We have learnt the basics of the R programming language, its syntax and semantics, and are now ready to delve into the statistics domain using R. In this eleventh article in the R series, we will learn to use the statistics functions available in the R stats package.
As we have done in the earlier parts of this series, we are going to use the R version 4.1.2 installed on Parabola GNU/Linux-libre (x86-64) for the code snippets.
$ R --version R version 4.1.2 (2021-11-01) -- “Bird Hippie” Copyright (C) 2021 The R Foundation for Statistical Computing Platform: x86_64-pc-linux-gnu (64-bit) R is free software and comes with ABSOLUTELY NO WARRANTY. You are welcome to redistribute it under the terms of the GNU General Public License versions 2 or 3. For more information about these matters see https://www.gnu.org/licenses/
Mean
The R function for calculating the arithmetic mean is mean. It accepts an R object ‘x’ as an argument, and a ‘trim’ option to trim any fractions before computing the mean value. The ‘na.rm’ logical argument can be used to ignore any NA values. Its syntax is as follows:
mean(x, trim = 0, na.rm = FALSE, ...)
The function supports numerical and logical values, as well as date and time intervals. A few examples for the mean function are given below:
> mean(c(1, 2, 3)) 2 > mean(c(1:5, 10, 20)) 6.428571 > mean(c(FALSE, TRUE, FALSE)) 0.3333333 > mean(c(TRUE, TRUE, TRUE)) 1
Consider the ‘Bank Marketing Data Set’ for a Portuguese banking institution that is available from the UCI Machine Learning Repository available at https://archive.ics.uci.edu/ml/datasets/Bank+Marketing. The data can be used for public research. There are four data sets available, and we will use the read.csv() function to import the data from a ‘bank.csv’ file.
> bank <- read.csv(file=”bank.csv”, sep=”;”) > bank[1:3,] age job marital education default balance housing loan contact day 1 30 unemployed married primary no 1787 no no cellular 19 2 33 services married secondary no 4789 yes yes cellular 11 3 35 management single tertiary no 1350 yes no cellular 16 month duration campaign pdays previous poutcome y 1 oct 79 1 -1 0 unknown no 2 may 220 1 339 4 failure no 3 apr 185 1 330 1 failure no
We can find the mean age from the bank data as follows:
> mean(bank$age) 41.1701
Median
The median function in the R stats package computes the sample median. It accepts a numeric vector ‘x’, and a logical value ‘na.rm’ to indicate if it should discard ‘NA’ values before computing the median. Its syntax is as follows:
median(x, na.rm = FALSE, ...)
A couple of examples are given below:
> median(3:5) 4 > median(c(3:5, 50, 150)) [1] 5
We can now find the median age from the bank data set as follows:
> median(bank$age) 39
Pair
The pair function can be used to combine two vectors. It accepts two arguments, and vectors ‘x’ and ‘y’. Both the vectors should have the same length. The syntax is as follows:
Pair(x, y)
The function returns a two column matrix of class ‘Pair’. An example is given below:
> Pair(c(1,2,3), c(4,5,6))
x y
[1,] 1 4
[2,] 2 5
[3,] 3 6
attr(,”class”)
[1] “Pair”
The function is used for paired tests such as t.test and wilcox.test.
dist
The dist function is used to calculate the distance matrix for the rows in a data matrix, and accepts the following arguments:
| Argument | Description |
| x | A numeric matrix |
| method | The distance measure to be used |
| diag | Prints diagonal of distance matrix if TRUE |
| upper | Prints upper triangle of distance matrix if TRUE |
| p | Power of the Minkowski distance |
The distance measurement methods supported are: ‘euclidean’, ‘maximum’, ‘manhattan’, ‘canberra’, ‘binary’ and ‘minkowski’. The distance measurement for the age data set using the Euclidean distance is given below:
> dist(bank$age, method=”euclidean”, diag=FALSE, upper=FALSE, p=2)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
2 3
3 5 2
4 0 3 5
5 29 26 24 29
6 5 2 0 5 24
7 6 3 1 6 23 1
8 9 6 4 9 20 4 3
9 11 8 6 11 18 6 5 2
10 13 10 8 13 16 8 7 4 2
11 9 6 4 9 20 4 3 0 2 4
12 13 10 8 13 16 8 7 4 2 0 4
13 6 3 1 6 23 1 0 3 5 7 3 7
14 10 13 15 10 39 15 16 19 21 23 19 23 16
15 1 2 4 1 28 4 5 8 10 12 8 12 5 11
16 10 7 5 10 19 5 4 1 1 3 1 3 4 20 9
17 26 23 21 26 3 21 20 17 15 13 17 13 20 36 25 16
18 7 4 2 7 22 2 1 2 4 6 2 6 1 17 6 3 19
19 5 8 10 5 34 10 11 14 16 18 14 18 11 5 6 15 31 12
20 1 2 4 1 28 4 5 8 10 12 8 12 5 11 0 9 25 6 6
21 8 5 3 8 21 3 2 1 3 5 1 5 2 18 7 2 18 1 13 7
22 12 9 7 12 17 7 6 3 1 1 3 1 6 22 11 2 14 5 17 11 4
23 14 11 9 14 15 9 8 5 3 1 5 1 8 24 13 4 12 7 19 13 6 2
26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50
...
The binary distance measurement output for the same bank age data is as follows:
> dist(bank$age, method=”binary”, diag=FALSE, upper=FALSE, p=2)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28
2 0
3 0 0
4 0 0 0
5 0 0 0 0
6 0 0 0 0 0
7 0 0 0 0 0 0
8 0 0 0 0 0 0 0
9 0 0 0 0 0 0 0 0
10 0 0 0 0 0 0 0 0 0
11 0 0 0 0 0 0 0 0 0 0
12 0 0 0 0 0 0 0 0 0 0 0
13 0 0 0 0 0 0 0 0 0 0 0 0
14 0 0 0 0 0 0 0 0 0 0 0 0 0
15 0 0 0 0 0 0 0 0 0 0 0 0 0 0
16 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
17 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
18 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
19 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
20 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
21 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
22 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
23 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53
Quantile
The quantiles can be generated for a numeric vector ‘x’ along with their given probabilities using the quantile function. The ‘NA’ and ‘NaN’ values are not allowed in the vector, unless ‘na.rm’ is set to TRUE. The probability of 0 is for the lowest observation and 1 for the highest. Its syntax is as follows:
quantile(x, ...)
The quantile function accepts the following arguments:
| Argument | Description |
| x | A numeric vector |
| probs | A vector of probabilities between 0 and 1 |
| na.rm | NA and NaN values are ignored if TRUE |
| names | If TRUE, the result has the names attribute |
| type | An integer to select any of the nine quantile algorithms |
| digits | The decimal precision to use |
| … | Additional arguments passed to or from other methods |
The rnorm function can be used to generate random values for the normal distribution. It can take ‘n’ number of observations, a vector of ‘means’, and a vector ‘sd’ of standard deviations as its arguments. We can obtain the quantiles for the values produced by the ‘rnorm’ function. For example:
> quantile(x <- rnorm(100))
0% 25% 50% 75% 100%
-1.978171612 -0.746829079 -0.009440368 0.698271134 1.897942805
The quantiles for bank age data with the following probabilities can be generated as follows:
> quantile(bank$age, probs = c(0.1, 0.5, 1, 2, 5, 10, 50)/100) 0.1% 0.5% 1% 2% 5% 10% 50% 20.0 22.6 24.0 25.0 27.0 29.0 39.0
Interquartile range
The IQR function computes the interquartile range for the numeric values of a vector. Its syntax is as follows:
IQR(x, na.rm = FALSE, type = 7)
The ‘type’ argument specifies an integer to select the quantile algorithm, which is discussed in Hyndman and Fan (1996). The interquartile range for the bank age can be computed as shown below:
> IQR(bank$age, na.rm = FALSE, type=7) 16
Standard deviation
The sd function is used to calculate the standard deviation for a set of values. It accepts a numeric vector ‘x’ and a logical value for ‘na.rm’ to remove missing values. Its syntax is as follows:
sd(x, na.rm = FALSE)
The standard deviation for a vector with length zero or 1 is ‘NA’. A couple of examples are given below:
> sd(1:10) 3.02765 > sd(1) NA
We can calculate the standard deviation for the bank age column as follows:
> sd(bank$age) 10.57621
You are encouraged to explore more functions available in the stats packages available in R.
