Introduction to Data Science Using R Runestone Version 1

One of the most basic and widely used methods of representing data is to use rows and columns, where each row is a case or instance and each column is a variable and attribute. Most spreadsheets arrange their data in rows and columns, although spreadsheets don’t usually refer to these as cases or variables. R represents rows and columns in an object called a Data Frame.

Although we live in a three dimensional world, where a box of cereal has height, width, and depth, it is a sad fact of modern life that pieces of paper, chalkboards, whiteboards, and computer screens are still only two dimensional. As a result, most of the statisticians, accountants, computer scientists, and engineers who work with lots of numbers tend to organize them in rows and columns. There’s really no good reason for this other than it makes it easy to fill a rectangular piece of paper with numbers. Rows and columns can be organized any way that you want, but the most common way is to have the rows be "cases" or "instances" and the columns be "attributes" or "variables." Take a look at this nice, two dimensional representation of rows and columns:

Pretty obvious what’s going on, right? The top line, in bold, is not really part of the data. Instead, the top line contains the attribute or variable names. Note that computer scientists tend to call them attributes while statisticians call them variables. Either term is OK. For example, age is an attribute that every living thing has, and you could count it in minutes, hours, days, months, years, or other units of time. Here we have the Age attribute calibrated in years. Technically speaking, the variable names in the top line are "meta data" or what you could think of as data about data. Imagine how much more difficult it would be to understand what was going on in that table without the metadata. There’s a lot of different kinds of metadata: variable names are just one simple type of metadata.

So if you ignore the top row, which contains the variable names, each of the remaining rows is an instance or a case. Again, computer scientists may call them instances, and statisticians may call them cases, but either term is fine. The important thing is that each row refers to an actual thing. In this case all of our things are living creatures in a family. You could think of the Name column as "case labels" in that each one of these labels refers to one and only one row in our data. Most of the time when you are working with a large dataset, there is a number used for the case label, and that number is unique for each case (in other words, the same number would never appear in more than one row). Computer scientists sometimes refer to this column of unique numbers as a key. A key is very useful particularly for matching things up from different data sources, and we will run into this idea again a bit later. For now, though, just take note that the "Dad" row can be distinguished from the "Bro" row, even though they are both Male. Even if we added an "Uncle" row that had the same Age, Gender, and Weight as "Dad" we would still be able to tell the two rows apart because one would have the name "Dad" and the other would have the name "Uncle."

One other important note: Look how each column contains the same kind of data all the way down. For example, the Age column is all numbers. There’s nothing in the Age column like "Old" or "Young." This is a really valuable way of keeping things organized. After all, we could not run the mean() function on the Age column if it contained a little piece of text, like "Old" or "Young." On a related note, every cell (that is an intersection of a row and a column, for example, Sis’s Age) contains just one piece of information. Although a spreadsheet or a word processing program might allow us to put more than one thing in a cell, a real data handling program will not. Finally, see that every column has the same number of entries, so that the whole forms a nice rectangle. When statisticians and other people who work with databases work with a dataset, they expect this rectangular arrangement.