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5: Descriptive Statistics

  • Page ID
    3971
  • 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.

    histogram1-1.png
    Figure 5.1: A histogram of the AFL 2010 winning margin data (the afl.margins variable). As you might expect, the larger the margin the less frequently you tend to see it.