John Ramey

Data frames in R are much like DataSets in SAS, SPSS, .NET, etc. Really, they are just spreadsheets that feel like a matrices. We can use these to look at numerical data along with any meta data or characteristics associated with the numbers though numbers are not required. From the R Documentation, “a data frame is a list of variables of the same length with unique row names”, and also it is “a matrix-like structure whose columns may be of differing types (numeric, logical, factor and character and so on)”.

Let’s take a look at an example. First, we start with generating a 3 x 3 identity matrix and assigning the matrix to the variable, mat.

mat = diag( 3 )

By typing mat, we can see the output.

     [,1] [,2] [,3]
[1,]    1    0    0
[2,]    0    1    0
[3,]    0    0    1

Next, we are going to convert this matrix to a data frame called mat_dataframe and output it.

 mat_dataframe = data.frame( mat )

  X1 X2 X3
1  1  0  0
2  0  1  0
3  0  0  1

Notice that the column names are X1, X2, and X3 and that the row names are 1, 2, and 3. Say we want to add more columns and rows to our data frame. Let’s first start by appending a row to the “mat_dataframe.”  We do this with rbind.

mat_dataframe = rbind(mat_dataframe, c(2,2,2))

We have added a vector of twos to the next row of the data frame.  Here’s what mat_dataframe looks like so far.

  X1 X2 X3
1  1  0  0
2  0  1  0
3  0  0  1
4  2  2  2

Now, we should try appending 2 columns to the mat_dataframe using 2 different methods. The first line will create a new data frame from the original data frame and append a column called “City” with “Dallas” as the entry for each row. The second takes this data frame and adds another column called Color with entries blue and green.

mat_dataframe = data.frame( mat_dataframe, City="Dallas" )
mat_dataframe = cbind( mat_dataframe, Color=c( "blue", "green" ) )

Now, the mat_dataframe looks like this.

  X1 X2 X3   City Color
1  1  0  0 Dallas  blue
2  0  1  0 Dallas green
3  0  0  1 Dallas  blue
4  2  2  2 Dallas green

Notice that once blue and green were both used, they were both repeated. Before we move on, let me mention a gotcha when adding columns. On the City column, I simply inserted Dallas for each row, but under the Color column, I added 2 different colors. What happens if we specify three values? Let’s try this with a new column called Country.

mat_dataframe = data.frame( mat_dataframe, Country=c( "USA", "Canada", "Mexico" ) )

We get the following error…

Error in data.frame(mat_dataframe, Country = c(“USA”, “Canada”, “Mexico”)) : arguments imply differing number of rows: 4, 3

A rule of thumb: make sure the number of values being assigned divides into the number of rows (or columns) of the data frame. If our data frame had 6 rows (or 9 or 12 or … ), we could have used the above code.

Our data frame is essentially a matrix with a couple of attached column vectors containing strings. This may not seem very useful at first, but it is a wonderful data structure, making some statistical methods among other things easier to use. Soon, I will post a basic ANOVA example using data frames.

I must have had this epiphany several times in the last few years, but I had it again this evening while being introduced to the dark side.  Many students are taught that

and that 0! is defined as 1.  But is there some higher level mathematics in which this factorial idea is just a corollary as with most pre-graduate school mathematics.  Well, there is!  This is the epic Gamma function.  It is defined as

.

If is a positive integer, then .

Here is the main event.  Suppose ; because is a positive integer,   But then, notice that

.

Hence, our conclusion is that 0! = 1.

My recent goal is to surround myself with things in my cubicle that will remind me of my work, so that when I inevitably become distracted, many “get back to work” signs act as a sometimes much needed slavedriver.  Among these signs are charts of probability distributions and their properties, but first, I needed to find a good set of them — concise but all the information I need is presented.  So, I Google’d for “lists of pdfs with properties,” forgetting momentarily that PDFs refer to more than just Probability Density (or Distribution) Functions.  I changed my query to  “probability distributions with properties” and was stunned to see Google’s following suggestion.

After being curious and clicking the 3rd of these links, I have manually turned on Google’s safe search feature for the first time.