1.00, 6.90]
Petal.Width
Mean (SD)	0.246 (0.105)	1.33 (0.198)	2.03 (0.275)	1.20 (0.762)
Median [Min, Max]	0.200 [0.100, 0.600]	1.30 [1.00, 1.80]	2.00 [1.40, 2.50]	1.30 [0.100, 2.50]

# plot relationship (what is happening here? )
plot( Sepal.Length   ~ Sepal.Width , data = iris )

model

library("tidyverse")  # plotting
library("ggeffects")  # plotting
library("ggplot2")  # plotting
library("patchwork") # arrange multiple plots
library("sjPlot")  # tables and plots

# basic model
m1<- lm(Sepal.Length ~ Sepal.Width, data = iris)
summary(m1)


Call:
lm(formula = Sepal.Length ~ Sepal.Width, data = iris)

Residuals:
    Min      1Q  Median      3Q     Max 
-1.5561 -0.6333 -0.1120  0.5579  2.2226 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept)   6.5262     0.4789   13.63   <2e-16 ***
Sepal.Width  -0.2234     0.1551   -1.44    0.152    
---
Signif. codes:  
0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 0.8251 on 148 degrees of freedom
Multiple R-squared:  0.01382,   Adjusted R-squared:  0.007159 
F-statistic: 2.074 on 1 and 148 DF,  p-value: 0.1519

results

# better summary method
sjPlot::tab_model(m1)

	Sepal.Length
Predictors	Estimates	CI	p
(Intercept)	6.53	5.58 – 7.47	<0.001
Sepal.Width	-0.22	-0.53 – 0.08	0.152
Observations	150
R² / R² adjusted	0.014 / 0.007

# plot the coefficients
sjPlot::plot_model(m1)

graph predicted effects

# plot the predicted relationship of Sepal Width on Sepal Length
p1 <- ggeffects::ggpredict(m1, terms = "Sepal.Width")
plot(p1)

What is the advantage of this graph?

pp1 <- plot(p1,
            add.data = TRUE,
            dot.alpha = .8,
            jitter = .2)
pp1

try another model

head(iris)

  Sepal.Length Sepal.Width Petal.Length Petal.Width Species
1          5.1         3.5          1.4         0.2  setosa
2          4.9         3.0          1.4         0.2  setosa
3          4.7         3.2          1.3         0.2  setosa
4          4.6         3.1          1.5         0.2  setosa
5          5.0         3.6          1.4         0.2  setosa
6          5.4         3.9          1.7         0.4  setosa

summary (m2 <- lm(Petal.Length ~ Petal.Width, data = iris))


Call:
lm(formula = Petal.Length ~ Petal.Width, data = iris)

Residuals:
     Min       1Q   Median       3Q      Max 
-1.33542 -0.30347 -0.02955  0.25776  1.39453 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept)  1.08356    0.07297   14.85   <2e-16 ***
Petal.Width  2.22994    0.05140   43.39   <2e-16 ***
---
Signif. codes:  
0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 0.4782 on 148 degrees of freedom
Multiple R-squared:  0.9271,    Adjusted R-squared:  0.9266 
F-statistic:  1882 on 1 and 148 DF,  p-value: < 2.2e-16

pp2<-plot(
  p2 <- ggeffects::ggpredict(m2, terms = "Petal.Width"),
  add.data = TRUE,
  dot.alpha = .8,
  jitter = .2
) 
pp2

## arange plots
library(patchwork)
pp1 / pp2 + plot_annotation(title = "two plots", tag_levels = "i")

Appendix: `#` symbol is for commenting code

In case you haven’t figured it out yet, the hash symbol # is for commenting:

r_comments <- 200 # here I am creating the variable for the number of time Jack says R is great

jill_roll <- 199 # here I'm creating a variable for the number of times Jill rolls here eyes

outcome <- log(r_comments) * sqrt(jill_roll) * pi # here I am illustrating some functions in r using the variables I just created

outcome # print outcome

[1] 234.8088

Rounding

It is often useful to round numbers:

round(outcome, digits = 2) # illustrate the useful `round` function.

[1] 234.81




## to be continued
```{.r .distill-force-highlighting-css}

Coding basics