Stats with R and RStudio
Probabilité et statistique pour la biologie (STAT1)
Jacques van Helden
2017-09-12
Scope
In this session we will explore basic manipulations of variables.
- Assigning a value to a variable
- Basic operations on numbers
R is a calculator
Convention:
- Dark boxes: commands to type in RStudio Console (bottom-left panel).
- White boxes: the result you should obtain.
Example: compute a simple addition.
[1] 7
Assign a value to a variable
In R <- means “create a variable and assign its value.”
Example:
- create a variable named \(a\),
- assign the value \(2\) to this variable,
- print the result.
[1] 2
Computing with variables
Example:
- create a variable named \(b\) having value \(5\),
- compute \(a + b\) and store the result in a variable named \(c\),
- print the result.
b <- 5
c <- a + b
print(c)
[1] 7
Variables need to be updated
Example:
- change the value of \(a\) to \(3\),
- print the value of \(c\)
- Is this the correct result for \(c = a + b\)? Why?
a <- 3 ## Change the value of a
print(c) ## Print the value of c
[1] 7
## Check whether c equals a + b
c == a + b
[1] FALSE
Note: == is used to test whether two variables have the same content.
Updating variable contents
Example:
- change the value of \(a\) to \(27\),
- recompute and print the value of \(c\)
a <- 27 ## Change the value of a
c <- a + b
print(c) ## Print the value of c
[1] 32
## Check whether c equals a + b
c == a + b
[1] TRUE
Vectors of values
The simplest data structure in R is a vector. In the previous example, the variable a was actually a vector with a single value.
Example: create a variable named three.numbers, and initialize it with a vector with values 27, 12 and 3000.
Tips: - variable names can comprize several parts, separated by dots. - the function c() combines several values into a vector
three.numbers <- c(27,12,3000)
print(three.numbers)
[1] 27 12 3000
Series
The simple way to create a series of numbers. The column operator permits to generate all integer values between two limits.
[1] 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14
Computing with vectors
R handles vectors in a very convenient way. An operation on a vector applies to all its elements.
x <- 1:10 # Define a series from 1 to 10
print(x)
[1] 1 2 3 4 5 6 7 8 9 10
y <- x^2 # Compute the square of each number
print(y)
[1] 1 4 9 16 25 36 49 64 81 100
Scatter plot
x <- -10:10
y <- x^2
plot(x,y)
Line plot
x <- -10:10
y <- x^2
plot(x,y, type="l")
Variables can also contain strings
# The # symbol allows to insert comments in R code
# Define a vector named "whoami", and
# containing two names
whoami <- c("Denis", "Siméon")
print(whoami) # Comment at the end of a line
[1] "Denis" "Siméon"
String concatenation
# Define a vector named "names", and
# containing two names
whoami <- c("Denis", "Siméon")
# Paste the values of a vector of string
print(paste(sep=" ", whoami[1], whoami[2]))
[1] "Denis Siméon"
Carl’s preferred distribution
The function dpois() computes the Poisson density, i.e. the probability to observe exactly \(x\) successes in a series of independent trials with equal probability.
The Poisson distribution is defined by a single parameter: the expected number of successes \(\lambda\) (read “lambda”).
\[P(X=x) = \frac{e^{-\lambda}\lambda^x}{x!}\]
x <- 0:14 # Define the X values from 0 to 14
y <- dpois(x, lambda = 2.5) # Poisson density
print(y) # Check the result
Plotting the Poisson distribution
x <- 0:14 # Define the X values from 0 to 14
y <- dpois(x, lambda = 2.5) # Poisson density
plot(x,y) # Check the result
This first plot is not very nice. Let us get some help to improve it.
Getting help for R functions
Need help? Type help().
A question? Type ?
Result: R displays the help message for the function dpois().
Exercise: improve Poisson density plot
- Do not (yet) look the next slide.
- Read the help page for the
dpois()function.
- draw a plot that provides a didactic illustration of the Poisson density.
Improve the plot: type = histogram
x <- 0:14
lambda <- 2.54
y <- dpois(x, lambda)
plot(x,y, type="h")
Improve the plot: Add a title
plot(x,y, type="h", lwd=5, col="blue",
main="Poisson density")
Improve the plot: define axis labels
plot(x,y, type="h", lwd=5, col="blue",
main="Poisson density",
xlab="x = number of successes",
ylab="P(X=x)")
Improve the plot: add a legend
plot(x,y, type="h", lwd=5, col="blue",
main="Poisson density",
xlab="x = number of successes",
ylab="P(X=x)")
legend("topright", paste("lambda =", lambda))
Poisson: a family of curves
Exercice: explore the properties of the Poisson density function, by changing the rang of \(x\) values, and the \(\lambda\) parameter.
Solution: a family of Poisson curves
\(lambda=0.01\)
lambda <- 0.01
x <- 0:20
plot(x, dpois(x,lambda=lambda), type="h",
col="darkblue", lwd=5, xlab="X",ylab="dpois(x)")
legend("topright", paste("lambda=",lambda))
Solution: a family of Poisson curves
\(lambda=0.1\)
lambda <- 0.1
x <- 0:20
plot(x, dpois(x,lambda=lambda), type="h",
col="darkblue", lwd=5, xlab="X",ylab="dpois(x)")
legend("topright", paste("lambda=",lambda))
Solution: a family of Poisson curves
\(lambda=1\)
lambda <- 1
x <- 0:20
plot(x, dpois(x,lambda=lambda), type="h",
col="darkblue", lwd=5, xlab="X",ylab="dpois(x)")
legend("topright", paste("lambda=",lambda))
Solution: a family of Poisson curves
\(lambda=2\)
lambda <- 2
x <- 0:20
plot(x, dpois(x,lambda=lambda), type="h",
col="darkblue", lwd=5, xlab="X",ylab="dpois(x)")
legend("topright", paste("lambda=",lambda))
Solution: a family of Poisson curves
\(lambda=5\)
lambda <- 5
x <- 0:20
plot(x, dpois(x,lambda=lambda), type="h",
col="darkblue", lwd=5, xlab="X",ylab="dpois(x)")
legend("topright", paste("lambda=",lambda))
Solution: a family of Poisson curves
\(lambda=5\)
lambda <- 5
x <- 0:40
plot(x, dpois(x,lambda=lambda), type="h",
col="darkblue", lwd=5, xlab="X",ylab="dpois(x)")
legend("topright", paste("lambda=",lambda))
Solution: a family of Poisson curves
\(lambda=10\)
lambda <- 10
x <- 0:(4*lambda)
plot(x, dpois(x,lambda=lambda), type="h",
col="darkblue", lwd=5, xlab="X",ylab="dpois(x)")
legend("topright", paste("lambda=",lambda))
Solution: a family of Poisson curves
\(lambda=20\)
lambda <- 20
x <- 0:(4*lambda)
plot(x, dpois(x,lambda=lambda), type="h",
col="darkblue", lwd=2, xlab="X",ylab="dpois(x)")
legend("topright", paste("lambda=",lambda))
Solution: a family of Poisson curves
\(lambda=30\)
lambda <- 30
x <- 0:(2*lambda)
plot(x, dpois(x,lambda=lambda), type="h",
col="darkblue", lwd=2, xlab="X",ylab="dpois(x)")
legend("topright", paste("lambda=",lambda))
Solution: a family of Poisson curves
\(lambda=50\)
lambda <- 50
x <- 0:(2*lambda)
plot(x, dpois(x,lambda=lambda), type="h",
col="darkblue", lwd=2, xlab="X",ylab="dpois(x)")
legend("topright", paste("lambda=",lambda))
Solution: a family of Poisson curves
\(lambda=100\)
lambda <- 100
x <- 0:(2*lambda)
plot(x, dpois(x,lambda=lambda), type="h",
col="darkblue", lwd=2, xlab="X",ylab="dpois(x)")
legend("topright", paste("lambda=",lambda))
Solution: a family of Poisson curves
\(lambda=1000\)
lambda <- 1000
x <- 0:(2*lambda)
plot(x, dpois(x,lambda=lambda), type="h",
col="darkblue", lwd=2, xlab="X",ylab="dpois(x)")
legend("topright", paste("lambda=",lambda))
Solution: a family of Poisson curves
\(lambda=10000\)
lambda <- 10000
x <- 0:(2*lambda)
plot(x, dpois(x,lambda=lambda), type="h",
col="darkblue", lwd=2, xlab="X",ylab="dpois(x)")
legend("topright", paste("lambda=",lambda))
Solution: a family of Poisson curves
\(lambda=100000\)
plot(95000:105000, dpois(95000:105000,lambda=100000), type="h", col="darkblue", xlab="X",ylab="dpois(x)")
Before finishing – keep track of your session
Tractability is an important issue in sciences. The R function sessionInfo() summarizes information about the versions of R, the operating system, and all the libraries used during a session.
R version 3.3.2 (2016-10-31)
Platform: x86_64-apple-darwin13.4.0 (64-bit)
Running under: macOS Sierra 10.12.6
locale:
[1] en_US.UTF-8/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/en_US.UTF-8
attached base packages:
[1] stats graphics grDevices utils datasets methods base
other attached packages:
[1] knitr_1.15.1
loaded via a namespace (and not attached):
[1] backports_1.0.5 magrittr_1.5 rprojroot_1.2 tools_3.3.2
[5] htmltools_0.3.5 yaml_2.1.14 Rcpp_0.12.10 stringi_1.1.5
[9] rmarkdown_1.5 stringr_1.2.0 digest_0.6.12 evaluate_0.10