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

More documents

Recommendations

Info

Notice that this time around we have variable names of the form MRT/block1/day2. As before, the first part of the name refers to the measured variable (response time), but there are now two suffixes, one indicating that the testing took place in block 1, and the other indicating that it took place on day 2. And just to complicate matters, it uses / as the separator character rather than _. Even so, reshaping this data set is pretty easy. The command to do it is, > choice.2 choice.2 id gender MRT PC block day 1 1 male 415 79 block1 day1 2 2 male 500 83 block1 day1 3 3 female 478 91 block1 day1 4 4 female 550 75 block1 day1 5 1 male 400 88 block1 day2 6 2 male 490 92 block1 day2 BLAH BLAH BLAH 15 3 female 474 100 block2 day2 16 4 female 588 95 block2 day2 In this long form data frame we have two between-subject variables (id and gender), two variables that define our within-subject manipulations (block and day), and two more contain the measurements we took (MRT and PC). To convert this back to wide form is equally straightforward. We use the longToWide() function, but this time around we need to alter the formula in order to tell it that we have two within-subject factors. The command is now > longToWide( choice.2, MRT+PC ~ block+day, sep="/" ) and this produces a wide form data set containing the same variables as the original choice data frame. 7.7.5 What other options are there? The advantage to the approach described in the previous section is that it solves a quite specific problem (but a commonly encountered one) with a minimum of fuss. The disadvantage is that the tools are quite limited in scope. They allow you to switch your data back and forth between two different formats that are very common in everyday data analysis. However, there a number of other tools that you can use if need be. Just within the core packages distributed with R thereisthereshape() function, as well as the stack() and unstack() functions, all of which can be useful under certain circumstances. And there are of course thousands of packages on CRAN that you can use to help you with different tasks. One popular package for this purpose is the reshape package, written by Hadley Wickham (see Wickham, 2007, for details). There are two key functions in this package, called melt() and cast() that are pretty useful for solving a lot of reshaping problems. In a future version of this book I intend to - 228 -
discuss melt() and cast() in a fair amount of detail. 7.8 Working with text Sometimes your data set is quite text heavy. This can be for a lot of different reasons. Maybe the raw data are actually taken from text sources (e.g., newspaper articles), or maybe your data set contains a lot of free responses to survey questions, in which people can write whatever text they like in response to some query. Or maybe you just need to rejig some of the text used to describe nominal scale variables. Regardless of what the reason is, you’ll probably want to know a little bit about how to handle text in R. Some things you already know how to do: I’ve discussed the use of nchar() to calculate the number of characters in a string (Section 3.8.1), and a lot of the general purpose tools that I’ve discussed elsewhere (e.g., the == operator) have been applied to text data as well as to numeric data. However, because text data is quite rich, and generally not as well structured as numeric data, R provides a lot of additional tools that are quite specific to text. In this section I discuss only those tools that come as part of the base packages, but there are other possibilities out there: the stringr package provides a powerful alternative that is a lot more coherent than the basic tools, and is well worth looking into. 7.8.1 Shortening a string The first task I want to talk about is how to shorten a character string. For example, suppose that I have a vector that contains the names of several different animals: > animals strtrim( x = animals, width = 3 ) [1] "cat" "dog" "kan" "wha" Note that the only thing that strtrim() does is chop off excess characters at the end of a string. It doesn’t insert any whitespace characters to fill them out if the original string is shorter than the width argument. For example, if I trim the animals data to 4 characters, here’s what I get: > strtrim( x = animals, width = 4 ) [1] "cat" "dog" "kang" "whal" The "cat" and "dog" strings still only use 3 characters. Okay, but what if you don’t want to start from the first letter? Suppose, for instance, I only wanted to keep the second and third letter of each word. That doesn’t happen quite as often, but there are some situations where you need to do something like that. If that does happen, then the function you need is substr(), inwhichyouspecifyastart point and a stop point instead of specifying the width. For instance, to keep only the 2nd and 3rd letters of the various animals, I can do the following: > substr( x = animals, start = 2, stop = 3 ) [1] "at" "og" "an" "ha" - 229 -
Page 2 and 3:
Learning statistics with R: A tutor
Page 4 and 5:
This book is published under a Crea
Page 6 and 7:
Preface Table of Contents I Backgro
Page 8 and 9:
8.6 Summary . . . . . . . . . . . .
Page 10 and 11:
VI Endings, alternatives and prospe
Page 12 and 13:
February 16, 2015 Preface to Versio
Page 14 and 15:
and density is discussed. A detaile
Page 17 and 18:
1. Why do we learn statistics? “T
Page 19 and 20:
And finally, an invalid argument wi
Page 21 and 22:
Admission rate (both genders) 0 20
Page 23 and 24:
experiment, and they don’t get an
Page 25 and 26:
2. A brief introduction to research
Page 27 and 28:
different ways: the length of time
Page 29 and 30:
that when I ask 100 people how they
Page 31 and 32:
Table 2.1: The relationship between
Page 33 and 34:
2.3 Assessing the reliability of a
Page 35 and 36:
2.5.1 Experimental research The key
Page 37 and 38:
things “inside” the study. Let
Page 39 and 40:
they lack face validity, you’ll f
Page 41 and 42:
that age is growing at an incredibl
Page 43 and 44:
then it can be a big problem. 2.7.7
Page 45 and 46:
2.7.10 Placebo effects The placebo
Page 47 and 48:
it doesn’t, which one do you thin
Page 49:
Part II. An introduction to R - 35
Page 52 and 53:
go out into the real world. It’s
Page 54 and 55:
download Rstudio. To understand why
Page 56 and 57:
Most of this text is pretty uninter
Page 58 and 59:
citation() To cite R in publication
Page 60 and 61:
Table 3.1: Basic arithmetic operati
Page 62 and 63:
Division / and Multiplication *, th
Page 64 and 65:
sales * royalty [1] 2450 As far as
Page 66 and 67:
x to the power of 0.5”. Personall
Page 68 and 69:
As you can see, specifying the argu
Page 70 and 71:
Figure 3.3: If you’ve typed the n
Page 72 and 73:
sales.by.month sales.by.month [1]
Page 74 and 75:
profit / days.per.month [1] 0.00000
Page 76 and 77:
not true of R. R is not infinitely
Page 78 and 79:
Table 3.3: Some more logical operat
Page 80 and 81:
In other words, any.sales.this.mont
Page 82 and 83:
and gotten exactly the same result.
Page 84 and 85:
Figure 3.6: The options window in R
Page 86 and 87:
- 72 -
Page 88 and 89:
print( keeper ) [1] 8.539539 So, fr
Page 90 and 91:
to import an SPSS data file into R,
Page 92 and 93:
The output here is telling you that
Page 94 and 95:
Figure 4.3: The Rstudio dialog box
Page 96 and 97:
Figure 4.5: The Rstudio “Environm
Page 98 and 99:
this should be obvious already. But
Page 100 and 101:
Figure 4.6: The “file panel” is
Page 102 and 103:
from this file into my workspace. T
Page 104 and 105:
2 February 28 100 high 3 March 31 2
Page 106 and 107:
Figure 4.9: The Rstudio window for
Page 108 and 109:
4.6.1 Special values The first thin
Page 110 and 111:
x y x * y Error in x * y : non-nu
Page 112 and 113:
4.7.1 Introducing factors Suppose,
Page 114 and 115:
factors in 7.11.2, but for now you
Page 116 and 117:
An alternative method is to use the
Page 118 and 119:
4.11 Generic functions There’s on
Page 120 and 121:
load (base) R Documentation The R D
Page 122 and 123:
Warning Saved R objects are binary
Page 124 and 125:
- 110 -
Page 127 and 128:
5. Descriptive statistics Any time
Page 129 and 130:
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
Page 139 and 140:
English: which game value deviation
Page 141 and 142:
and you get the same... no, wait...
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
Page 165 and 166:
pay 0.760 0.720 . 0.137 . 0.196 . d
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 and 182:
Fibonacci 2 4 6 8 10 12 1 2 3 4 5 6
Page 183 and 184:
Figure 6.8: Altering the scale and
Page 185 and 186:
y the height of the leftmost bar in
Page 187 and 188:
6.3.1 Visual style of your histogra
Page 189 and 190:
0 20 40 60 80 100 120 (a) (b) Figur
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
Page 205 and 206: value for mar is c(5.1, 4.1, 4.1, 2
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
Page 221 and 222: fact R does provide a function for
Page 223 and 224: But suppose, on the other hand, tha
Page 225 and 226: is select several different variabl
Page 227 and 228: column number. So, if we want to pi
Page 229 and 230: case.2 upsy-daisy pip 2 case.4 makk
Page 231 and 232: Note that R will only allow you to
Page 233 and 234: 7.6.2 Sorting a factor You can also
Page 235 and 236: Two other methods that I want to br
Page 237 and 238: At this point you should have two q
Page 239 and 240: (alcohol, caffeine or no drug). Bec
Page 241: 3 3 female 4.6 643 7.4 226 7.3 412
Page 245 and 246: paste( hw, ng, sep = ".", collapse
Page 247 and 248: Table 7.3: The ordering of various
Page 249 and 250: Table 7.4: Standard escape characte
Page 251 and 252: sub( pattern = "a", replacement = "
Page 253 and 254: Figure 7.1: The booksales2.csv data
Page 255 and 256: note that if you don’t have the R
Page 257 and 258: etween the two. However, there are
Page 259 and 260: a third variable to the cross-tabs
Page 261 and 262: today print(today) # display the d
Page 263 and 264: encode numbers in binary, 29 0.1 is
Page 265 and 266: environment. And so when you type i
Page 267 and 268: 8. Basic programming Machine dreams
Page 269 and 270: for ages, you figure out some reall
Page 271 and 272: Figure 8.2: A screenshot showing th
Page 273 and 274: 8.1.5 Differences between scripts a
Page 275 and 276: to the second value in vector; and
Page 277 and 278: crunching, we tell R (on line 21) t
Page 279 and 280: What this does is create a function
Page 281 and 282: hundreds of other things besides. H
Page 283: Part IV. Statistical theory - 269 -
Page 286 and 287: me: I guess I don’t see that. Sur
Page 288 and 289: - 274 -
Page 290 and 291: discussion of probability theory is
Page 292 and 293:
In this case 11 of these 20 coin fl
Page 294 and 295:
frequentists do this sometimes. And
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
Page 300 and 301:
(a) Probability 0.00 0.05 0.10 0.15
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
Page 312 and 313:
work rather than rchisq() - the obs
Page 314 and 315:
- 300 -
Page 316 and 317:
10.1.1 Defining a population A samp
Page 318 and 319:
Figure 10.2: Biased sampling withou
Page 320 and 321:
a stratified sampling technique you
Page 322 and 323:
10.2 The law of large numbers In th
Page 324 and 325:
Table 10.1: Ten replications of the
Page 326 and 327:
Sample Size = 1 Sample Size = 2 Sam
Page 328 and 329:
Sample Size = 1 Sample Size = 2 0.0
Page 330 and 331:
efer to them. For instance, if true
Page 332 and 333:
Average Sample Mean 96 98 100 102 1
Page 334 and 335:
10.5 Estimating a confidence interv
Page 336 and 337:
sense idea of what it means to say
Page 338 and 339:
Average Attendance 0 10000 30000 19
Page 340 and 341:
Here’s how to plot the means and
Page 342 and 343:
Let’s suppose that this glorious
Page 344 and 345:
Dan’s research hypothesis: “ESP
Page 346 and 347:
the type I error rate. As Blackston
Page 348 and 349:
Critical Regions for a Two−Sided
Page 350 and 351:
Critical Region for a One−Sided T
Page 352 and 353:
one based on Neyman’s approach to
Page 354 and 355:
alternative hypothesis is a near ce
Page 356 and 357:
Sampling Distribution for X if θ=.
Page 358 and 359:
Table 11.2: A crude guide to unders
Page 360 and 361:
ureaucratic process. It’s not par
Page 362 and 363:
(binomial test was non significant)
Page 365 and 366:
12. Categorical data analysis Now t
Page 367 and 368:
observations that fall within the i
Page 369 and 370:
it is when it predicts too many (wh
Page 371 and 372:
df = 3 df = 4 df = 5 0 2 4 6 8 10 V
Page 373 and 374:
That’s why I told R to use the up
Page 375 and 376:
clubs 35 40 0.2 diamonds 51 60 0.3
Page 377 and 378:
only one of many (albeit one of the
Page 379 and 380:
That’s more or less what we’re
Page 381 and 382:
Well, since these probabilities hav
Page 383 and 384:
Chapek 9 has an unfortunate tendenc
Page 385 and 386:
12.5 Assumptions of the test(s) All
Page 387 and 388:
To get the test of independence, al
Page 389 and 390:
This is a bit more output than we g
Page 391 and 392:
subj.1 : 1 no :70 no :90 subj.10 :
Page 393 and 394:
13. Comparing two means In the prev
Page 395 and 396:
40 50 60 70 80 90 Grades Figure 13.
Page 397 and 398:
Two Sided Test One Sided Test −1.
Page 399 and 400:
lower.area print( lower.area ) [1]
Page 401 and 402:
df = 2 df = 10 −4 −2 0 2 4 valu
Page 403 and 404:
than I’ve done here. For instance
Page 405 and 406:
Anastasia’s students Bernadette
Page 407 and 408:
null hypothesis μ alternative hypo
Page 409 and 410:
ut once again I’m going to start
Page 411 and 412:
for the difference “(mean 1) minu
Page 413 and 414:
null hypothesis μ alternative hypo
Page 415 and 416:
13.5.1 The data The data set that w
Page 417 and 418:
ciMean( x = chico$improvement ) 2.5
Page 419 and 420:
Paired samples t-test Variables: gr
Page 421 and 422:
Grouping variable: ID variable: tim
Page 423 and 424:
In a one-sided confidence interval,
Page 425 and 426:
are different tests. Secondly, I wa
Page 427 and 428:
Table 13.1: A (very) rough guide to
Page 429 and 430:
ut you no longer believe that the c
Page 431 and 432:
Frequency 0 5 10 15 20 Normally Dis
Page 433 and 434:
Sampling distribution of W (for nor
Page 435 and 436:
We then count up the number of chec
Page 437 and 438:
• A paired samples t-test is used
Page 439 and 440:
14. Comparing several means (one-wa
Page 441 and 442:
Mood Gain 0.5 1.0 1.5 placebo anxif
Page 443 and 444:
This formula looks pretty much iden
Page 445 and 446:
is true, then you’d expect all th
Page 447 and 448:
mean square, MS w , can be viewed a
Page 449 and 450:
3 placebo 0.1 0.45 -0.350 0.1225 4
Page 451 and 452:
is choose an α level (i.e., accept
Page 453 and 454:
names( my.anova ) [1] "coefficients
Page 455 and 456:
etaSquared( x = my.anova ) eta.sq e
Page 457 and 458:
One thing that bugs me slightly abo
Page 459 and 460:
If we compare these three p-values
Page 461 and 462:
• Homogeneity of variance. Notice
Page 463 and 464:
Secondly, I did mention that it’s
Page 465 and 466:
Frequency 0 1 2 3 4 5 6 7 Sample Qu
Page 467 and 468:
Looking at this table, notice that
Page 469 and 470:
• Post hoc analysis and correctio
Page 471 and 472:
15. Linear regression The goal in t
Page 473 and 474:
The Best Fitting Regression Line No
Page 475 and 476:
• data. The data frame containing
Page 477 and 478:
Figure 15.4: A 3D visualisation of
Page 479 and 480:
Wonderful. A big number that doesn
Page 481 and 482:
If our regression model has K predi
Page 483 and 484:
You can see why this is handy, sinc
Page 485 and 486:
what it is. The test for the signif
Page 487 and 488:
Fortunately, confidence intervals f
Page 489 and 490:
• Uncorrelated predictors. The id
Page 491 and 492:
Outlier Outcome Predictor Figure 15
Page 493 and 494:
Outcome High influence Predictor Fi
Page 495 and 496:
Cook’s distance 0.00 0.02 0.04 0.
Page 497 and 498:
Standardized residuals −2 −1 0
Page 499 and 500:
78 Residuals vs Fitted Residuals
Page 501 and 502:
In a lot of cases, the solution to
Page 503 and 504:
Signif. codes: 0 *** 0.001 ** 0.01
Page 505 and 506:
15.10.1 Backward elimination Okay,
Page 507 and 508:
+ day 1 1.55760 1837.2 297.08 + bab
Page 509 and 510:
etween those two SS values as a sum
Page 511 and 512:
16. Factorial ANOVA Over the course
Page 513 and 514:
At this point we have 12 different
Page 515 and 516:
drug 2 3.45 1.727 18.6 8.6e-05 ***
Page 517 and 518:
means can be organised into the sam
Page 519 and 520:
attributable to the “ANOVA model
Page 521 and 522:
Only Factor A has an effect Only Fa
Page 523 and 524:
The effect of CBT (difference betwe
Page 525 and 526:
Now, if you go back to the formulas
Page 527 and 528:
Here’s what I mean. Again, let’
Page 529 and 530:
Speaking of interaction effects, he
Page 531 and 532:
16.4 Assumption checking As with on
Page 533 and 534:
16.5.1 The F test comparing two mod
Page 535 and 536:
the degrees of freedom here is 15.
Page 537 and 538:
tfm.2 grade attend reading 1 90 yes
Page 539 and 540:
line, we obtain the following: Ŷ 7
Page 541 and 542:
Estimate Std. Error t value Pr(>|t|
Page 543 and 544:
that contains the same data as clin
Page 545 and 546:
What about the case when there does
Page 547 and 548:
R comes with a variety of functions
Page 549 and 550:
enlightening read. There are a lot
Page 551 and 552:
16.8 Post hoc tests Time to switch
Page 553 and 554:
diff lwr upr p adj anxifree:no.ther
Page 555 and 556:
1 yes none 3.700 2 no none 5.550 3
Page 557 and 558:
Analysis of Variance Table Response
Page 559 and 560:
III tests (which are simple) before
Page 561 and 562:
sugar 2.13 2 4.0446 0.045426 * milk
Page 563 and 564:
even simpler. The main effect of su
Page 565 and 566:
However, when we do the same thing
Page 567:
Part VI. Endings, alternatives and
Page 570 and 571:
first I want to work through a simp
Page 572 and 573:
This is a very useful table, so it
Page 574 and 575:
P pd|hqP phq P ph|dq “ P pdq And
Page 576 and 577:
Bayesian approach relative to the o
Page 578 and 579:
hardly unusual: in my experience, m
Page 580 and 581:
Cumulative Probability of Type I Er
Page 582 and 583:
are wrong. Worse yet, because we do
Page 584 and 585:
library( BayesFactor ) # ...because
Page 586 and 587:
make sense to people who already un
Page 588 and 589:
-------------- [1] Non-indep. (a=1)
Page 590 and 591:
Before moving on, it’s worth high
Page 592 and 593:
17.6.2 The Bayesian version Okay, s
Page 594 and 595:
[2] day : 0.2724027 ˘0% [3] baby.s
Page 596 and 597:
therapy 0.4672 1 8.5816 0.01262 * d
Page 598 and 599:
command that I use when I want to g
Page 600 and 601:
- 586 -
Page 602 and 603:
• Other types of correlations. In
Page 604 and 605:
measurements mean that independence
Page 606 and 607:
the list that I’ve given above is
Page 608 and 609:
So if you were forced to guess my w
Page 610 and 611:
to be able to do more than ANOVA, m
Page 612 and 613:
Fisher, R. A. (1922a). On the inter
show all

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

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?