This document is written using R Markdown. The source code is available in 01-intro-lab.R.
- Create and manipulate vectors (numeric and factor)
- Compute basic summary statistics
- Manipulate rectangular data structure (data frames)
- Interact with external data sets
There are several types of objects' in R. For the time being, we will mainly focus on vectors and data frames.
Suppose that we recorded the following reaction times in a simple psychophysical experiment: (Heathcote, 1996)
474.688 506.445 524.081 530.672 530.869
566.984 582.311 582.940 603.574 792.358
We can represent this series of measurements as follows:
x <- c(474.688, 506.445, 524.081, 530.672, 530.869, 566.984, 582.311, 582.94, 603.574,
792.358)
Note that the decimal point follows English notation. It is also recommended to use <- instead of = for variable assignment.
Now, to display the values, we can simply type x at the R prompt:
x
## [1] 474.7 506.4 524.1 530.7 530.9 567.0 582.3 582.9 603.6 792.4
We can access the first or third element of x (i.e., the first observation) by using the corresponding index position (integer starting at 1) enclosed in square brackets:
x[1]
## [1] 474.7
x[3]
## [1] 524.1
We could also display the first three observations using range notation or by giving explicit values, e.g.
x[1:3]
## [1] 474.7 506.4 524.1
x[c(1, 2, 3)]
## [1] 474.7 506.4 524.1
The c() (concatenate) command tells R to group together values in a vector. We call such operation indexation. When values correspond to different statistical units, this allow to perform individual selection.
It is also possible to use logical filters to select part of a variable. For example, if we want to keep only values that are less or equal to 600, we would use:
x[x <= 600]
## [1] 474.7 506.4 524.1 530.7 530.9 567.0 582.3 582.9
This instruction will return those values of x that fulfill the criterion x less or equal to 600. If we are interested in returning the position (index) of these values in x, we can use
which(x <= 600)
## [1] 1 2 3 4 5 6 7 8
We can check that there are 10 observations in total, and what are the minimum and maximum values of x, for instance, using built-in R functions:
length(x)
## [1] 10
min(x)
## [1] 474.7
max(x)
## [1] 792.4
The latter can be grouped together using c() as seen before, e.g.
c(min(x), max(x))
## [1] 474.7 792.4
or, in shorter form,
range(x)
since the range() function returns the minimum and maximum values of a list of numbers.
Moreover, we can save the above results in another variable, say, res:
res <- c(min(x), max(x))
To display values stored in res, we would just type the name of the variable at R prompt or use print(res). However, in interactive mode, we rarely need to use a print() statement:
res
print(res)
R has a lot of built-in commands, including functions for basic data transformation and arithmetic operations.
x[1] + x[2]
## [1] 981.1
or equivalently
sum(x[1:2])
To convert values stored in x to their log counterpart (by default, natural logarithm), we would use:
log(x)
## [1] 6.163 6.227 6.262 6.274 6.275 6.340 6.367 6.368 6.403 6.675
The base for the logarithm can be changed by using the named parameter base= when calling the function, e.g. log(100, base=10).
In most cases, it is useless to write an explicit loop when we can benefit from R vectorized operations. (In the following example the print() statement is mandatory.)
for (i in 1:10) print(log(x[i]))
## [1] 6.163
## [1] 6.227
## [1] 6.262
## [1] 6.274
## [1] 6.275
## [1] 6.34
## [1] 6.367
## [1] 6.368
## [1] 6.403
## [1] 6.675
Variables live in R workspace, and they can be updated at any time. Using a statement like
x <- log(x)
would replace all values of x by their log, and old values would be lost.
Missing values are represented by the symbol NA (not available).
x[5]
## [1] 530.9
x[5] <- NA
x
## [1] 474.7 506.4 524.1 530.7 NA 567.0 582.3 582.9 603.6 792.4
We can check at any time what variables are available in R workspace with ls(): (You can safely ignore the bib variable.)
ls()
## [1] "bib" "i" "res" "x"
Don't forget the parentheses! To delete a variable, we can use rm(x), for example.
- Display the last two observations of
x.- Compute the minimum and maximum values of the updated variable
x. Seehelp(min)orhelp(max).- How would you replace the 5th observation (set to missing) with the mean computed from the remaining observations. See
help(mean).
In the preceding section, we have discussed the representation of numerical values in R. Categorical variables are best expressed as factors in R, rather than simple strings.
In the following example, we generate 10 random values (male or female) for a variable gender. Sampling is done with replacement.
gender <- sample(c("male", "female"), size = 10, replace = TRUE)
gender
## [1] "male" "male" "female" "female" "male" "male" "female" "male"
## [9] "female" "female"
str(gender)
## chr [1:10] "male" "male" "female" "female" "male" "male" ...
As gender is just a vector of strings, we will convert it to a factor using the factor(): R will now associate levels to unique values found in gender.
gender <- factor(gender)
str(gender)
## Factor w/ 2 levels "female","male": 2 2 1 1 2 2 1 2 1 1
We can tabulate gender's levels using table():
table(gender)
## gender
## female male
## 5 5
Here is another example where we start with numeric codes, and then associate labels to each code.
cond <- c(1, 2, 1, 2, 2, 2, 1, 1, 2)
table(cond)
## cond
## 1 2
## 4 5
cond <- factor(cond, levels = c(1, 2), labels = c("A", "B"))
table(cond)
## cond
## A B
## 4 5
To sum up, factors are represented as numerical codes, but it is always a good idea to associate labels to them.
Data frames are special R objects that can hold mixed data type (numeric and factor). This is a convenient placeholder for rectangular data sets as we will see later during the course.
Suppose you are now given two series of RTs, which were collected in two separate sessions on the same 10 subjects: (example from help(timefit, package=retimes))
x1 <- c(451.536, 958.612, 563.538, 505.735, 1266.825, 860.663, 457.707, 268.679,
587.303, 669.594)
x2 <- c(532.474, 525.185, 1499.471, 480.732, 631.752, 672.419, 322.341, 571.356,
428.832, 680.848)
It is easy to manipulate these two vectors separately. To compute the mean in each condition, we would use
mean(x1)
## [1] 659
mean(x2)
## [1] 634.5
Likewise, to get reaction times for the first individual we would write
x1[1]
## [1] 451.5
x2[1]
## [1] 532.5
However, a more elegant way to represent such data is to make it explicit that data are ordered and that each pair of values correspond to the same subject. A first attempt would be to simply create a 2-column matrix, like this
x12 <- cbind(x1, x2)
head(x12, n = 3) # or x12[1:3,]
## x1 x2
## [1,] 451.5 532.5
## [2,] 958.6 525.2
## [3,] 563.5 1499.5
In this case, line numbers (row names in R parlance) would help to identify each subject. However, it would be more handy to create a variable holding subjects' ID.
id <- paste("id", 1:10, sep = "")
id
## [1] "id1" "id2" "id3" "id4" "id5" "id6" "id7" "id8" "id9" "id10"
d <- data.frame(id, x1, x2)
head(d)
## id x1 x2
## 1 id1 451.5 532.5
## 2 id2 958.6 525.2
## 3 id3 563.5 1499.5
## 4 id4 505.7 480.7
## 5 id5 1266.8 631.8
## 6 id6 860.7 672.4
- Display the second RT for the 8th subject.
- Compute the range of observed values for the first session (
x1).- Check whether all individual values are greater in the second session, compared to the first session.
Here is an alternate way for representing the same data set, this time using two variables to code for subjects and condition number, and one variable holding associated RTs. Note that we will use an external package that should be installed first in R directory (this is done automatically by the system, though).
if (!require(reshape2)) install.packages("reshape2")
## Loading required package: reshape2
dm <- melt(d)
## Using id as id variables
head(dm)
## id variable value
## 1 id1 x1 451.5
## 2 id2 x1 958.6
## 3 id3 x1 563.5
## 4 id4 x1 505.7
## 5 id5 x1 1266.8
## 6 id6 x1 860.7
Note that if the package is already installed on your system, you can simply type
library(reshape2)
Our data frame now has 20 lines, instead of 10 (d).
summary(dm)
## id variable value
## id1 :2 x1:10 Min. : 269
## id10 :2 x2:10 1st Qu.: 475
## id2 :2 Median : 567
## id3 :2 Mean : 647
## id4 :2 3rd Qu.: 674
## id5 :2 Max. :1500
## (Other):8
str(dm)
## 'data.frame': 20 obs. of 3 variables:
## $ id : Factor w/ 10 levels "id1","id10","id2",..: 1 3 4 5 6 7 8 9 10 2 ...
## $ variable: Factor w/ 2 levels "x1","x2": 1 1 1 1 1 1 1 1 1 1 ...
## $ value : num 452 959 564 506 1267 ...
We can access any variable by using the name of the data frame, followed by the name of the variable as follows:
dm$variable
## [1] x1 x1 x1 x1 x1 x1 x1 x1 x1 x1 x2 x2 x2 x2 x2 x2 x2 x2 x2 x2
## Levels: x1 x2
The $ operator is used to select a specific variable in a data frame, hence the need to have variables names.
Among other things, it is now possible to index values of the response variable depending on the values taken by other variables, like in a dictionnary (key-value). E.g.,
dm$value[dm$variable == "x1"]
## [1] 451.5 958.6 563.5 505.7 1266.8 860.7 457.7 268.7 587.3 669.6
or
dm$variable[dm$value > 567] # dm$variable[dm$value > median(dm$variable)]
## [1] x1 x1 x1 x1 x1 x2 x2 x2 x2 x2
## Levels: x1 x2
Finally, should we want to update variable names, we could use:
names(dm) <- c("subject", "condition", "RT")
head(dm, n = 3)
## subject condition RT
## 1 id1 x1 451.5
## 2 id2 x1 958.6
## 3 id3 x1 563.5
- There is a 'slight' problem with the way subjects' ID were handled. Can you fix it? See
help(factor)and theordered=parameter.- Display all observed values for the second subject.
- Compute the range of observed values in the second session.
R has a built-in data format to save data files.
save(dm, file = "data_lab1.rda")
We can also use the .RData extension. To load data saved as RData files, we can use load(). The full pathname should be given to this command. Otherwise, we might want to change our current working directory (setwd(), or Session > Set Working Directory > Choose Directory in RStudio).
load("data_lab.rda")
## Warning: impossible d'ouvrir le fichier compressé 'data_lab.rda', cause
## probable : 'No such file or directory'
## Error: impossible d'ouvrir la connexion
To save data in CSV format, we will replace save() by write.csv(). The default settings for this command correspond to English conventions (dot as decimal separator, comma as record separator). A localized version (French) is available with read.csv2().
write.csv(dm, file = "data_lab1.csv")
dir(pattern = ".csv")
## [1] "data_lab1.csv"
To read a CSV file, we just replace write.csv() with read.csv().
rm(dm) # clean up the workspace
dm <- read.csv("data_lab1.csv")
ls()
## [1] "bib" "cond" "d" "dm" "gender" "i" "id" "res"
## [9] "x" "x1" "x12" "x2"
More generally, the read.table() command can be used to process a large majority of data files (tab or space delimited files, specific codes for missing values, etc.). See help(read.table) for more information.
Here are the number of words recalled by 5 subjects. Factor levels are given as: Neg, Neu, Pos (http://personality-project.org/).
Jim, 32, 15, 45
Victor, 30, 13, 40
Faye, 26, 12, 42
Ron, 22, 10, 38
Jason, 29, 8, 35
dfrm, will have 3 columns named subject, condition, and words.If you feel comfortable with IO operations in R, you can work directly with the data file words.dat.
The file brain_size.csv contains data from a study on the relationship between brain size and weight and intelligence (Willerman et al. 1991).
Heathcote A (1996). “RTSYS: A DOS application for the analysis of
reaction time data.” Behavior Research Methods, Instruments, &
Computers, 28(3), pp. 427-445.
Willerman L, Schultz R, Rutledge J and Bigler E (1991). “In Vivo Brain Size and Intelligence.” Intelligence, 15, pp. 223-228.