5: Descriptive Statistics
Any time that you get a new data set to look at, one of the first tasks that you have to do is find ways of summarising the data in a compact, easily understood fashion. This is what
descriptive statistics
(as opposed to inferential statistics) is all about. In fact, to many people the term “statistics” is synonymous with descriptive statistics. It is this topic that we’ll consider in this chapter, but before going into any details, let’s take a moment to get a sense of why we need descriptive statistics. To do this, let’s load the
aflsmall.Rdata
file, and use the
who()
function in the
lsr
package to see what variables are stored in the file:
load( "./data/aflsmall.Rdata" )
library(lsr)
## Warning: package 'lsr' was built under R version 3.5.2
who()
## -- Name -- -- Class -- -- Size --
## afl.finalists factor 400
## afl.margins numeric 176
There are two variables here,
afl.finalists
and
afl.margins
. We’ll focus a bit on these two variables in this chapter, so I’d better tell you what they are. Unlike most of data sets in this book, these are actually real data, relating to the Australian Football League (AFL)
64
The
afl.margins
variable contains the winning margin (number of points) for all 176 home and away games played during the 2010 season. The
afl.finalists
variable contains the names of all 400 teams that played in all 200 finals matches played during the period 1987 to 2010. Let’s have a look at the
afl.margins
variable:
print(afl.margins)
## [1] 56 31 56 8 32 14 36 56 19 1 3 104 43 44 72 9 28
## [18] 25 27 55 20 16 16 7 23 40 48 64 22 55 95 15 49 52
## [35] 50 10 65 12 39 36 3 26 23 20 43 108 53 38 4 8 3
## [52] 13 66 67 50 61 36 38 29 9 81 3 26 12 36 37 70 1
## [69] 35 12 50 35 9 54 47 8 47 2 29 61 38 41 23 24 1
## [86] 9 11 10 29 47 71 38 49 65 18 0 16 9 19 36 60 24
## [103] 25 44 55 3 57 83 84 35 4 35 26 22 2 14 19 30 19
## [120] 68 11 75 48 32 36 39 50 11 0 63 82 26 3 82 73 19
## [137] 33 48 8 10 53 20 71 75 76 54 44 5 22 94 29 8 98
## [154] 9 89 1 101 7 21 52 42 21 116 3 44 29 27 16 6 44
## [171] 3 28 38 29 10 10
This output doesn’t make it easy to get a sense of what the data are actually saying. Just “looking at the data” isn’t a terribly effective way of understanding data. In order to get some idea about what’s going on, we need to calculate some descriptive statistics (this chapter) and draw some nice pictures (Chapter 6. Since the descriptive statistics are the easier of the two topics, I’ll start with those, but nevertheless I’ll show you a histogram of the
afl.margins
data, since it should help you get a sense of what the data we’re trying to describe actually look like. But for what it’s worth, this histogram – which is shown in Figure 5.1 – was generated using the
hist()
function. We’ll talk a lot more about how to draw histograms in Section 6.3. For now, it’s enough to look at the histogram and note that it provides a fairly interpretable representation of the
afl.margins
data.
-
- 5.3: Skew and Kurtosis
- There are two more descriptive statistics that you will sometimes see reported in the psychological literature, known as skew and kurtosis. In practice, neither one is used anywhere near as frequently as the measures of central tendency and variability that we’ve been talking about. Skew is pretty important, so you do see it mentioned a fair bit; but I’ve actually never seen kurtosis reported in a scientific article to date.