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

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arguments. For instance, if I decide I want the vertical scale of the plot to run from 0 to 100, then I’d set ylim = c(0, 100). • Suppress labelling: ann. This is a logical-valued argument that you can use if you don’t want R to include any text for a title, subtitle or axis label. To do so, set ann = FALSE. This will stop R from including any text that would normally appear in those places. Note that this will override any of your manual titles. For example, if you try to add a title using the main argument, but you also specify ann = FALSE, no title will appear. • Suppress axis drawing: axes. Again, this is a logical valued argument. Suppose you don’t want R to draw any axes at all. To suppress the axes, all you have to do is add axes = FALSE. This will remove the axes and the numbering, but not the axis labels (i.e. the xlab and ylab text). Note that you can get finer grain control over this by specifying the xaxt and yaxt graphical parameters instead (see below). • Include a framing box: frame.plot. Suppose you’ve removed the axes by setting axes = FALSE, but you still want to have a simple box drawn around the plot; that is, you only wanted to get rid of the numbering and the tick marks, but you want to keep the box. To do that, you set frame.plot = TRUE. Note that this list isn’t exhaustive. There are a few other arguments to the plot.default function that you can play with if you want to, but those are the ones you are probably most likely to want to use. As always, however, if these aren’t enough options for you, there’s also a number of other graphical parameters that you might want to play with as well. That’s the focus of the next section. In the meantime, here’s a command that makes use of all these different options: > plot( x = Fibonacci, # the data + xlim = c(0, 15), # expand the x-scale + ylim = c(0, 15), # expand the y-scale + ann = FALSE, # delete all annotations + axes = FALSE, # delete the axes + frame.plot = TRUE # but include a framing box + ) The output is shown in Figure 6.8, and it’s pretty much exactly as you’d expect. The axis scales on both the horizontal and vertical dimensions have been expanded, the axes have been suppressed as have the annotations, but I’ve kept a box around the plot. Before moving on, I should point out that there are several graphical parameters relating to the axes, the box, and the general appearance of the plot which allow finer grain control over the appearance of the axes and the annotations. • Suppressing the axes individually: xaxt, yaxt. These graphical parameters are basically just fancier versions of the axes argument we discussed earlier. If you want to stop R from drawing the vertical axis but you’d like it to keep the horizontal axis, set yaxt = "n". I trust that you can figure out how to keep the vertical axis and suppress the horizontal one! • Box type: bty. In the same way that xaxt, yaxt are just fancy versions of axes, thebox type parameter is really just a fancier version of the frame.plot argument, allowing you to specify exactly which out of the four borders you want to keep. The way we specify this parameter is a bit stupid, in my opinion: the possible values are "o" (the default), "l", "7", "c", "u", or"]", each of which will draw only those edges that the corresponding character suggests. That is, the letter "c" has a top, a bottom and a left, but is blank on the right hand side, whereas "7" has a top and a right, but is blank on the left and the bottom. Alternatively a value of "n" means that no box will be drawn. - 168 -
Figure 6.8: Altering the scale and appearance of the plot axes. ....................................................................................................... 12 10 Fibonacci 8 6 4 2 Index Figure 6.9: Other ways to customise the axes. ....................................................................................................... - 169 -
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Learning statistics with R: A tutor
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This book is published under a Crea
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Preface Table of Contents I Backgro
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8.6 Summary . . . . . . . . . . . .
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VI Endings, alternatives and prospe
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February 16, 2015 Preface to Versio
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and density is discussed. A detaile
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1. Why do we learn statistics? “T
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And finally, an invalid argument wi
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Admission rate (both genders) 0 20
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experiment, and they don’t get an
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2. A brief introduction to research
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different ways: the length of time
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that when I ask 100 people how they
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Table 2.1: The relationship between
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2.3 Assessing the reliability of a
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2.5.1 Experimental research The key
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things “inside” the study. Let
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they lack face validity, you’ll f
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that age is growing at an incredibl
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then it can be a big problem. 2.7.7
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2.7.10 Placebo effects The placebo
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it doesn’t, which one do you thin
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Part II. An introduction to R - 35
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go out into the real world. It’s
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download Rstudio. To understand why
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Most of this text is pretty uninter
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citation() To cite R in publication
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Table 3.1: Basic arithmetic operati
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Division / and Multiplication *, th
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sales * royalty [1] 2450 As far as
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x to the power of 0.5”. Personall
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As you can see, specifying the argu
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Figure 3.3: If you’ve typed the n
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sales.by.month sales.by.month [1]
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profit / days.per.month [1] 0.00000
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not true of R. R is not infinitely
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Table 3.3: Some more logical operat
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In other words, any.sales.this.mont
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and gotten exactly the same result.
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Figure 3.6: The options window in R
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- 72 -
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print( keeper ) [1] 8.539539 So, fr
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to import an SPSS data file into R,
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The output here is telling you that
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Figure 4.3: The Rstudio dialog box
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Figure 4.5: The Rstudio “Environm
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this should be obvious already. But
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Figure 4.6: The “file panel” is
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from this file into my workspace. T
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2 February 28 100 high 3 March 31 2
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Figure 4.9: The Rstudio window for
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4.6.1 Special values The first thin
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x y x * y Error in x * y : non-nu
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4.7.1 Introducing factors Suppose,
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factors in 7.11.2, but for now you
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An alternative method is to use the
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4.11 Generic functions There’s on
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load (base) R Documentation The R D
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Warning Saved R objects are binary
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5. Descriptive statistics Any time
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mean of these observations is just:
Page 131 and 132: mean( afl.margins[1:5] ) [1] 36.6 A
Page 133 and 134: the median rises only to $62,500. I
Page 135 and 136: Next, let’s calculate means and m
Page 137 and 138: 5.2 Measures of variability The sta
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Page 143 and 144: Mean − SD Mean Mean + SD Figure 5
Page 145 and 146: Negative Skew No Skew Positive Skew
Page 147 and 148: Platykurtic ("too flat") Mesokurtic
Page 149 and 150: e useful, let’s try this for a ne
Page 151 and 152: argument specifies the grouping var
Page 153 and 154: grumpiness score. 13 If the mean is
Page 155 and 156: Frequency 0 5 10 15 20 Frequency 0
Page 157 and 158: My grumpiness 40 50 60 70 80 90 4 6
Page 159 and 160: following extract illustrates the b
Page 161 and 162: Y1 4 5 6 7 8 9 10 Y2 3 4 5 6 7 8 9
Page 163 and 164: Okay, so let’s have a look at our
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Page 167 and 168: 5 6.68 9.75 NA 5 6 5.99 5.04 72 6 B
Page 169 and 170: • Measures of variability. In con
Page 171 and 172: 6. Drawing graphs Above all else sh
Page 173 and 174: delete the plot and then type a new
Page 175 and 176: Fibonacci 2 4 6 8 10 12 1 2 3 4 5 6
Page 177 and 178: high-level functions all rely on th
Page 179 and 180: type = ’p’ type = ’o’ type
Page 181: Fibonacci 2 4 6 8 10 12 1 2 3 4 5 6
Page 185 and 186: y the height of the leftmost bar in
Page 187 and 188: 6.3.1 Visual style of your histogra
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Page 191 and 192: 0 20 40 60 80 100 120 Winning Margi
Page 193 and 194: 0 50 100 150 200 250 300 Winning Ma
Page 195 and 196: 6.5.3 Drawing multiple boxplots One
Page 197 and 198: Winning Margin 0 50 100 150 1987 19
Page 199 and 200: The second way do to it is to use a
Page 201 and 202: cor( x = parenthood ) # calculate c
Page 203 and 204: 0 10 20 30 0 10 20 30 Adelaide Fitz
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Page 207 and 208: This takes the “active” figure
Page 209 and 210: 7. Pragmatic matters The garden of
Page 211 and 212: in the command above I didn’t nam
Page 213 and 214: speaker ee onk oo pip makka-pakka 0
Page 215 and 216: 2 7 3 3 1 3 3 -1 1 -1 BLAH BLAH BLA
Page 217 and 218: seen it before. In any case, those
Page 219 and 220: Table 7.2: Two more arithmetic oper
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Page 223 and 224: But suppose, on the other hand, tha
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7.6.2 Sorting a factor You can also
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Two other methods that I want to br
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At this point you should have two q
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(alcohol, caffeine or no drug). Bec
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3 3 female 4.6 643 7.4 226 7.3 412
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discuss melt() and cast() in a fair
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paste( hw, ng, sep = ".", collapse
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Table 7.3: The ordering of various
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Table 7.4: Standard escape characte
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sub( pattern = "a", replacement = "
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Figure 7.1: The booksales2.csv data
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note that if you don’t have the R
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etween the two. However, there are
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a third variable to the cross-tabs
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today print(today) # display the d
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encode numbers in binary, 29 0.1 is
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environment. And so when you type i
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8. Basic programming Machine dreams
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for ages, you figure out some reall
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Figure 8.2: A screenshot showing th
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8.1.5 Differences between scripts a
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to the second value in vector; and
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crunching, we tell R (on line 21) t
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What this does is create a function
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hundreds of other things besides. H
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Part IV. Statistical theory - 269 -
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me: I guess I don’t see that. Sur
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discussion of probability theory is
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In this case 11 of these 20 coin fl
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frequentists do this sometimes. And
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Probability of event 0.0 0.1 0.2 0.
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proceed to roll all 20 dice, what
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(a) Probability 0.00 0.05 0.10 0.15
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In other words, there is a 76.9% ch
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Probability Density 0.0 0.1 0.2 0.3
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Shaded Area = 68.3% Shaded Area = 9
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Probability Density 0.0 0.1 0.2 0.3
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• The χ 2 distribution is anothe
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work rather than rchisq() - the obs
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10.1.1 Defining a population A samp
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Figure 10.2: Biased sampling withou
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a stratified sampling technique you
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10.2 The law of large numbers In th
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Table 10.1: Ten replications of the
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Sample Size = 1 Sample Size = 2 Sam
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Sample Size = 1 Sample Size = 2 0.0
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efer to them. For instance, if true
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Average Sample Mean 96 98 100 102 1
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10.5 Estimating a confidence interv
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sense idea of what it means to say
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Average Attendance 0 10000 30000 19
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Here’s how to plot the means and
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Let’s suppose that this glorious
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Dan’s research hypothesis: “ESP
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the type I error rate. As Blackston
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Critical Regions for a Two−Sided
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Critical Region for a One−Sided T
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one based on Neyman’s approach to
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alternative hypothesis is a near ce
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Sampling Distribution for X if θ=.
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Table 11.2: A crude guide to unders
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ureaucratic process. It’s not par
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(binomial test was non significant)
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12. Categorical data analysis Now t
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observations that fall within the i
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it is when it predicts too many (wh
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df = 3 df = 4 df = 5 0 2 4 6 8 10 V
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That’s why I told R to use the up
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clubs 35 40 0.2 diamonds 51 60 0.3
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only one of many (albeit one of the
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That’s more or less what we’re
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Well, since these probabilities hav
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Chapek 9 has an unfortunate tendenc
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12.5 Assumptions of the test(s) All
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To get the test of independence, al
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This is a bit more output than we g
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subj.1 : 1 no :70 no :90 subj.10 :
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13. Comparing two means In the prev
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40 50 60 70 80 90 Grades Figure 13.
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Two Sided Test One Sided Test −1.
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lower.area print( lower.area ) [1]
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df = 2 df = 10 −4 −2 0 2 4 valu
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than I’ve done here. For instance
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Anastasia’s students Bernadette
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null hypothesis μ alternative hypo
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ut once again I’m going to start
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for the difference “(mean 1) minu
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null hypothesis μ alternative hypo
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13.5.1 The data The data set that w
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ciMean( x = chico$improvement ) 2.5
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Paired samples t-test Variables: gr
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Grouping variable: ID variable: tim
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In a one-sided confidence interval,
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are different tests. Secondly, I wa
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Table 13.1: A (very) rough guide to
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ut you no longer believe that the c
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Frequency 0 5 10 15 20 Normally Dis
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Sampling distribution of W (for nor
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We then count up the number of chec
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• A paired samples t-test is used
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14. Comparing several means (one-wa
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Mood Gain 0.5 1.0 1.5 placebo anxif
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This formula looks pretty much iden
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is true, then you’d expect all th
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mean square, MS w , can be viewed a
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3 placebo 0.1 0.45 -0.350 0.1225 4
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is choose an α level (i.e., accept
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names( my.anova ) [1] "coefficients
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etaSquared( x = my.anova ) eta.sq e
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One thing that bugs me slightly abo
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If we compare these three p-values
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• Homogeneity of variance. Notice
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Secondly, I did mention that it’s
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Frequency 0 1 2 3 4 5 6 7 Sample Qu
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Looking at this table, notice that
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• Post hoc analysis and correctio
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15. Linear regression The goal in t
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The Best Fitting Regression Line No
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• data. The data frame containing
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Figure 15.4: A 3D visualisation of
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Wonderful. A big number that doesn
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If our regression model has K predi
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You can see why this is handy, sinc
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what it is. The test for the signif
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Fortunately, confidence intervals f
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• Uncorrelated predictors. The id
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Outlier Outcome Predictor Figure 15
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Outcome High influence Predictor Fi
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Cook’s distance 0.00 0.02 0.04 0.
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Standardized residuals −2 −1 0
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78 Residuals vs Fitted Residuals
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In a lot of cases, the solution to
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Signif. codes: 0 *** 0.001 ** 0.01
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15.10.1 Backward elimination Okay,
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+ day 1 1.55760 1837.2 297.08 + bab
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etween those two SS values as a sum
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16. Factorial ANOVA Over the course
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At this point we have 12 different
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drug 2 3.45 1.727 18.6 8.6e-05 ***
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means can be organised into the sam
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attributable to the “ANOVA model
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Only Factor A has an effect Only Fa
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The effect of CBT (difference betwe
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Now, if you go back to the formulas
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Here’s what I mean. Again, let’
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Speaking of interaction effects, he
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16.4 Assumption checking As with on
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16.5.1 The F test comparing two mod
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the degrees of freedom here is 15.
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tfm.2 grade attend reading 1 90 yes
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line, we obtain the following: Ŷ 7
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Estimate Std. Error t value Pr(>|t|
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that contains the same data as clin
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What about the case when there does
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R comes with a variety of functions
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enlightening read. There are a lot
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16.8 Post hoc tests Time to switch
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diff lwr upr p adj anxifree:no.ther
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1 yes none 3.700 2 no none 5.550 3
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Analysis of Variance Table Response
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III tests (which are simple) before
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sugar 2.13 2 4.0446 0.045426 * milk
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even simpler. The main effect of su
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However, when we do the same thing
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Part VI. Endings, alternatives and
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first I want to work through a simp
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This is a very useful table, so it
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P pd|hqP phq P ph|dq “ P pdq And
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Bayesian approach relative to the o
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hardly unusual: in my experience, m
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Cumulative Probability of Type I Er
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are wrong. Worse yet, because we do
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library( BayesFactor ) # ...because
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make sense to people who already un
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-------------- [1] Non-indep. (a=1)
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Before moving on, it’s worth high
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17.6.2 The Bayesian version Okay, s
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[2] day : 0.2724027 ˘0% [3] baby.s
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therapy 0.4672 1 8.5816 0.01262 * d
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command that I use when I want to g
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- 586 -
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• Other types of correlations. In
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measurements mean that independence
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the list that I’ve given above is
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So if you were forced to guess my w
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to be able to do more than ANOVA, m
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Fisher, R. A. (1922a). On the inter
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