Kickstarting R - Descriptive statistics

## Writing a descriptive stats function

Assume that we want a function that will give us the mean, variance and valid n for one or more numeric variables in a data frame. Here's a very simple example of such a function, dstats().

Note that two things have been done before any calculation. First the function checks whether the required argument `x` is missing, then it checks whether `x` is a data frame or matrix. This avoids any messy errors that would result by calling the function without any arguments or with objects that didn't make any sense to the function. If these checks fail, a simple usage message is printed to inform the user.

After all this preparation, what does the function do? First, it works out which columns of the input data are numeric. It then computes the vector of means as above. Then it makes almost exactly the same call, except using the function `var()` to get the variances. You won't find the third function in the R help listing.

```validn<-function(datavec) {
return(sum(!is.na(datavec)))
}```

All it does is add up the vector of `TRUE` and `FALSE` values (which happen to equal 1 and 0) produced by the function `is.na()` and reversed by the NOT (!) operator. That value is the number of valid (NOT NA) observations in the object passed to it, which will be each column of the incoming data to `dstats()`. So `validn()` had to be written before `dstats()` would run. This is a good time to consider when it is worth writing a separate function to do something. `validn()` has the advantage that it returns a useful value that might be used by many other functions. Also, it's slightly easier to use a function name in `sapply()` than writing in the function definition. It has the disadvantage that it is a one-liner and could simply be inserted into the code of the other functions rather than a call. Your own style of programming will probably dictate at what point you begin to write separate functions.

`dstats()` then calls `rbind()` to stick the three vectors together into a matrix row by row, and calls `rownames()` to assign the desired row labels to the matrix. Finally, `dstats()` assigns the class of "dstat", which will allow objects produced by it to be recognized as a specific sort of object. The object `dstat` is then returned, which means that it will be displayed, and optionally assigned to another object.

Assume that you would like to have more control over which variables are included in the output. You know that the mean is a suitable description for `age` and `parity`. `dstats()` as written allows you to pass a vector of either integers or names that will specify the variables to be used.

So, why do we go to all this trouble to define a special object and write a function to produce it? I find that an object that contains means, variances and ns allows me to easily display a summary and produce a basic plot, including error bars, etc. It also allows functions to recognize the object as the correct sort without extensive testing of the contents. Apparently other people have noticed the same thing, and there is at least one other "dstat" object out there. One of the really valuable things about being able to program your stats is that you can customize such objects to suit the sort of work that you do. Therefore, I encourage readers to devise and refine their own objects, a good way to learn the capabilities of R and more importantly, to get what you want.

## What about median and mode?

Say that you wanted the median and mode in your `dstat` object. You could add a call to the `median()` function and include that in the object returned. mode is a bit more difficult. We can use the `tabulate()` function to calculate it - if the data are all positive numbers:

```> x<-sample(1:10,30,TRUE)
xt<-tabulate(x)
xmode<-which(xt == max(xt))
if(sum(xt == max(xt))>1) xmode<-NA```

`xmode` will be the value of the first category that has a frequency equal to the highest frequency in the table. If there is more than one category with the maximum frequency, `xmode` will be set to NA.