Preface to First Edition - lib

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70 CONDITIONAL INFERENCEtest statistic can be computed by means of Fisher’s exact test (Freeman andHalton, 1951). This test procedure is based on the hyper-geometric probabilityof the observed contingency table. All possible tables can be ordered withrespect to this metric and p-values are computed from the fraction of tablesmore extreme than the observed one.When both the x and the y measurements are numeric, the test statisticcan be formulated as the product, i.e., by the sum of all x i y i , i = 1, ...,n.Again, we can fix the x values and shuffle the y values in order to approximatethe distribution of the test statistic under the laws of the null hypothesis ofindependence of x and y.4.2.2 Testing Marginal HomogeneityIn contrast to the independence problem treated above the data analyst isoften confronted with situations where two (or more) measurements of onevariable taken from the same observational unit are to be compared. In thiscase one assumes that the measurements are independent between observationsand the test statistics are aggregated over all observations. Where twonominal variables are taken for each observation (for example see the case ofMcNemar’s test for binary variables as discussed in Chapter 3), the measurementof each observation can be summarised by a k ×k matrix with cell (i,j)being equal to one if the first measurement is the ith level and the second measurementis the jth level. All other entries are zero. Under the null hypothesisof independence of the first and second measurement, all k × k matrices withexactly one non-zero element are equally likely. The test statistic is now basedon the elementwise sum of all n matrices.4.3 Analysis Using R4.3.1 Estimating the Width of a Room RevisedThe unconditional analysis of the room width estimated by two groups ofstudents in Chapter 3 led to the conclusion that the estimates in metres areslightly larger than the estimates in feet. Here, we reanalyse these data in aconditional framework. First, we convert metres into feet and store the vectorof observations in a variable y:R> data("roomwidth", package = "HSAUR2")R> convert feet metre y T T[1] -8.858893© 2010 by Taylor and Francis Group, LLC
ANALYSIS USING R 71R> hist(meandiffs)R> abline(v = T, lty = 2)R> abline(v = -T, lty = 2)Histogram of meandiffsFrequency0 500 1000 1500 2000−15 −10 −5 0 5 10meandiffsFigure 4.1An approximation for the conditional distribution of the difference ofmean roomwidth estimates in the feet and metres group under the nullhypothesis. The vertical lines show the negative and positive absolutevalue of the test statistic T obtained from the original data.In order to approximate the conditional distribution of the test statistic Twe compute 9999 test statistics for shuffled y values. A permutation of the yvector can be obtained from the sample function.R> meandiffs for (i in 1:length(meandiffs)) {+ sy
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A Handbook ofStatisticalAnalysesUsi
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DedicationTo our wives, Mary-Elizab
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Preface to First EditionThis book i
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List of Figures1.1 Histograms of th
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6.8 Normal probability plot of resi
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12.2 R output of the linear mixed-e
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18.7 Within-cluster sum of squares
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4.6 Lanza data. Misoprostol randomi
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15.2 BCG data. Meta-analysis on BCG
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6 Simple and Multiple Linear Regres
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CHAPTER 1An Introduction to R1.1 Wh
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INSTALLING R 3One can change the ap
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DATA OBJECTS IN R 5http://CRAN.R-pr
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DATA OBJECTS IN R 7R> help("Forbes2
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DATA IMPORT AND EXPORT 9As a simple
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BASIC DATA MANIPULATION 11The funct
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BASIC DATA MANIPULATION 13name sale
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COMPUTING WITH DATA 15Max. : 20.960
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Page 45 and 46: SUMMARY 23examples of these functio
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Page 65 and 66: CHAPTER 3Simple Inference: Guessing
Page 67 and 68: INTRODUCTION 47table. Here there ar
Page 69 and 70: STATISTICAL TESTS 49Table 3.4:pisto
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Page 73 and 74: ANALYSIS USING R 53procedure is McN
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Page 83 and 84: SUMMARY 63R> mcnemar.test(rearrests
Page 85 and 86: CHAPTER 4Conditional Inference: Gue
Page 87 and 88: INTRODUCTION 67Table 4.4:Lanza data
Page 89: CONDITIONAL TEST PROCEDURES 69and x
Page 93 and 94: ANALYSIS USING R 73R> wilcox_test(y
Page 95 and 96: ANALYSIS USING R 75For the first st
Page 97 and 98: SUMMARY 77R> mh_test(anomalies)Asym
Page 99 and 100: CHAPTER 5Analysis of Variance: Weig
Page 101 and 102: INTRODUCTION 81The data in Table 5.
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Page 115 and 116: SUMMARY 95Table 5.4:schooldays data
Page 117 and 118: CHAPTER 6Simple and Multiple Linear
Page 119 and 120: SIMPLE LINEAR REGRESSION 99hours be
Page 121 and 122: MULTIPLE LINEAR REGRESSION 101The e
Page 123 and 124: ANALYSIS USING R 1036.3.1 Regressio
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Page 135 and 136: SUMMARY 115R> plot(clouds_lm)Cook's
Page 137 and 138: CHAPTER 7Logistic Regression and Ge
Page 139 and 140: INTRODUCTION 119Table 7.2:womensrol
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LOGISTIC REGRESSION AND GENERALISED
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ANALYSIS USING R 123R> data("plasma
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ANALYSIS USING R 125R> summary(plas
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ANALYSIS USING R 1277.3.2 Women’s
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ANALYSIS USING R 129R> myplot(role.
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ANALYSIS USING R 131R> role.fitted2
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ANALYSIS USING R 133R> summary(poly
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ANALYSIS USING R 1357.3.4 Driving a
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SUMMARY 137Table 7.5:bladdercancer
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CHAPTER 8Density Estimation: Erupti
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DENSITY ESTIMATION 141The Hertzspru
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DENSITY ESTIMATION 143rectangular:
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DENSITY ESTIMATION 1451 R> plot(xgr
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ANALYSIS USING R 1478.3 Analysis Us
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2.2ANALYSIS USING R 149R> library("
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ANALYSIS USING R 1510.360891 54.612
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ANALYSIS USING R 153The results are
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SUMMARY 155R> layout(matrix(1:2, nc
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SUMMARY 157Table 8.4: birthdeathrat
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SUMMARY 159Table 8.5:schizophrenia
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162 RECURSIVE PARTITIONINGTable 9.1
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164 RECURSIVE PARTITIONINGBoth sets
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166 RECURSIVE PARTITIONINGR> librar
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168 RECURSIVE PARTITIONINGR> DEXfat
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170 RECURSIVE PARTITIONINGOne way o
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172 RECURSIVE PARTITIONINGR> librar
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174 RECURSIVE PARTITIONINGR> plot(g
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CHAPTER 10Scatterplot Smoothers and
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INTRODUCTION 179Table 10.2:USairpol
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SMOOTHERS AND GENERALISED ADDITIVE
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ANALYSIS USING R 187R> plot(time ~
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ANALYSIS USING R 189R> x y men150
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ANALYSIS USING R 191R> USair_gam l
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ANALYSIS USING R 193R> layout(matri
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ANALYSIS USING R 195ter 9) where th
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198 SURVIVAL ANALYSISTable 11.1:gli
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200 SURVIVAL ANALYSISspect to time
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202 SURVIVAL ANALYSISHazard0.00 0.0
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204 SURVIVAL ANALYSISIn the Cox mod
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206 SURVIVAL ANALYSISExact Logrank
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208 SURVIVAL ANALYSISR> summary(GBS
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210 SURVIVAL ANALYSISR> layout(matr
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212 SURVIVAL ANALYSISmodels includi
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214 ANALYSING LONGITUDINAL DATA Iti
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216 ANALYSING LONGITUDINAL DATA ITa
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218 ANALYSING LONGITUDINAL DATA Iot
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220 ANALYSING LONGITUDINAL DATA IR>
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226 ANALYSING LONGITUDINAL DATA IKe
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228 ANALYSING LONGITUDINAL DATA Ido
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CHAPTER 13Analysing Longitudinal Da
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METHODS FOR NON-NORMAL DISTRIBUTION
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ANALYSIS USING R: GEE 239R> summary
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ANALYSIS USING R: GEE 245R> layout(
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ANALYSIS USING R: RANDOM EFFECTS 24
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ANALYSIS USING R: RANDOM EFFECTS 24
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SUMMARY 251Table 13.3:schizophrenia
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254 SIMULTANEOUS INFERENCE AND MULT
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CHAPTER 15Meta-Analysis: Nicotine G
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SYSTEMATIC REVIEWS AND META-ANALYSI
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STATISTICS OF META-ANALYSIS 271Sele
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ANALYSIS USING R 273the parameters
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ANALYSIS USING R 275R> plot(smoking
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PUBLICATION BIAS 277R> summary(BCG_
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SUMMARY 279R> summary(BCG_mod)Call:
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SUMMARY 2811 / standard error2 4 6
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Table 15.4:aspirin data. Meta-analy
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CHAPTER 16Principal Component Analy
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PRINCIPAL COMPONENT ANALYSIS 287nie
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ANALYSIS USING R 289R> score plot(
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ANALYSIS USING R 291R> score plot(
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ANALYSIS USING R 293Yuping (CHN) Ha
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SUMMARY 295R> biplot(heptathlon_pca
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SUMMARY 297rainJuly: rainfall in Ju
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Table 17.1:watervoles data. Water v
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302 MULTIDIMENSIONAL SCALINGn in nu
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304 MULTIDIMENSIONAL SCALINGwill be
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306 MULTIDIMENSIONAL SCALINGR> x y
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308 MULTIDIMENSIONAL SCALINGR> libr
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310 MULTIDIMENSIONAL SCALINGR> plot
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Table 17.3:eurodist data (package d
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CHAPTER 18Cluster Analysis: Classif
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INTRODUCTION 317mass, mass), the pe
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CLUSTER ANALYSIS 319x 20 2 4 6 8 10
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CLUSTER ANALYSIS 32141031678925Figu
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CLUSTER ANALYSIS 3231. Find some in
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ANALYSIS USING R 32518.3 Analysis U
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ANALYSIS USING R 327R> pottery_sing
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ANALYSIS USING R 329R> rge planet.
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ANALYSIS USING R 331R> plot(planet_
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ANALYSIS USING R 333R> scatterplot3
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BibliographyAdler, D. and Murdoch,
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BIBLIOGRAPHY 337Chambers, J. M. and
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BIBLIOGRAPHY 339Everitt, B. S. and
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BIBLIOGRAPHY 341Heitjan, D. F. (199
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BIBLIOGRAPHY 343Leisch, F. and Ross
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BIBLIOGRAPHY 345Proudfoot, J., Gold
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BIBLIOGRAPHY 347Stevens, J. (2001),
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