# Statistical Analysis: an Introduction using R/R/Vectors

*vector*, used to store multiple measurements of the same type (e.g. data variables). There are several different sorts of data that can be stored in a vector. Most common is the

**numeric vector**, in which each element of the vector is simply a number. Other commonly used types of vector are

**character vectors**(where each element is a piece of text) and

**logical vectors**(where each element is either

`TRUE`

or `FALSE`

^{[1]}). In this topic we will use some example vectors provided by the "datasets" package, containing data on States of the USA (see

`?state`

).
R is an inherently vector-based program; in fact the numbers we have been using in previous calculations are just treated as vectors with a single element. This means that most basic functions in R will behave sensibly when given a vector as a argument, as shown below.```
state.area #a NUMERIC vector giving the area of US states, in square miles
state.name #a CHARACTER vector (note the quote marks) of state names
sq.km <- state.area*2.59 #Arithmetic works on numeric vectors, e.g. convert sq miles to sq km
sq.km #... the new vector has the calculation applied to each element in turn
sqrt(sq.km) #Many mathematical functions also apply to each element in turn
range(state.area) #But some functions return different length vectors (here, just the max & min).
length(state.area) #and some, like this useful one, just return a single value.
```

[1] 51609 589757 113909 53104 158693 104247 5009 2057 58560 58876 6450 83557 56400

[14] 36291 56290 82264 40395 48523 33215 10577 8257 58216 84068 47716 69686 147138 [27] 77227 110540 9304 7836 121666 49576 52586 70665 41222 69919 96981 45333 1214 [40] 31055 77047 42244 267339 84916 9609 40815 68192 24181 56154 97914 > state.name #a CHARACTER vector (note the quote marks) of state names

[1] "Alabama" "Alaska" "Arizona" "Arkansas" [5] "California" "Colorado" "Connecticut" "Delaware" [9] "Florida" "Georgia" "Hawaii" "Idaho"

[13] "Illinois" "Indiana" "Iowa" "Kansas" [17] "Kentucky" "Louisiana" "Maine" "Maryland" [21] "Massachusetts" "Michigan" "Minnesota" "Mississippi" [25] "Missouri" "Montana" "Nebraska" "Nevada" [29] "New Hampshire" "New Jersey" "New Mexico" "New York" [33] "North Carolina" "North Dakota" "Ohio" "Oklahoma" [37] "Oregon" "Pennsylvania" "The smallest state" "South Carolina" [41] "South Dakota" "Tennessee" "Texas" "Utah" [45] "Vermont" "Virginia" "Washington" "West Virginia" [49] "Wisconsin" "Wyoming" > sq.km <- state.area*2.59 #Standard arithmatic works on numeric vectors, e.g. convert sq miles to sq km > sq.km #... giving another vector with the calculation performed on each element in turn

[1] 133667.31 1527470.63 295024.31 137539.36 411014.87 269999.73 12973.31 5327.63 [9] 151670.40 152488.84 16705.50 216412.63 146076.00 93993.69 145791.10 213063.76

[17] 104623.05 125674.57 86026.85 27394.43 21385.63 150779.44 217736.12 123584.44 [25] 180486.74 381087.42 200017.93 286298.60 24097.36 20295.24 315114.94 128401.84 [33] 136197.74 183022.35 106764.98 181090.21 251180.79 117412.47 3144.26 80432.45 [41] 199551.73 109411.96 692408.01 219932.44 24887.31 105710.85 176617.28 62628.79 [49] 145438.86 253597.26 > sqrt(sq.km) #Many mathematical functions also apply to each element in turn

[1] 365.60540 1235.90883 543.16140 370.86299 641.10441 519.61498 113.90044 72.99062 [9] 389.44884 390.49819 129.24976 465.20171 382.19890 306.58390 381.82601 461.58830

[17] 323.45487 354.50609 293.30334 165.51263 146.23826 388.30328 466.62203 351.54579 [25] 424.83731 617.32278 447.23364 535.06878 155.23324 142.46136 561.35100 358.33202 [33] 369.04978 427.81111 326.74911 425.54695 501.17940 342.65503 56.07370 283.60615 [41] 446.71213 330.77479 832.11058 468.96955 157.75712 325.13205 420.25859 250.25745 [49] 381.36447 503.58441 > range(state.area) #But some functions return different length vectors (here, just the max & min). [1] 1214 589757 > length(state.area) #and some, like this useful one, just return a single value. [1] 50

`c()`

, so named because it __c__oncatenates objects together. However, if you wish to create vectors consisting of regular sequences of numbers (e.g. 2,4,6,8,10,12, or 1,1,2,2,1,1,2,2) there are several alternative functions you can use, including

`seq()`

, `rep()`

, and the `:`

operator.```
c("one", "two", "three", "pi") #Make a character vector
c(1,2,3,pi) #Make a numeric vector
seq(1,3) #Create a sequence of numbers
1:3 #A shortcut for the same thing (but less flexible)
i <- 1:3 #You can store a vector
i
i <- c(i,pi) #To add more elements, you must assign again, e.g. using c()
i
i <- c(i, "text") #A vector cannot contain different data types, so ...
i #... R converts all elements to the same type
i+1 #The numbers are now strings of text: arithmetic is impossible
rep(1, 10) #The "rep" function repeats its first argument
rep(3:1,10) #The first argument can also be a vector
huge.vector <- 0:(10^7) #R can easily cope with very big vectors
#huge.vector #VERY BAD IDEA TO UNCOMMENT THIS, unless you want to print out 10 million numbers
rm(huge.vector) #"rm" removes objects. Deleting huge unused objects is sensible
```

[1] "one" "two" "three" "pi" > c(1,2,3,pi) #Make a numeric vector [1] 1.000000 2.000000 3.000000 3.141593 > seq(1,3) #Create a sequence of numbers [1] 1 2 3 > 1:3 #A shortcut for the same thing (but less flexible) [1] 1 2 3 > i <- 1:3 #You can store a vector > i [1] 1 2 3 > i <- c(i,pi) #To add more elements, you must assign again, e.g. using c() > i [1] 1.000000 2.000000 3.000000 3.141593 > i <- c(i, "text") #A vector cannot contain different data types, so ... > i #... R converts all elements to the same type [1] "1" "2" "3" "3.14159265358979" "text" > i+1 #The numbers are now strings of text: arithmetic is impossible Error in i + 1 : non-numeric argument to binary operator > rep(1, 10) #The "rep" function repeats its first argument

[1] 1 1 1 1 1 1 1 1 1 1

> rep(3:1,10) #The first argument can also be a vector

[1] 3 2 1 3 2 1 3 2 1 3 2 1 3 2 1 3 2 1 3 2 1 3 2 1 3 2 1 3 2 1

> huge.vector <- 0:(10^7) #R can easily cope with very big vectors > #huge.vector #VERY BAD IDEA TO UNCOMMENT THIS, unless you want to print out 10 million numbers > rm(huge.vector) #"rm" removes objects. Deleting huge unused objects is sensible

## Notes

edit- ↑ These are special words in R, and cannot be used as names for objects. The objects
`T`

and`F`

are temporary shortcuts for`TRUE`

and`FALSE`

, but if you use them, watch out: since T and F are just normal object names you can change their meaning by overwriting them.