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

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Figure 7.2: The environment panel in Rstudio can actually show you the contents of any loaded package: each package defines a separate environment, so you can select the one you want to look at in this panel. ....................................................................................................... [1] 1 2 1 2 1 Warning message: In x + y : longer object length is not a multiple of shorter object length 7.12.3 An introduction to environments In this section I want to ask a slightly different question: what is the workspace exactly? This question seems simple, but there’s a fair bit to it. This section can be skipped if you’re not really interested in the technical details. In the description I gave earlier, I talked about the workspace as an abstract location in which R variables are stored. That’s basically true, but it hides a couple of key details. For example, any time you have R open, it has to store lots of things in the computer’s memory, not just your variables. For example, the who() function that I wrote has to be stored in memory somewhere, right? If it weren’t I wouldn’t be able to use it. That’s pretty obvious. But equally obviously it’s not in the workspace either, otherwise you should have seen it! Here’s what’s happening. R needs to keep track of a lot of different things, so what it does is organise them into environments, each of which can contain lots of different variables and functions. Your workspace is one such environment. Every package that you have loaded is another environment. And every time you call a function, R briefly creates a temporary environment in which the function itself can work, which is then deleted after the calculations are complete. So, when Itypeinsearch() at the command line > search() [1] ".GlobalEnv" "package:lsr" "tools:rstudio" [4] "package:stats" "package:graphics" "package:grDevices" [7] "package:utils" "package:datasets" "package:methods" [10] "Autoloads" "package:base" what I’m actually looking at is a sequence of environments. The first one, ".GlobalEnv" is the technicallycorrect name for your workspace. No-one really calls it that: it’s either called the workspace or the global - 250 -
environment. And so when you type in objects() or who() what you’re really doing is listing the contents of ".GlobalEnv". But there’s no reason why we can’t look up the contents of these other environments using the objects() function (currently who() doesn’t support this). You just have to be a bit more explicit in your command. If I wanted to find out what is in the package:stats environment (i.e., the environment into which the contents of the stats package have been loaded), here’s what I’d get > objects("package:stats") [1] "acf" "acf2AR" "add.scope" [4] "add1" "addmargins" "aggregate" [7] "aggregate.data.frame" "aggregate.default" "aggregate.ts" [10] "AIC" "alias" "anova" [13] "anova.glm" "anova.glmlist" "anova.lm" BLAH BLAH BLAH where this time I’ve hidden a lot of output in the BLAH BLAH BLAH because the stats package contains about 500 functions. In fact, you can actually use the environment panel in Rstudio to browse any of your loaded packages (just click on the text that says “Global Environment” and you’ll see a dropdown menu like the one shown in Figure 7.2). The key thing to understand then, is that you can access any of the R variables and functions that are stored in one of these environments, precisely because those are the environments that you have loaded! 30 7.12.4 Attaching a data frame The last thing I want to mention in this section is the attach() function, which you often see referred to in introductory R books. Whenever it is introduced, the author of the book usually mentions that the attach() function can be used to “attach” the data frame to the search path, so you don’t have to use the $ operator. That is, if I use the command attach(df) to attach my data frame, I no longer need to type df$variable, and instead I can just type variable. This is true as far as it goes, but it’s very misleading and novice users often get led astray by this description, because it hides a lot of critical details. Here is the very abridged description: when you use the attach() function, what R does is create an entirely new environment in the search path, just like when you load a package. Then, what it does is copy all of the variables in your data frame into this new environment. When you do this, however, you end up with two completely different versions of all your variables: one in the original data frame, and one in the new environment. Whenever you make a statement like df$variable you’re working with the variable inside the data frame; but when you just type variable you’re working with the copy in the new environment. And here’s the part that really upsets new users: changes to one version are not reflected in the other version. As a consequence, it’s really easy for R to end up with different value stored in the two different locations, and you end up really confused as a result. To be fair to the writers of the attach() function, the help documentation does actually state all this quite explicitly, and they even give some examples of how this can cause confusion at the bottom of the help page. And I can actually see how it can be very useful to create copies of your data in a separate location (e.g., it lets you make all kinds of modifications and deletions to the data without having to touch the original data frame). However, I don’t think it’s helpful for new users, since it means you have to be very careful to keep track of which copy you’re talking about. As a consequence of all this, for the purpose of this book I’ve decided not to use the attach() function. It’s something that you can 30 For advanced users: that’s a little over simplistic in two respects. First, it’s a terribly imprecise way of talking about scoping. Second, it might give you the impression that all the variables in question are actually loaded into memory. That’s not quite true, since that would be very wasteful of memory. Instead R has a “lazy loading” mechanism, in which what R actually does is create a “promise” to load those objects if they’re actually needed. For details, check out the delayedAssign() function. - 251 -
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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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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:
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mean( afl.margins[1:5] ) [1] 36.6 A
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the median rises only to $62,500. I
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Next, let’s calculate means and m
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5.2 Measures of variability The sta
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English: which game value deviation
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and you get the same... no, wait...
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Mean − SD Mean Mean + SD Figure 5
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Negative Skew No Skew Positive Skew
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Platykurtic ("too flat") Mesokurtic
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e useful, let’s try this for a ne
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argument specifies the grouping var
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grumpiness score. 13 If the mean is
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Frequency 0 5 10 15 20 Frequency 0
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My grumpiness 40 50 60 70 80 90 4 6
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following extract illustrates the b
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Y1 4 5 6 7 8 9 10 Y2 3 4 5 6 7 8 9
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Okay, so let’s have a look at our
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pay 0.760 0.720 . 0.137 . 0.196 . d
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5 6.68 9.75 NA 5 6 5.99 5.04 72 6 B
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• Measures of variability. In con
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6. Drawing graphs Above all else sh
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delete the plot and then type a new
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Fibonacci 2 4 6 8 10 12 1 2 3 4 5 6
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high-level functions all rely on th
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type = ’p’ type = ’o’ type
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Fibonacci 2 4 6 8 10 12 1 2 3 4 5 6
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Figure 6.8: Altering the scale and
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y the height of the leftmost bar in
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6.3.1 Visual style of your histogra
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0 20 40 60 80 100 120 (a) (b) Figur
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0 20 40 60 80 100 120 Winning Margi
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0 50 100 150 200 250 300 Winning Ma
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6.5.3 Drawing multiple boxplots One
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Winning Margin 0 50 100 150 1987 19
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The second way do to it is to use a
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cor( x = parenthood ) # calculate c
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0 10 20 30 0 10 20 30 Adelaide Fitz
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value for mar is c(5.1, 4.1, 4.1, 2
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This takes the “active” figure
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7. Pragmatic matters The garden of
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in the command above I didn’t nam
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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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Page 233 and 234: 7.6.2 Sorting a factor You can also
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Page 237 and 238: At this point you should have two q
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Page 247 and 248: Table 7.3: The ordering of various
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Page 253 and 254: Figure 7.1: The booksales2.csv data
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Page 267 and 268: 8. Basic programming Machine dreams
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Page 286 and 287: me: I guess I don’t see that. Sur
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Page 290 and 291: discussion of probability theory is
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Page 296 and 297: Probability of event 0.0 0.1 0.2 0.
Page 298 and 299: proceed to roll all 20 dice, what
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Page 302 and 303: In other words, there is a 76.9% ch
Page 304 and 305: Probability Density 0.0 0.1 0.2 0.3
Page 306 and 307: Shaded Area = 68.3% Shaded Area = 9
Page 308 and 309: Probability Density 0.0 0.1 0.2 0.3
Page 310 and 311: • The χ 2 distribution is anothe
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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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