Statistiek I

Introduction to R

Martijn Wieling

This lecture

General information about the course
Introduction to dataset used in the course
Why use statistics?
Introduction to RStudio and R
- R as calculator
- Variables
- Functions and help
- Importing data in R
- Viewing and modifying data
- Visualization in R
- Statistics in R

General information about the course setup (1)

Important information (including studiehandleiding and FAQ) on Brightspace!
Teacher of lectures:
- Martijn Wieling, m.b.wieling@rug.nl, 1311.434
Teachers for lab sessions:
- Janiek de Rijke, j.de.rijke.1@student.rug.nl
- Stijn Schreven, s.schreven@student.rug.nl
- Patrick Jans, p.m.jans@student.rug.nl

General information about the course setup (2)

7 weekly lectures:
- Slides will be made available via Brightspace
- Interactive questions during lecture
7 weekly lab sessions
- You should have registered via Brightspace for one of the groups
  - If problems, contact secretary: sec-MILLC@rug.nl
- No switching when groups are full
- Attendance obligatory!
- Finishing lab exercises results in at most 1 bonus point
  - Only when final test score $T$ at least 5.0
  - Calculation: $T + 0.25 \times P\, \textrm{(max 2)} \times H\, \textrm{(max 2)}$

Language policy in this course

Lecture slides, book and lab sessions are in English. Why?
- Most statistics terminology you encounter will be in English
You may choose the language of the lab reports (either Dutch or English)
The final exam is in Dutch
- (but with English-Dutch translation of statistical terminology when necessary)

Some remarks about the lab sessions

Lab reports due one week after lab
Late or sub-optimal lab report: (max.) 1 point (out of 2)
Lab report over 1 week late or insufficient: 0 points
Exam requirement: average lab score of 1 point, with at most two times 0 points
Lab attendance required:
- You can miss at most 1 lab session, but timely lab report ($\geq$ 1 point) required
- If you miss 2 or more lab sessions: course failed
Why required lab attendance?
- Actively participating in lab session increases chances of passing the exam!
- Lab score correlates significantly ($r = .4, p < .001$) with exam grade
Lab score of last year may be used, but only as a whole (same restrictions)

Lab reports and plagiarism

Lab sessions are individual, and lab reports are to be made individually
Questions about lab exercises should be addressed to lab teachers
It is never allowed to copy from another student or external source (= fraud)
Allowing another student to copy from you is likewise not allowed (= fraud)
Using ChatGPT (etc.) to provide answers to exercises is not allowed (= fraud)
If fraud is suspected, the board of examiners are always notified
- Sanctions include a fraud registration and usually removal from the course
Better safe than sorry!

Goals of this course

Understand basics of descriptive and inferential statistics
- Emphasis on statistical reasoning
- Practical approach, but some mathematics to help understand the concepts
Understand and apply basic statistical analyses
Report on results of statistical analyses
Understand reports using statistical analyses
Conduct basic statistical analyses in R

Statistics in Language Studies

Many experiments are conducted in communication, information science and linguistics
- Effect of comics vs. normal text on understanding?
- Effect of algorithm on quality of an automatically generated summary?
- Influence of sex on learning a second language?
Availability of online data increases opportunities for statistical analysis (e.g., Digital Humanities)
In this course we will work with several real world datasets

The main dataset used during this course

Dataset based on a survey of students who followed this course in the past:
- Age, sex, handedness, study, etc.
- Information about language history
- Information about English use and (subjective) proficiency
We are interested in investigating which factors are related to English proficiency
- Measured by English grade in high school
- And via an automatically calculated approximate measure of proficiency (English score) based on a speech sample

Some of the data (1)

participant	year	sex	bl_edu	study	english_grade	english_score
1	2020	M	N	LING	5.0	6.10
2	2020	F	N	CIS	6.0	6.67
3	2020	F	N	CIS	7.0	7.42
4	2020	F	N	LING	8.0	9.10
5	2020	F	N	CIS	7.0	7.47
6	2020	M	N	LING	8.4	8.14
7	2020	F	N	LING	8.0	7.65
8	2020	F	N	CIS	6.0	7.35
9	2020	F	N	LING	8.0	8.54
10	2020	M	N	IS	8.0	8.39
11	2020	F	N	LING	7.0	7.98

Some of the data (2)

participant	year	sex	bl_edu	study	english_grade	english_score
103	2021	F	N	LING	6	5.19
104	2021	M	N	LING	7	6.82
105	2021	M	N	LING	8	8.21
106	2021	F	N	CIS	7	7.34
107	2021	F	N	LING	7	6.59
108	2021	F	N	LING	8	7.55
109	2021	F	N	LING	7	7.19
110	2021	F	Y	LING	8	7.63
111	2021	F	N	LING	6	6.58
112	2021	M	N	IS	8	8.89
113	2021	M	N	CIS	7	6.76

Some of the data (3)

participant	year	sex	bl_edu	study	english_grade	english_score
225	2022	M	N	LING	8.0	9.02
226	2022	F	N	LING	8.0	7.44
227	2022	F	N	CIS	9.0	9.74
228	2022	F	N	CIS	7.0	9.06
229	2022	F	N	CIS	8.0	8.35
230	2022	F	N	LING	7.3	8.55
231	2022	F	N	CIS	6.0	6.51
232	2022	F	N	LING	7.0	7.87
233	2022	M	N	CIS	6.0	7.22
234	2022	F	N	LING	7.0	7.08
235	2022	F	N	OTHER	8.0	8.69

Some of the data (4)

participant	year	sex	bl_edu	study	english_grade	english_score
316	2023	M	N	OTHER	6.0	6.86
317	2023	M	N	LING	8.5	8.07
318	2023	M	N	IS	8.0	7.72
319	2023	F	N	LING	7.4	7.53
320	2023	F	Y	CIS	8.0	9.23
321	2023	M	N	IS	7.0	7.64
322	2023	M	N	IS	7.0	7.82
323	2023	F	N	LING	8.0	8.65
324	2023	M	N	LING	9.3	9.09
325	2023	M	N	IS	6.0	7.61
326	2023	F	N	LING	8.0	8.26

Some of the data (5)

participant	year	sex	bl_edu	study	english_grade	english_score
422	2024	F	N	CIS	7	7.26
423	2024	F	N	LING	7	7.62
424	2024	F	N	OTHER	7	8.40
425	2024	M	N	LING	7	8.00
426	2024	F	N	CIS	8	8.77
427	2024	F	N	CIS	7	7.78
428	2024	M	Y	IS	9	9.50
429	2024	F	N	CIS	7	7.55
430	2024	F	N	CIS	6	6.81
431	2024	F	N	LING	7	7.43
432	2024	F	N	LING	7	7.05

Question 1

Question 2

We use statistics because…

We would like to make sense of the data
For this we need to:
- Summarize the data (descriptive statistics)
- Assess relationships in the data (inferential statistics)
  - (During other courses, some of you will have already encountered inferential statistical tests, such as the $t$-test, which can be used for this)
The requirement of the data is that it is variable (there must be variation)
Note that statistics is not mathematics (it’s data analysis)!

What you will learn during this course (1)

Descriptive statistics (describe data without conclusions)
- Measures of central tendency and spread
  - E.g.: mean English grade (7.3), and range of English grades (5 - 9.5)
- Visualization
  - E.g.: showing number of participants per study with a bar plot

What you will learn during this course (2)

Inferential statistics (link findings based on sample to population)
- Comparing 2 groups
  - E.g.: is the pronunciation of females better than males?
- Associations between 2 numerical variables
  - E.g.: is the proficiency in English dependent on age?
- Internal consistency of questions in a survey
  - E.g.: does a group of questions measure a single construct?
How to do statistics in R (this lecture)
- And how to make reproducible lab reports in R

What your lab reports will look like

Why do we use `R`?

Very nice reproducible lab reports (no copy-paste necessary!)
Other advantages of R compared to (e.g.,) SPSS
- Free for everybody
- Customizable: people can create their own statistical functions
- State-of-the-art statistical methods are integrated very quickly
Also some disadvantages:
- No substantial graphical user interface: typing instead of clicking
- Takes more time to learn
- State-of-the-art statistical methods sometimes contain bugs

Our tool: RStudio (frontend to `R`)

RStudio: quick overview

Basic functionality: `R` as calculator

# Addition (this is a comment: preceded by '#')
5 + 5

[1] 10

# Multiplication
5 * 3

[1] 15

# Division
5 / 3

[1] 1.6667

Basic functionality: using variables

a <- 5 # store a single value; instead of "<-" you can also use "="
a # display the value

[1] 5

b <- a * a # b contains the value of multiplying a with itself
b

[1] 25

(d <- NA) # set value of d to missing (NA) and show value

[1] NA

Storing multiple values in a variable

b <- c(2,4,6,7,8) # store a series of values in a vector (reusing variable b)
b

[1] 2 4 6 7 8

b[4] <- a # assign value 5 (stored in 'a') to the 4th element of vector b
b

[1] 2 4 6 5 8

b <- c(b,NA) # add element NA to b
b

[1]  2  4  6  5  8 NA

Question 3

Basic functionality: using functions

b # show values in variable b (b contains a vector: a list of values)

[1]  2  4  6  5  8 NA

mn <- mean(b) # calculating the mean and storing in variable mn
mn

[1] NA

# mn is NA (missing) as one of the values is missing
mean(b, na.rm = TRUE) # we can use the function parameter na.rm to ignore NAs

[1] 5

# But which parameters does a function have: use help!
help(mean) # alternatively: ?mean

Basic functionality: a help file

Question 4

Getting data into `R`: exporting a dataset

Getting data into `R`: importing a dataset

setwd('C:/Users/Martijn/Desktop/Statistiek-I/HC1') # set working directory
dat <- read.csv('survey.csv',sep=',',dec='.') # reads csv file from work dir
str(dat) # shows structure of the data frame (i.e. table is 2-dimensional)

'data.frame':   500 obs. of  7 variables:
 $ participant  : int  1 2 3 4 5 6 7 8 9 10 ...
 $ year         : int  2020 2020 2020 2020 2020 2020 2020 2020 2020 2020 ...
 $ sex          : chr  "M" "F" "F" "F" ...
 $ bl_edu       : chr  "N" "N" "N" "N" ...
 $ study        : chr  "LING" "CIS" "CIS" "LING" ...
 $ english_grade: num  5 6 7 8 7 8.4 8 6 8 8 ...
 $ english_score: num  6.1 6.67 7.42 9.1 7.47 ...

dim(dat) # number of rows and columns of dataset

[1] 500   7

Investigating the data: using `head`

head(dat) # show first few rows of dat

  participant year sex bl_edu study english_grade english_score
1           1 2020   M      N  LING           5.0        6.1000
2           2 2020   F      N   CIS           6.0        6.6736
3           3 2020   F      N   CIS           7.0        7.4229
4           4 2020   F      N  LING           8.0        9.0964
5           5 2020   F      N   CIS           7.0        7.4698
6           6 2020   M      N  LING           8.4        8.1369

Investigating the data: RStudio viewer

Accessing table data using numbers

Access parts of table by specifying row and/or column numbers
dat[a,b]:
- a indicates the selected rows of dat
- b indicates the selected columns of dat

dat[1,] # values in first row (dat[,1]: values in first column)

  participant year sex bl_edu study english_grade english_score
1           1 2020   M      N  LING             5           6.1

dat[c(1,5),c(1,2,3)] # values in rows 1 and 5 and columns 1, 2 and 3

  participant year sex
1           1 2020   M
5           5 2020   F

Accessing table data using names (1)

Additionally, we can access parts of the table by specifying the names of the columns we want to look at

dat[c(1,3,5),c("participant","study")] # rows 1, 3 and 5, and 2 named columns

  participant study
1           1  LING
3           3   CIS
5           5   CIS

Accessing table data using names (2)

We may also select a single column by its name (not nr.) using the $ operator
- E.g., dat$sex accesses the column sex of dat

head(dat$sex,200) # show sex of first 200 students

  [1] "M" "F" "F" "F" "F" "M" "F" "F" "F" "M" "F" "M" "F" "M" "M" "F" "M" "F"
 [19] "F" "M" "M" "F" "F" "M" "F" "F" "F" "F" "F" "F" "F" "M" "F" "F" "F" "F"
 [37] "M" "M" "F" "F" "F" "F" "F" "F" "F" "M" "M" "F" "F" "F" "M" "F" "F" "M"
 [55] "F" "F" "F" "F" "F" "F" "F" "F" "F" "F" "F" "M" "F" "F" "M" "F" "F" "F"
 [73] "F" "F" "F" "F" "F" "F" "F" "F" "F" "F" "F" "F" "M" "F" "F" "F" "F" "F"
 [91] "F" "F" "M" "F" "F" "F" "M" "M" "F" "F" "F" "F" "F" "M" "M" "F" "F" "F"
[109] "F" "F" "F" "M" "M" "F" "M" "F" "F" "F" "F" "F" "F" "F" "F" "F" "F" "F"
[127] "M" "F" "M" "M" "F" "F" "F" "F" "F" "F" "F" "F" "M" "M" "F" "F" "F" "M"
[145] "M" "F" "F" "F" "M" "M" "M" "F" "F" "F" "M" "M" "F" "F" "F" "F" "F" "F"
[163] "F" "F" "M" "F" "M" "F" "F" "F" "M" "F" "F" "M" "M" "M" "M" "F" "F" "F"
[181] "F" "F" "F" "F" "F" "F" "F" "F" "M" "F" "F" "M" "M" "F" "M" "F" "M" "M"
[199] "F" "F"

Storing accessed table data

tmp <- dat[5:8,c(1,3)] # store columns 1 and 3 for rows 5 to 8 in variable tmp 
tmp # show what is stored in variable tmp

  participant sex
5           5   F
6           6   M
7           7   F
8           8   F

Question 5

Accessing table data using conditional indexing (1)

Conditional indexing allows us the select parts of the data on the basis of conditions

tmp <- dat[dat$sex == 'M',] # only observations for male participants
head(tmp)

   participant year sex bl_edu study english_grade english_score
1            1 2020   M      N  LING           5.0        6.1000
6            6 2020   M      N  LING           8.4        8.1369
10          10 2020   M      N    IS           8.0        8.3883
12          12 2020   M      N OTHER           7.0        6.1467
14          14 2020   M      N    IS           9.0        9.1297
15          15 2020   M      N   CIS           7.0        8.2633

Accessing table data using conditional indexing (2)

Methods to combine conditions:
- and: &
- or: |

# only participants who study IS *and- are male
tmp <- dat[dat$sex == 'M' & dat$study == 'IS',] 
head(tmp)

   participant year sex bl_edu study english_grade english_score
10          10 2020   M      N    IS             8        8.3883
14          14 2020   M      N    IS             9        9.1297
17          17 2020   M      N    IS             8        7.1360
20          20 2020   M      N    IS             8        8.4594
21          21 2020   M      N    IS             7        8.2508
32          32 2020   M      N    IS             7        7.5851

Accessing table data using conditional indexing (3)

Invert a condition with ! (not)
- is not equal to: !=

# only females (i.e. not males) *or* everybody with an English grade over 7
tmp <- dat[dat$sex != 'M' | dat$english_grade > 7,] 
tail(tmp) # tail shows final 6 rows

    participant year sex bl_edu study english_grade english_score
493         493 2024   M      N    IS           8.0        8.1840
494         494 2024   M      N    IS           8.0        8.0375
495         495 2024   F      N OTHER           8.0        8.4751
497         497 2024   F      N OTHER           7.0        7.1963
498         498 2024   F      N  LING           6.0        7.2741
500         500 2024   M      N    IS           7.5        6.2609

Question 6

Supplementing the data: adding columns (1)

Frequently, you need to add columns to the data, for example by computing a new value on the basis of the values in two columns
- the operator $ helps us to do that

# new column 'diff': English grade - English proficiency score
dat$diff <- dat$english_grade - dat$english_score 
head(dat)

  participant year sex bl_edu study english_grade english_score     diff
1           1 2020   M      N  LING           5.0        6.1000 -1.09996
2           2 2020   F      N   CIS           6.0        6.6736 -0.67357
3           3 2020   F      N   CIS           7.0        7.4229 -0.42291
4           4 2020   F      N  LING           8.0        9.0964 -1.09636
5           5 2020   F      N   CIS           7.0        7.4698 -0.46977
6           6 2020   M      N  LING           8.4        8.1369  0.26309

Supplementing the data: adding columns (2)

Conditional indexing allows us additional flexibility

dat$pass_fail <- 'PASS' # new column, initially PASS for everybody
dat[dat$english_grade < 5.5,]$pass_fail <- 'FAIL' # if grade too low, then FAIL
tail(dat[dat$english_grade > 4 & dat$english_grade < 6, 2:9]) # show subset of data

    year sex bl_edu study english_grade english_score      diff pass_fail
341 2023   F      N    IS           5.8        5.7252  0.074803      PASS
359 2023   F      N  LING           5.0        6.1166 -1.116598      FAIL
373 2023   F      Y   CIS           5.0        4.3000  0.700000      FAIL
395 2023   F      N  LING           5.8        6.0576 -0.257642      PASS
399 2023   F      N  LING           5.8        5.1720  0.627971      PASS
469 2024   F      N  LING           5.0        5.9713 -0.971288      FAIL

Question 7

Visualization in `R`

Many basic visualization options are available in R
In this course, we will learn how to use the following functions (list not exhaustive):
- barplot() (illustrated in the following)
- plot()
- boxplot()
- hist()
- qqnorm() and qqline()

Example of using a plotting function: barplot()

The bar plot is used to visualize frequencies of categorical variables

(counts <- table(dat$sex)) # first create frequency table


  F   M 
346 154

barplot(counts)

Graphical parameters

There are various graphical parameters to allow you to customize your graphics

barplot(counts, col = c("pink", "lightblue"), ylim = c(0, 350), main = "My barplot", 
    xlab = "Sex", ylab = "Frequency")

Question 8

Another example: segmented bar plot

(counts <- table(dat$sex,dat$study))

   
    CIS  IS LING OTHER
  F  99  26  179    42
  M  24  98   16    16

barplot(counts, col=c("pink","lightblue"), legend = c('F','M'), ylim=c(0,185))

Statistics in `R`

The main purpose of R is to conduct statistical analyses
Many different functions to obtain descriptive and inferential statistics are available in R
The following examples illustrate how to conduct some statistical analyses in R
- The why and what is covered in the next lectures

Descriptive statistics: central tendency

mean(dat$english_score) # mean of all people for English score

[1] 7.6178

mean(dat[dat$sex == 'F',]$english_score) # mean of females for English score

[1] 7.5342

median(dat$english_score) # median of all people for English score

[1] 7.6377

Descriptive statistics: spread

min(dat$english_score) # minimum value

[1] 4.3

max(dat$english_score) # maximum value

[1] 9.7421

var(dat$english_score) # variance: average squared deviation from mean

[1] 0.85021

sd(dat$english_score) # standard deviation (square root of variance)

[1] 0.92207

Descriptive statistics: frequency tables

table(dat$sex)


  F   M 
346 154

table(dat$study)


  CIS    IS  LING OTHER 
  123   124   195    58

Question 9

Descriptive statistics: cross tables

table(dat$sex,dat$study)

   
    CIS  IS LING OTHER
  F  99  26  179    42
  M  24  98   16    16

table(dat$sex,dat$bl_edu)

Inferential statistics

A large number of statistical inference functions are available in R
In this course we will mainly use the function lm() (linear regression)

Example of inferential statistics: regression

Assessing average group differences for a numerical variable (lecture 5)

summary(lm(english_grade ~ bl_edu, data=dat))


Call:
lm(formula = english_grade ~ bl_edu, data = dat)

Residuals:
   Min     1Q Median     3Q    Max 
-2.640 -0.246 -0.246  0.754  2.154 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept)   7.2457     0.0404  179.28   <2e-16 ***
bl_eduY       0.3947     0.1318    2.99   0.0029 ** 
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 0.86 on 498 degrees of freedom
Multiple R-squared:  0.0177,    Adjusted R-squared:  0.0157 
F-statistic: 8.97 on 1 and 498 DF,  p-value: 0.00289

Recap

In this lecture, we’ve covered the basics of R
- R as calculator
- Variables
- Functions and help
- Importing data in R
- Viewing and modifying data
- Some examples of visualizations
- Some examples of descriptive and inferential statistics
See Winter (Ch. 1 and 2) for more information about the functionality of R
In the lab session, you will experiment with using R
Next lecture: Descriptive statistics
Evaluation: if at least 50 people evaluate the lecture, exam-like question visible

Please evaluate this lecture!

Exam question

Questions?

Thank you for your attention!

https://www.martijnwieling.nl

m.b.wieling@rug.nl

Statistiek I

This lecture

General information about the course setup (1)

General information about the course setup (2)

Language policy in this course

Some remarks about the lab sessions

Lab reports and plagiarism

Goals of this course

Statistics in Language Studies

The main dataset used during this course

Some of the data (1)

Some of the data (2)

Some of the data (3)

Some of the data (4)

Some of the data (5)

Question 1

Question 2

We use statistics because…

What you will learn during this course (1)

What you will learn during this course (2)

What your lab reports will look like

Why do we use R?

Our tool: RStudio (frontend to R)

RStudio: quick overview

Basic functionality: R as calculator

Basic functionality: using variables

Storing multiple values in a variable

Question 3

Basic functionality: using functions

Basic functionality: a help file

Question 4

Getting data into R: exporting a dataset

Getting data into R: importing a dataset

Investigating the data: using head

Investigating the data: RStudio viewer

Accessing table data using numbers

Accessing table data using names (1)

Accessing table data using names (2)

Storing accessed table data

Question 5

Accessing table data using conditional indexing (1)

Accessing table data using conditional indexing (2)

Accessing table data using conditional indexing (3)

Question 6

Supplementing the data: adding columns (1)

Supplementing the data: adding columns (2)

Question 7

Visualization in R

Example of using a plotting function: barplot()

Graphical parameters

Question 8

Another example: segmented bar plot

Statistics in R

Descriptive statistics: central tendency

Descriptive statistics: spread

Descriptive statistics: frequency tables

Question 9

Descriptive statistics: cross tables

Inferential statistics

Example of inferential statistics: regression

Recap

Please evaluate this lecture!

Exam question

Questions?

Why do we use `R`?

Our tool: RStudio (frontend to `R`)

Basic functionality: `R` as calculator

Getting data into `R`: exporting a dataset

Getting data into `R`: importing a dataset

Investigating the data: using `head`

Visualization in `R`

Statistics in `R`