Using R for Introductory Statistics : John Verzani

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Goodness of fit 259A consequence is that we can’t use the Kolmogorov-Smirnov test to test for normality ofa data set unless we know the parameters of the underlying distribution. † The Shapiro-Wilk test allows us to do this. This test statistic is based on the ideas behind the quantilequantileplot, which we’ve used to gauge normality. Its definition is a bit involved, but itsusage in R is straightforward.The Shapiro-Wilk test for normalityIf X 1 , X 2 , …, X n is an i.i.d. sample from a continuous distribution, a significance test ofH 0 : parent distribution is normal,H A : the parent distribution is not normal† The Lilliefors test, implemented by lillie.test() in the contributed package nortest, will make thenecessary adjustments to use this test statistic. As well, the nortest package implements other testsof normality. In many installations of R, nortest may be installed from a menubar or with thecommand install, packages (“nortest”). See Chapter 1 for further information about packageinstallation.can be carried out with the Shapiro-Wilk test statistic.In R, the function shapiro. test() will perform the test. The usage is simplyshapiro.test(x)where the data vector x contains the sample data.■ Example 9.4: Normality of SAT scores For the SAT data in the stud. recs (UsingR)data set, we saw in Example 9.3 that the two distributions are different. Are theynormally distributed? We can answer with the Shapiro-Wilk test:> attach(stud.recs)> shapiro.test(sat.m)Shapiro-Wilk normality testdata: sat.mW = 0.9898, p-value = 0.3056> shapiro.test(sat.v)...W=0.994, p-value=0.752> detach(stud.recs)In each case, the p-value is not statistically significant. There is no evidence that the datais not normally distributed. ■■ Example 9.5: Is on-base percentage normally distributed? In Example 2.8 thedistribution of the on-base percentage from the 2002 major league baseball season wasshown. It appears bell shaped except for one outlier. Does the data come from a normallydistributed population?Using the Shapiro-Wilk test gives us> shapiro.test(OBP)Shapiro-Wilk normality test
Using R for introductory statistics 260data: OBPW = 0.9709, p-value = 1.206e-07So it is unlikely. Perhaps this is due to the one outlier. We eliminate this and try again> shapiro.test(OBP[OBP data(babyboom, package="UsingR") # or library(UsingR)> fitdistr(babyboom$wt,"normal")mean sd3275.95 522.00
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Using R for Introductory Statistics
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This edition published in the Taylo
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PrefaceWhat is R?R is a computer la
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Web accompanimentsThe home page for
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Chapter 1Data1.1 What is data?When
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Data 3Journal of Economics that leg
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Data 5When R starts, it searches fo
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Data 71.2.3 AssignmentIt is often c
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Data 9Giving data vectors named ent
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Data 11> x = c(2,3,5,7,11)> xbar =
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Data 13Simple sequences A sequence
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Data 153. Find the differences of t
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Data 17> ebay[−1] # all but the f
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Data 19empty vector if i=0x[c (2, 3
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Data 21Many R functions have an arg
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Data 231.4 Reading in other sources
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Data 25A convenient method, which r
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Data 27Using source () to read in R
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Data 291.4.4 Problems1.20 The built
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Chapter 2Univariate dataIn statisti
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Univariate data 33The table() funct
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Univariate data 35There are names o
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Univariate data 37Why are pie chart
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Univariate data 392.5 Web developer
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Univariate data 4121:Read 20 items>
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Univariate data 43compare different
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Univariate data 45Figure 2.8 The me
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Univariate data 47numbers first and
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Univariate data 49> var(test.scores
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Univariate data 51As with the quant
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Univariate data 532.13 Can you copy
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Univariate data 55Comment on any pa
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Univariate data 57> hist(waiting) #
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Univariate data 59Figure 2.13 Frequ
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Univariate data 61Figure 2.15 Galax
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Univariate data 63Figure 2.17 Amoun
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Univariate data 652.3.4 Problems2.3
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Chapter 3Bivariate dataThis chapter
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Bivariate data 69> colnames(x) = c(
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Bivariate data 71unbuckled 56 8 64b
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Bivariate data 73Figure 3.1 Segment
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Bivariate data 75interested in comp
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Bivariate data 77> stripchart(list(
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Bivariate data 79Figure 3.5 Six qqn
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Bivariate data 81Figure 3.6 Assesse
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Bivariate data 83> plot(height, wei
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Bivariate data 85correlation only i
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Bivariate data 873.17 The data set
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Bivariate data 89Figure 3.10 Predic
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Bivariate data 91That is, the y-val
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Bivariate data 93■ Example 3.6: K
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Bivariate data 95[1] 13 50> florida
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Bivariate data 97Just like the mean
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Bivariate data 99Figure 3.16 Temper
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Bivariate data 101produce a scatter
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Multivariate data 10310 Y N Y N Nan
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Multivariate data 105Figure 4.1 Tax
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Multivariate data 107> plot(gestati
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Multivariate data 109Make the above
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Multivariate data 111One difference
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Multivariate data 113Accessing a da
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Multivariate data 115Figure 4.4 Sca
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Multivariate data 117To illustrate,
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Multivariate data 119mtcars[[’mpg
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Multivariate data 121We can apply f
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Multivariate data 123appropriate. T
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Multivariate data 125pickup 70 71 5
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Multivariate data 1272 42 stomach
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Multivariate data 129make several p
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Multivariate data 131+ subset=(wt !
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Multivariate data 133When a factor
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Multivariate data 135Coercion is th
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Multivariate data 137[1,] 1 3 5 7[2
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Describing populations 1395.1.1 Dis
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Describing populations 141This is a
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Describing populations 1435.1.3 Sam
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Describing populations 1455.7 Toss
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Describing populations 147In R the
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Describing populations 149variance
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Describing populations 151> res = r
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Describing populations 153> hist(re
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Describing populations 155more woul
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Describing populations 157Figure 5.
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Describing populations 159use the n
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Chapter 6SimulationOne informal des
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Simulation 163Figure 6.2 Quantile-n
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Simulation 1656.4 Defining a functi
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Simulation 1676.4.3 The function bo
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Simulation 169> summary(res.25)Min.
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Simulation 1716.5.2 The geometric d
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Simulation 173> xbarstar = c()> for
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Simulation 1756.3 For what value of
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Simulation 177This function will do
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Confidence intervals 179Figure 7.1
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Confidence intervals 181which, when
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Confidence intervals 183In R this b
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Confidence intervals 185alternative
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Confidence intervals 1877.3 Confide
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Confidence intervals 189> zstar = q
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Confidence intervals 191correlates
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Confidence intervals 193In general,
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Confidence intervals 195contains th
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Confidence intervals 197distributed
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Confidence intervals 199mean of x m
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Confidence intervals 201in Table 7.
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Confidence intervals 203data is mor
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Confidence intervals 205−18 282sa
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Chapter 8Significance testsFinding
Page 220 and 221: Significance tests 209against the a
Page 222 and 223: Significance tests 2111. Identify H
Page 224 and 225: Significance tests 213simple random
Page 226 and 227: Significance tests 2158.5 On a numb
Page 228 and 229: Significance tests 217> mpg =c(11.4
Page 230 and 231: Significance tests 2198.16 We can p
Page 232 and 233: Significance tests 221Sign test for
Page 234 and 235: Significance tests 223parameters. A
Page 236 and 237: Significance tests 225A natural tes
Page 238 and 239: Significance tests 227audience at t
Page 240 and 241: Significance tests 229If the two va
Page 242 and 243: Significance tests 231Figure 8.5 De
Page 244 and 245: Significance tests 233H 0 :µ x =µ
Page 246 and 247: Significance tests 235Figure 8.6 Tw
Page 248 and 249: Significance tests 237group n sechi
Page 250 and 251: Chapter 9Goodness of fitIn this cha
Page 252 and 253: Goodness of fit 241This gives the t
Page 254 and 255: Goodness of fit 243The function ret
Page 256 and 257: Goodness of fit 2459.3 A package of
Page 258 and 259: Goodness of fit 247This is the squa
Page 260 and 261: Goodness of fit 249We now have all
Page 262 and 263: Goodness of fit 251whether any diff
Page 264 and 265: Goodness of fit 253Table 9.10 Accid
Page 266 and 267: Goodness of fit 255theoretical dens
Page 268 and 269: Goodness of fit 257D = 0.0745, p-va
Page 272 and 273: Goodness of fit 261( 78.69) ( 55.65
Page 274 and 275: Goodness of fit 2639.20 The rivers
Page 276 and 277: Linear regression 265response ~ pre
Page 278 and 279: Linear regression 26710.1.4 Using l
Page 280 and 281: Linear regression 269Extractor func
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Page 284 and 285: Linear regression 273The scale-loca
Page 286 and 287: Linear regression 275Figure 10.5 Fo
Page 288 and 289: Linear regression 277the simulation
Page 290 and 291: Linear regression 279Confidence int
Page 292 and 293: Linear regression 281Signif. codes:
Page 294 and 295: Linear regression 283Figure 10.7 Re
Page 296 and 297: Linear regression 285home in 1970.
Page 298 and 299: Linear regression 287Let Y be a res
Page 300 and 301: Linear regression 289Coefficients:(
Page 302 and 303: Linear regression 291+ tot=a+ for(i
Page 304 and 305: Linear regression 293Y i =β 0 +β
Page 306 and 307: Linear regression 295Call:lm(formul
Page 308 and 309: Linear regression 297Let y t be the
Page 310 and 311: Analysis of variance 299Figure 11.1
Page 312 and 313: Analysis of variance 301> SSE=(5-1)
Page 314 and 315: Analysis of variance 303163.2 173.3
Page 316 and 317: Analysis of variance 305can be perf
Page 318 and 319: Analysis of variance 307Repeat with
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Analysis of variance 309> dvalues i
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Analysis of variance 311Figure 11.4
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Analysis of variance 313> ewr.out=s
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Analysis of variance 31511.11 The T
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Analysis of variance 317Figure 11.6
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Analysis of variance 31911.24 The d
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Analysis of variance 321Signif. cod
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Analysis of variance 323factors, al
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Analysis of variance 325(Intercept)
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Chapter 12Two extensions of the lin
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Two extensions of the linear model
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Appendix AGetting, installing, and
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Appendix A 345A.1.4 Installing from
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Appendix BGraphical user interfaces
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Appendix B 350Figure B.2 Multi-docu
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Appendix B 352If you forget to inst
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Appendix CTeaching with RUsing R in
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Appendix DMore on graphics with RTh
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Appendix D 358A device is set up wi
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Appendix D 360Adding a box around t
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Appendix D 362> x = seq(−2, 2, le
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Appendix D 364D.2 Creating new grap
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Appendix D 366Figure D.3 Per-capita
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Appendix EProgramming in ROne of R
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Appendix E 371arg1, arg2, arg3When
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Appendix E 373freedman-diaconis, sc
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Appendix E 375return(summary(x))sum
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Appendix E 377In this example varna
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Appendix E 379editor and ESS extend
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Appendix E 381[1] 26> size(data.fra
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Appendix E 383"[.String" = function
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Appendix E 385})We need to use the
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Appendix E 387For our String class
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Appendix E 389Now, instances of the
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Appendix E 391old.x=xx=x—(x^2—s
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Index 393heat.colors(), 378rainbow(
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Index 395pch=, 86, 378type=, 60, 86
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Index 397command line, 411>, 5confi
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Index 399extra sum of squares, 307f
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Index 401robust statistic, 193sampl
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Using R for Introductory Statistics : John Verzani

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