Learning Statistics with R - A tutorial for psychology students and other beginners, 2018a

16.6.1 Some data
To make things concrete, let’s suppose that our outcome variable is the grade that a student receives
in my class, a ratio-scale variable corresponding to a mark from 0% to 100%. There are two predictor
variables of interest: whether or not the student turned up to lectures (the attend variable), and whether
or not the student actually read the textbook (the reading variable). We’ll say that attend = 1 if the
student attended class, and attend = 0 if they did not. Similarly, we’ll say that reading = 1 if the student
read the textbook, and reading = 0 if they did not.
Okay, so far that’s simple enough. The next thing we need to do is to wrap some maths around this
(sorry!). For the purposes of this example, let Y p denote the grade of the p-th student in the class. This
is not quite the same notation that we used earlier in this chapter: previously, we’ve used the notation
Y rci to refer to the i-thpersoninther-th group for predictor 1 (the row factor) and the c-th group
for predictor 2 (the column factor). This extended notation was really handy for describing how the
SS values are calculated, but it’s a pain in the current context, so I’ll switch notation here. Now, the
Y p notation is visually simpler than Y rci , but it has the shortcoming that it doesn’t actually keep track
of the group memberships! That is, if I told you that Y 0,0,3 “ 35, you’d immediately know that we’re
talking about a student (the 3rd such student, in fact) who didn’t attend the lectures (i.e., attend = 0)
and didn’t read the textbook (i.e. reading = 0), and who ended up failing the class (grade = 35). But if
I tell you that Y p “ 35 all you know is that the p-th student didn’t get a good grade. We’ve lost some
key information here. Of course, it doesn’t take a lot of thought to figure out how to fix this: what we’ll
do instead is introduce two new variables X 1p and X 2p that keep track of this information. In the case
of our hypothetical student, we know that X 1p “ 0 (i.e., attend = 0) andX 2p “ 0 (i.e., reading = 0). So
the data might look like this:
person, p grade, Y p attendance, X 1p reading, X 2p
1 90 1 1
2 87 1 1
3 75 0 1
4 60 1 0
5 35 0 0
6 50 0 0
7 65 1 0
8 70 0 1
This isn’t anything particularly special, of course: it’s exactly the format in which we expect to see our
data! In other words, if your data have been stored as a data frame in R then you’re probably expecting
to see something that looks like the rtfm.1 data frame:
> rtfm.1
grade attend reading
1 90 1 1
2 87 1 1
3 75 0 1
4 60 1 0
5 35 0 0
6 50 0 0
7 65 1 0
8 70 0 1
Well, sort of. I suspect that a few readers are probably frowning a little at this point. Earlier on in the
book I emphasised the importance of converting nominal scale variables such as attend and reading to
factors, rather than encoding them as numeric variables. The rtfm.1 data frame doesn’t do this, but the
rtfm.2 data frame does, and so you might instead be expecting to see data like this:
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