Lesson 3: Vectors and Indices

Say we want to find the mean river flow after year 1950.

The above output said that the Nile series starts in 1871. That means 1951 will be the 81st year, and the 100th will be 1970. How do we designate the 81st through 100th elements in this data?

Individual elements can be accessed using subscripts or indices (singular is index), which are specified using brackets, e.g.

> Nile[2]
[1] 1160

for the second element (the output we saw earlier shows that the second element is indeed 1160). The value 2 here is the index.

The c (“concatenate”) function builds a vector, stringing several numbers together. E.g. we can get the 2nd, 5th and 6th elements of Nile:

> Nile[c(2,5,6)]
[1] 1160 1160 1160

If we wish to build a vector of consecutive numbers, we can use the “colon” notation:

> Nile[c(2,3,4)]
[1] 1160  963 1210
> Nile[2:4]
[1] 1160  963 1210

As you can see, 2:4 is shorter way to specify the vector c(2,3,4).

So, 81:100 means all the numbers from 81 to 100. Thus Nile[81:100] specifies the 81st through 100th elements in the Nile vector.

Then to answer the above question on the mean flow during 1951-1971, we can do

> mean(Nile[81:100])
[1] 877.05

NOTE: Observe how the above reasoning process worked. We had a goal, to find the mean river flow after 1950. We knew we had some tools available to us, namely the mean function and R vector indices. We then had to figure out a way to combine these tools in a manner that achieves our goal, which we did.

This is how use of R works in general. As you go through this tutorial, you’ll add more and more to your R “toolbox.” Then for any given goal, you’ll rummage around in that toolbox, and eventually figure out the right set of tools for the goal at hand. Sometimes this will require some patience, but you’ll find that the more you do, the more adept you become.

If we plan to do more with that time period, we should make a copy of it:

> n81100 <- Nile[81:100]
> mean(n81100)
[1] 877.05
> sd(n81100)
[1] 125.5583

The function sd finds the standard deviation.

Note that we used R’s assignment operator here to copy (“assign”) those particular Nile elements to n81100. (In most situations, you can use = instead of <-, but why worry about what the exceptions might be? They are arcane, so it’s easier just to always use <-. And though “keyboard shortcuts” for this are possible, again let’s just stick to the basics for now.)

Note too that though we will speak of the above operation as having “extracted” the 81st through 100th elements of Nile, we have merely made a copy of those elements. The original vector Nile remains intact.

Tip: We can pretty much choose any name we want; n81100 just was chosen to easily remember this new vector’s provenance. (But names can’t include spaces, and must start with a letter.)

Note that n81100 now is a 21-element vector. Its first element is now element 81 of Nile:

> n81100[1]
[1] 744
> Nile[81]
[1] 744

Keep in mind that although Nile and n81100 now have identical contents, they are separate vectors; if one changes, the other will not.

Another oft-used function is length, which gives the number of elements in the vector, e.g.

> length(Nile)
[1] 100

Can you guess the value of length(n81100)? Type this expression in at the > prompt to check your answer.

Leave R by typing q() or ctrl-d. (Answer no to saving the workspace.)

Recap: What have we learned in these first two lessons?

• Starting and existing R.

• Some R functions: mean, hist, length.

• R vectors, and vector indices.

• Extracting vector subsets.

• Forming vectors, using c() and :.

Not bad for Lesson 1! And needless to say, you’ll be using all of these frequently in the subsequent lessons and in your own usage of R.