- What is R?
- What is Rweb?
- The Relation between R and Rweb
- Variables and Assignment
- Output (Print and Plot)
- Vectors
- Indexing Vectors
- Functions
- Missing Data and Computer Arithmetic

First there was S, a general-purpose, interpreted, computer language especially designed for statistics. S by itself is no longer commercially available. S together with additional functions and features is marketed by Insightful Corporation under the name S-PLUS.

R is free S. It is free as in "free beer" (you can download it with no charge) and free as in "free speech" (you can do whatever you want with it except make it non-free). More precisely, R is a dialect of the S language. R and S-PLUS are more or less compatible. Roughly 90% of things you want to do work in both. Most other things work with minor variations. R is available from the Comprehensive R Archive Network (CRAN).

R is the the language of choice for research statistics. If it's statistics, you can do it in R.

If you have the time and want to know more about R, the Introduction to R that comes with the R software is the first thing to read, but it is way more than you need to know for this course.

Free software is amazing. Creative programmers can use it to do anything they can think of. There's no vendor controlling use of the software to protect their profits.

Prof. Jeff Banfield at Montana State University put R on the web. You can run simple R commands from any computer connected to the internet. A similar program could be easily done for S-PLUS but would be illegal because the vendor couldn't profit from it.

The local Rweb server is at http://rweb.stat.umn.edu/Rweb. This link is also at the top of every course web page.

There are two "interfaces" to Rweb. The simple one found by clicking on the Rweb link on the main Rweb page, is the only one we will explain. It has the virtue of being embeddable in web pages to make examples.

Here is a simple example (not having much to do with nonparametrics, just one of the examples on the Rweb page)

To see how the example works, just click the "Submit" button.

When you have seen the example, click the "Back" button on you web browser to return to this page.

For now, don't bother with what the example does. Just notice that it does some calculations on some data and draws a picture.

Rweb is just R. You type R statements into a web form. You submit them. They get executed on the server. The results get stuffed into a web page sent back to your computer. So Rweb is just R run over the web.

So mostly we will use R

and Rweb

interchangeably.

One important difference between Rweb and R is that the server remembers
*nothing* between Rweb submissions.
The *entire calculation* you want done must be submitted
to Rweb in one web form.
R run on your own computer
does remember. You can build up a complicated analysis a little bit at
a time.

Thus Rweb is fairly useless for really complicated problems, but is fine for coursework.

Like all other computer languages, R has variables, which are referred to
by variable names. Variable names may contain any letter, digit, or the dot
(`.`

) and cannot begin with a digit. Names are case sensitive,
thus `fred`

, `Fred`

, and `FRED`

refer to
different variables.

The assignment operator in R is an arrow "`<-`

" constructed
from two characters. An assignment statement looks like

fred <- 4

or

sally <- 2 + 2

or

a.very.long.variable.name <- sqrt(16)

Each assigns the value of the expression on the right side of the assignment operator to the variable name on the left side. In each case the variable gets the value 4.

In order to see any results from R. You have to execute a command that
makes output, the most common being `print`

and `plot`

.

When a calculation is done or an assignment made, you don't see anything unless you ask explicitly.

prints the value (4) assigned to the variable `sally`

.

If the `print`

statement were omitted, there wouldn't be
any point because you wouldn't see anything and Rweb would't remember
the results for future use.

Actually this example can be shortened to

because an expression that is not an assignment usually prints its value so

sally

does the same thing as

print(sally)

If in doubt, put in the `print`

.

Not all R variable values are single numbers (in fact most aren't). Most R variables are vectors, which is R's name for a list of objects of the same type (often numbers but character variables and other types are possible).

There are many ways to create vectors in R. Many functions and operators return vector values if given vector values as arguments. Here we will only look at a few ways to create a vector and a few functions and operators that work vectorwise.

`c`

Function
The R function `c`

(on-line help)
"combines" or "collects" all its arguments into one vector, for example

`seq`

Function
The R function `seq`

(on-line help)
creates a sequence, for example

Variables can also be read into Rweb from an external file, either a file on your own computer or one on the web. We'll only illustrate the latter. An example file is

The file has the following properties.

- The file is
*plain text*. The garbage inserted into files by many so-calledword processors

(like Microsoft Word) is not allowed. - Each variable is
*one column*of the file. - The column heading is the name of the variable.
- The rest of the column is the list of values of the variable.

This has the result that all of the variables must be vectors of the same length. This can usually be arranged somehow.

When a job is submitted to Rweb, the first thing it does is read
the "External Data Entry" file (if there is one) and create the variables
in it. The example blurfle.txt creates
three variables, `color`

, `x`

, and `y`

and prints them out.

It is an important and generally useful fact about R that most functions and operators work vectorwise (operating on each element of the vector).

Note that multiplication needs an explicit operator `*`

as in
most computer languages. The `^`

operator is exponentiation:
`bob^2`

is "bob squared".

That's all for now (admittedly too brief, see
Simple manipulations; numbers and vectors in
the *Introduction to R* document if you need to know more, but don't
look at it your first time through this).

Indexing operations allow you to modify or pick out or remove specified elements of a vector.

The simplest form of indexing uses positive integers in the range from one to the length of the vector. For example

do what is obvious (after you get used to vector indexing). Not quite so obvious is that subscripts work the same way on the other side of the assignment operator.

Negative index values indicate "everything but"

do the same thing (why? figure it out!).

Perhaps the most useful form of indexing uses logical vectors. First the example, then the explanation.

bob[bob != 42]

is the (vector of) elements of `bob`

not equal to 42.

(The operator `!=`

is "not equal". Similarly `<=`

is
"less than or equal" and `>=`

is "greater than or equal".)

The result of

bob != 42

is a logical vector (all elements having values `TRUE`

or `FALSE`

. Indexing with such a vector picks out the elements
for which the index is `TRUE`

.

When the logical vector is the result of a comparison (as here), it
picks out the elements for which the comparison was `TRUE`

.

That all for this web page. If you need to know more, see
Index vectors; selecting and modifying subsets of a data set in
the *Introduction to R* document if you need to know more, but don't
look at it your first time through this.

We've already mentioned a few R functions. There are lots and lots of
others. By built-in

functions, we mean those that you don't have
to do anything special to use. Strictly, speaking R doesn't have any
built-in

functions. Any function is like any other function.
None are more special than any other. But seven packages

of functions
called
`base`

,
`datasets`

,
`utils`

,
`grDevices`

,
`graphics`

,
`stats`

,
and
`methods`

,
are automatically available
with no special effort.

These functions are listed on the documentation for the base and so forth.

To use an R function, you just type the function name followed by the list of arguments in parentheses. We've already seen examples, like

plot(x, y)

Most R functions also have *named arguments*. The syntax
for that is

The named arguments here, `main`

, `xlab`

and `ylab`

can appear in any order so long as they
are after the unnamed arguments.

This makes the functions much simpler to use. Many functions have dozens of arguments, and you only need to use a few (the others have default values or aren't used the way you are invoking the function).

If you actually know the order of all the arguments, then you don't need the name. For example, the three functions

rnorm(10, 0.0, 1.0) rnorm(10, mean = 0.0, sd = 1.0) rnorm(10)

all do the same thing (generate 10 independently distributed standard
normal random numbers) because the second argument is `mean`

and the third is `sd`

and the defaults for these arguments
are 0.0 and 1.0, respectively.

Your choice.

Some functions are not available until the library

containing it is added. For example

library(exactRankTests)

adds the `exactRankTests`

library, which does
pretty much what the name suggests. We'll use it soon.

Other than needing a `library`

command first,
functions in such a package, such as the `wilcox.exact`

function in the `exactRankTests`

library are just like any other
functions.

The list of all packages available on our Rweb server is
here. It can also be found by going to the
main Rweb page
(follow the link on the navigation bar at the top of any 5601 web page)
then clicking on the link HTML documentation

in the second paragraph
and then on the link Packages

on the main R documentation page.

Many more packages can be found at the contributed packages page at CRAN.

The `function`

function defines new functions. For example

trim <- function(x, lower = 0.0, upper = 1.0) { inies <- x >= lower & x <= upper return(x[inies]) }

trims off the values of the argument `x`

that are
below or above the arguments `lower`

and `upper`

,
respectively.

The `lower = 0.0`

and `upper = 1.0`

in the
definition specify *default values* for these arguments that
are used when the user does not supply values.

Let's check it out.

As the assignment suggests, an R function is just an R variable
like any other. In this example, `trim`

is an R variable
that happens to be a function and `x`

is an R variable
that happens to be a numeric vector.

This allows functions to be passed as arguments to other functions, a very useful technique that we will use often (that's the only reason we will want to define our own functions).

A return statement is not strictly necessary. Functions return the value of the last expression if there is no return. The curly brackets are not necessary if there is only one statement.

Thus

trim <- function(x, lower = 0.0, upper = 1.0) x[x >= lower & x <= upper]

works just as well as the other definition. But it is a lot harder to read, and we generally won't use this trick.

*Local variables* are variables defined inside a function.
They exist only inside the function and have no influence on anything
outside the function.

The following example shows this behavior.

Inside the function `x`

is defined to be the value
of `y`

, but outside the function `x`

is unchanged.

*Global variables* are variables defined outside a function.
They are not defined inside the function, either in the argument list
or in the body. They can, however, be used inside the function.

This is sometimes very convenient, but can lead to confusing code. It probably shouldn't be overused.

This section only scratches the surface. There's a lot more to be said about R functions. The section on writing your own functions in the Introduction to R book is a good place to start.

The data system has two sorts of accomodation to values the computer can't handle or at least isn't supposed to deal with.

`NA`

: Not Available
Any data value, numeric or not, can be `NA`

. This is what
you use for missing data

. Always use `NA`

for this
purpose. Never use `999`

or some other code that is actually
a number. Sad experience of many scientists shows this sort of code is
always forgotten at some point and the data analysis thereby ruined.

`NaN`

: Not a Number
This is a special value that only numeric variables can take. It is
the result of an undefined operation like `0 / 0`

.
It is produced by the low level arithmetic of all modern computers.
R is just going along with the standard here.

`Inf`

: Infinity
Numeric variables can also take the values `-Inf`

and `Inf`

. These are produce by the low level arithmetic
of all modern computers by operations such as `-1 / 0`

and
`1 / 0`

.
R is just going along with the standard here.

You shouldn't think of these as real infinities, like in calculus, but
rather that the correct calculation, if the computer could do it would
*probably* (but not certainly) be very large, larger than the
largest numbers the computer can hold (about 10^{300}) and of
the sign of the infinity

.