Basic components of a function

name <- function(arg1, aug2, ...){
<FUNCTION BODY>
return(value)
}

cal_sqrt <- function(x){
a <- x^2
b <- x^3
out <- c(a, b)
names(out) <- c("squared", "cubed")
out # or return(out)
}

Function name: cal_sqrt

• use verbs, where possible.

• should be meaningful.

• Use an underscore (_) to separate words.

• avoid names of built-in functions.

• start with lower case letters. Note that R is a case sensitive language.

Basic components of a function

name <- function(arg1, aug2, ...){
<FUNCTION BODY>
return(value)
}

cal_sqrt <- function(x){
 a <- x^2
 b <- x^3
 out <- c(a, b)
 names(out) <- c("squared", "cubed")
 out # or return(out)
}

Function arguments: x

• value passed to the function to obtain the function's result.

Basic components of a function

name <- function(arg1, aug2, ...){
<FUNCTION BODY>
return(value)
}

cal_sqrt <- function(x){
  a <- x^2
  b <- x^3
  out <- c(a, b)
  names(out) <- c("squared", "cubed")
  out # or return(out)
}

Function body

Function body (Cont.)

• Spacing inside parentheses or square brackets

# Good ---
a[1, 2]
a[1, ]
if(x < 2)
# Bad ---
a[1,2]
a[1,]
if(x<2)
if( x<2 )

• {} do not go in one single line, always two lines

# Good ---
if(y == 2){
print("even")
}
# Bad ---
if(y == 2){ print("even")}

Built-in Functions

How to call a built-in function in R

function_name(arg1 = 1, arg2 = 3)

Argument matching

The following calls to mean are all equivalent

mydata <- c(rnorm(20), 100000)
mean(mydata) # matched by position
mean(x = mydata) # matched by name
mean(mydata, na.rm = FALSE)
mean(x = mydata, na.rm = FALSE) 
mean(na.rm = FALSE, x = mydata) 
mean(na.rm = FALSE, mydata)

[1] 4761.94

⚠️ Even though it works, do not change the order of the arguments too much.

Argument matching (cont.)

• some arguments have default values

mean(mydata, trim=0)

[1] 4761.94

mean(mydata) # Default value for trim is 0

[1] 4761.94

mean(mydata, trim=0.1)

[1] 0.1449313

mean(mydata, tr=0.1) # Partial Matching

[1] 0.1449313

?mean

1. Calculate the mean of 1, 2, 3, 8, 10, 20, 56, NA.

Basic maths functions

Basic statistic functions

Remove missing values in the following vector

 [1]  0.61940020 -0.93808729  0.95518590 -0.22663938  0.29591186          NA
 [7]  0.36788089  0.71791098  0.71202022  0.22765782          NA          NA
[13] -0.74024324  0.02081516 -0.14979979 -0.22351308  0.98729725          NA
[19]          NA          NA          NA          NA          NA          NA
[25]          NA          NA          NA -1.50016003  0.18682734  0.20808590
[31]  0.70102264 -0.10633074 -1.18460046  0.06475501  0.11568817 -0.04333140
[37] -0.22020064  0.02764713  0.10165760 -0.18234246  1.32914659 -1.29704248
[43]  1.05317749 -0.70109051  0.09798707  0.10457263 -0.21449845

Probability distribution functions

• Each probability distribution in R is associated with four functions.

• Naming convention for the four functions:

  For each function there is a root name. For example, the root name for the normal distribution is norm. This root is prefixed by one of the letters d, p, q, r.

  • d prefix for the distribution function

  • p prefix for the cumulative probability

  • q prefix for the quantile

  • r prefix for the random number generator

• Example: dnorm, pnorm, qnorm, rnorm

Illustration with Standard normal distribution

The general formula for the probability density function of the normal distribution with mean $\mu$ and variance $\sigma$ is given by

$$f_X\left(x\right)=\frac{1}{\sigma \sqrt{\left(2\pi \right)}}{e}^{-(x-\mu {)}^2/2{\sigma }^2}$$

If we let the mean $\mu =0$ and the standard deviation $\sigma =1$, we get the probability density function for the standard normal distribution.

$$f_X\left(x\right)=\frac{1}{\sqrt{\left(2\pi \right)}}{e}^{-(x{)}^2/2}$$

Standard Normal Distribution

$$f_X\left(x\right)=\frac{1}{\sqrt{\left(2\pi \right)}}{e}^{-(x{)}^2/2}$$

dnorm(0)

[1] 0.3989423

Standard Normal Distribution

$$f_X\left(x\right)=\frac{1}{\sqrt{\left(2\pi \right)}}{e}^{-(x{)}^2/2}$$

pnorm(0)

[1] 0.5

Standard Normal Distribution

$$f_X\left(x\right)=\frac{1}{\sqrt{\left(2\pi \right)}}{e}^{-(x{)}^2/2}$$

pnorm(0)

[1] 0.5

Standard Normal Distribution

$$f_X\left(x\right)=\frac{1}{\sqrt{\left(2\pi \right)}}{e}^{-(x{)}^2/2}$$

qnorm(0.5)

[1] 0

Standard Normal Distribution: rnorm

set.seed(262020)
random_numbers <- rnorm(10)
random_numbers

 [1]  0.20078181  0.95873346  1.18369056  1.49513750  1.18109222 -0.57789570
 [7]  0.01790671  0.81185245  0.39488199 -0.44337927

sort(random_numbers) ## sort the numbers then it is easy to map with the graph

 [1] -0.57789570 -0.44337927  0.01790671  0.20078181  0.39488199  0.81185245
 [7]  0.95873346  1.18109222  1.18369056  1.49513750

1. Suppose $Z\sim N(0,1)$. Calculate the following standard normal probabilities.

   • $P(Z\le 1.25)$,

   • $P(Z>1.25)$,

   • $P(Z\le -1.25)$,

   • $P(-.38\le Z\le 1.25)$.

2. Find the following percentiles for the standard normal distribution.

   • 90th,

   • 95th,

   • 97.5th,

3. Determine the $Z_{\alpha }$ for the following

   • $\alpha =0.1$

   • $\alpha =0.95$

1. Suppose $X\sim N(15,9)$. Calculate the following probabilities

   • $P(X\le 15)$,

   • $P(X<15)$,

   • $P(X\ge 10)$.

2. A particular mobile phone number is used to receive both voice messages and text messages. Suppose 20% of the messages involve text messages, and consider a sample of 15 messages. What is the probability that

   • At most 8 of the messages involve a text message?

   • Exactly 8 of the messages involve a text message.

3. Generate 20 random values from a Poisson distribution with mean 10 and calculate the mean. Compare your answer with your friend's answer.

Reproducibility of scientific results

rnorm(10) # first attempt

 [1]  1.4701904 -0.2375662  0.1765985 -0.5257483 -1.3674764 -1.4422500
 [7]  0.7576607  0.6475122 -1.1543034  0.9066248

rnorm(10) # second attempt

 [1] -1.7603264 -0.3402939 -1.0335807  1.0645014 -0.3874459  0.5975271
 [7] -2.1535707  0.6602928  1.1581404  0.6133446

As you can see above you will get different results

set.seed(1)
rnorm(10) # First attempt with set.seed

 [1] -0.6264538  0.1836433 -0.8356286  1.5952808  0.3295078 -0.8204684
 [7]  0.4874291  0.7383247  0.5757814 -0.3053884

set.seed(1)
rnorm(10) # Second attempt with set.seed

 [1] -0.6264538  0.1836433 -0.8356286  1.5952808  0.3295078 -0.8204684
 [7]  0.4874291  0.7383247  0.5757814 -0.3053884

Calculate the row and column wise standard deviation of the following matrix

     [,1] [,2] [,3] [,4]
[1,]    1    6   11   16
[2,]    2    7   12   17
[3,]    3    8   13   18
[4,]    4    9   14   19
[5,]    5   10   15   20

Assignment 1: Individual

Find about the following variants of apply family functions in R lapply(), sapply(), vapply(), mapply(), rapply(), and tapply() functions.

Resourses: You can follow the DataCamp tutorial here.

• You should clearly explain,

  • syntax for each function

  • function inputs

  • how each function works?/ The task of the function.

  • output of the function.

  • differences between the functions (apply vs lapply, apply vs sapply, etc.)

• Provide your own example for each function.

Use only 1 A4 sheet, you may use both sides.

Assignment due date: 3 March 2020

Installing R Packages

Method 1

Method 2

install.packages("ggplot2")

Load package

library(ggplot2)

Now search ?qplot

Note: You shouldn't have to re-install packages each time you open R. However, you do need to load the packages you want to use in that session via library.

mozzie dataset

library(mozzie)
data(mozzie)

Data Visualization with qplot

plot vs qplot

plot(mozzie$Colombo, mozzie$Gampaha)

qplot(Colombo, Gampaha, data=mozzie)

Data Visualization with qplot

qplot(Colombo, Gampaha, data=mozzie)

qplot(Colombo, Gampaha, data=mozzie, colour=Year)

Data Visualization with qplot

qplot(Colombo, Gampaha, data=mozzie)

qplot(Colombo, Gampaha, data=mozzie, size=Year)

Data Visualization with qplot

qplot(Colombo, Gampaha, data=mozzie)

qplot(Colombo, Gampaha, data=mozzie, geom="point")

Data Visualization with qplot

qplot(ID, Gampaha, data=mozzie)

qplot(ID, Gampaha, data=mozzie, geom="line")

Data Visualization with qplot

qplot(ID, Gampaha, data=mozzie)

qplot(ID, Gampaha, data=mozzie, geom="path")

Data Visualization with qplot

qplot(Colombo, Gampaha, data=mozzie, geom="line")

qplot(Colombo, Gampaha, data=mozzie, geom="path")

Data Visualization with qplot

qplot(Colombo, Gampaha, data=mozzie, geom=c("line", "point"))

qplot(Colombo, Gampaha, data=mozzie, geom=c("path", "point"))

Data Visualization with qplot

boxplot(Colombo~Year, data=mozzie)

qplot(factor(Year), Colombo, data=mozzie, geom="boxplot")

Data Visualization with qplot

qplot(factor(Year), Colombo, data=mozzie, geom="boxplot")

qplot(factor(Year), Colombo, data=mozzie) # geom="point"-default

Data Visualization with qplot

qplot(factor(Year), Colombo, data=mozzie, geom="point")

qplot(factor(Year), Colombo, data=mozzie, geom=c("jitter", "point")) # geom="point"-default

Data Visualization with qplot

qplot(factor(Year), Colombo, data=mozzie, geom=c("jitter", "point"))

qplot(factor(Year), Colombo, data=mozzie, geom=c("jitter", "point", "boxplot")) # geom="point"-default

Data Visualization with qplot

qplot(Colombo, data=mozzie)

`stat_bin()` using `bins = 30`. Pick better value with `binwidth`.

qplot(Colombo, data=mozzie, geom="density")

Explore iris dataset with suitable graphics.

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