THE FUNDAMENTALS OF STATISTICS
PART I PRELIMINARIES 1 INTRODUCING R 11 PRESENTATION OF THE SOFTWARE 111 ORIGINS 112 WHY USE R? 12 R AND STATISTICS 13 R AND PLOTS 14 THE R GRAPHICAL USER INTERFACE 15 FIRST STEPS IN R 151 USING RCOMMANDER 1511 LAUNCHING RCOMMANDERCMM]RCOMMANDER@RCOMMANDER 1512 HANDLING DATA WITH RCOMMANDERCMM]RCOMMANDER@RCOMMANDER 1513 A FEW STATISTICAL TASKS WITH RCOMMANDERCMM]RCOMMANDER@RCOMMANDER 1514 ADDING FUNCTIONALITIES TO THE RCOMMANDER INTERFACE 152 USING R WITH THE CONSOLE 1521 THE STRENGTH OF R SHOWN ON AN EXAMPLE 1522 A BRIEF INTRODUCTION OF R SYNTAX THROUGH SOME INSTRUCTIONS TO TYPE 2 A FEW DATA SETS AND RESEARCH QUESTIONS 21 BODY MASS INDEX OF CHILDREN 22 WEIGHT AT BIRTH 23 INTIMA–MEDIA THICKNESS 24 DIET OF ELDERLY PEOPLE 25 STUDY CASE OF MYOCARDIAL INFARCTION 26 SUMMARY TABLE OF USE OF DATA SETS PART II THE BASES OF R 3 BASIC CONCEPTS AND DATA ORGANISATION 31 YOUR FIRST SESSION 311 R IS A CALCULATOR 312 DISPLAYING RESULTS AND VARIABLE REDIRECTING 313 WORK STRATEGY 314 USING FUNCTIONS 32 DATA IN R 321 DATA NATURE (OR TYPE, OR MODE) 3211 NUMERIC TYPE (NUMERIC) 3212 † COMPLEX TYPE (COMPLEX) 3213 BOOLEAN OR LOGICAL TYPE (LOGICAL) 3214 MISSING DATA (NA) 3215 CHARACTER STRING TYPE (CHARACTER) 3216 † RAW DATA (RAW) SUMMARY 322 DATA STRUCTURES 3221 VECTORS (VECTOR) 3222 MATRICES (MATRIX) AND ARRAYS (ARRAY) 3223 LISTS (LIST) 3224 THE INDIVIDUALVARIABLE TABLE(DATAFRAME) 3225 FACTORS (FACTOR), ORDINAL VARIABLES(ORDERED) 3226 DATES 3227 TIME SERIES MEMORANDUM EXERCISES WORKSHEET 4 IMPORTING, EXPORTING AND PRODUCING DATA 41 IMPORTING DATA 411 IMPORTING DATA FROM AN ASCII TEXT FILE 4111 READING DATA WITH READTABLE() 4112 READING DATA WITH READFTABLE() 4113 READING DATA WITH THE FUNCTION SCAN() 412 IMPORTING DATA FROM EXCEL OR THE OPEN OFFICESPREADSHEET 4121 COPY-PASTING 4122 USING AN INTERMEDIARY ASCII FILE 4123 USING SPECIALIZED PACKAGES 413 IMPORTING DATA FROM SPSS, MINITAB, SAS OR MATLAB 414 LARGE DATA FILES 42 EXPORTING DATA 421 EXPORTING DATA TO AN ASCII TEXT FILE 422 EXPORTING DATA TO EXCEL OR OPENOFFICE CALC 43 CREATING DATA 431 ENTERING TOY DATA 432 GENERATING PSEUDO-RANDOM NUMBERS 433 ENTERING DATA FROM A HARD COPY 44 † READING/WRITING IN DATABASES 441 CREATING A DATABASE AND A TABLE 442 CREATING A DATA SOURCE COMPATIBLE WITH MYSQL 443 WRITING IN A TABLE 444 READING A TABLE 5 DATA MANIPULATION, FUNCTIONS 51 OPERATIONS ON VECTORS, MATRICES AND LISTS 511 VECTOR ARITHMETIC 512 RECYCLING 513 BASIC FUNCTIONS 514 OPERATIONS ON MATRICES AND DATAFRAMES 5141 INFORMATION ON ARCHITECTURE 5142 MERGING TABLES 5143 THE FUNCTION APPLY() 5144 THE FUNCTION SWEEP() 5145 THE FUNCTION STACK() 5146 THE FUNCTION AGGREGATE() 5147 THE FUNCTION TRANSFORM() 515 OPERATIONS ON LISTS 52 LOGICAL AND RELATIONAL OPERATIONS 53 OPERATIONS ON SETS 54 EXTRACTING AND INSERTING ELEMENTS 541 EXTRACTING FROM/INSERTING INTO VECTORS 542 EXTRACTING FROM/INSERTING INTO MATRICES 543 EXTRACTING FROM/INSERTING INTO ARRAYS 544 EXTRACTING FROM/INSERTING INTO LISTS 55 MANIPULATING CHARACTER STRINGS 56 MANIPULATING DATES AND TIME UNITS 561 DISPLAYING THE CURRENT DATE 562 EXTRACTING DATES 563 OPERATIONS ON DATES 57 CONTROL FLOW 571 CONDITIONAL INSTRUCTIONS 572 LOOP INSTRUCTIONS 58 CREATING FUNCTIONS 59 † FIXED-POINT AND FLOATING POINT NUMBER REPRESENTATION 591 REPRESENTING A NUMBER IN A BASE 592 FLOATING POINT REPRESENTATIONS 5921 DEFINITIONS 5922 LIMITATIONS OF THIS REPRESENTATION DUE TO THE SIGNIFICAND 5923 AVOIDING SOME NUMERICAL PITFALLS 5924 LIMITATIONS OF THIS REPRESENTATION DUE TO THE EXPONENT 6 R AND ITS DOCUMENTATION 61 INTEGRATED HELP 611 THE COMMAND HELP() 612 SOME COMPLEMENTARY COMMANDS 62 † HELP ON THE WEB 621 SEARCH ENGINES 622 MESSAGE BOARDS 623 MAILING LISTS 624 INTERNET RELAY CHAT (IRC) 625 WIKI 63 † LITERATURE ABOUT R 631 ONLINE 632 PRINTED MATERIAL 7 DRAWING CURVES AND PLOTS 71 GRAPHICS WINDOWS 711 BASIC GRAPHICS WINDOWS, MANIPULATION AND SAVING 712 SPLITTING THE GRAPHICS WINDOW: LAYOUT() 72 LOW-LEVEL DRAWING FUNCTIONS 721 THE FUNCTIONS PLOT() AND POINTS() 722 THE FUNCTIONS SEGMENTS(), LINES()AND ABLINE() 723 THE FUNCTION ARROWS() 724 THE FUNCTION POLYGON() 725 THE FUNCTION CURVE() 726 THE FUNCTION BOX() 73 MANAGING COLOURS 731 THE FUNCTION COLORS() 732 HEXADECIMAL COLOUR CODING 733 THE FUNCTION IMAGE() 74 ADDING TEXT 741 THE FUNCTION TEXT() 742 THE FUNCTION MTEXT() 75 TITLES, AXES AND CAPTIONS 751 THE FUNCTION TITLE() 752 THE FUNCTION AXIS() 753 THE FUNCTION LEGEND() 76 INTERACTING WITH THE PLOT 761 THE FUNCTION LOCATOR() 762 THE FUNCTION IDENTIFY() 77 † FINE-TUNING GRAPHICAL PARAMETERS: PAR() 78 † ADVANCED PLOTS: RGLCMM]RGL@RGL, LATTICECMM]LATTICE@LATTICE AND GGPLOT2CMM]GGPLOT2@GGPLOT2 8 PROGRAMMING IN R 81 PREAMBLE 82 DEVELOPING FUNCTIONS 821 QUICK START: DECLARING, CREATING AND CALLINGFUNCTIONS 822 BASIC CONCEPTS ON FUNCTIONS 8221 BODY OF A FUNCTION 8222 LIST OF FORMAL AND EFFECTIVE ARGUMENTS 8223 OBJECT RETURNED BY A FUNCTION 8224 VARIABLE SCOPE IN THE BODY OF A FUNCTION 823 APPLICATION TO THE PRACTICAL PROBLEM 824 OPERATORS 825 R SEEN AS A FUNCTIONAL LANGUAGE 83 † OBJECT-ORIENTED PROGRAMMING 831 HOW THE INTERNAL OBJECT-ORIENTED MECHANISM WORKS 8311 CLASS OF AN OBJECT AND DECLARING AN OBJECT 8312 DECLARING OBJECTS AND USING METHODS 832 BACK TO THE PRACTICAL PROBLEM 833 INFORMATION ABOUT METHODS 834 INHERITING CLASSES 84 † GOING FURTHER IN R PROGRAMMING 841 R ATTRIBUTES 8411 ATTRIBUTE CLASS 8412 ATTRIBUTE DIM 8413 ATTRIBUTES NAMES AND DIMNAMES 842 OTHER R OBJECTS 8421 R EXPRESSIONS 8422 R FORMULAE 8423 THE R ENVIRONMENT 85 † INTERFACING R AND C/C++ OR FORTRAN 851 CREATING AND RUNNING A C/C++ OR FORTRAN FUNCTION 852 CALLING C/C++ (OR FORTRAN) FROM R 853 CALLING EXTERNAL C/C++ OR FORTRAN LIBRARIES 8531 THE R API 8532 THE NEWMAT LIBRARY 8533 THE BLAS AND LAPACK PACKAGES 8534 MIXING C/C++ AND FORTRAN PACKAGES 854 CALLING R CODE FROM A C/C++ PROGRAM CALLED BY R 855 CALLING R CODE FROM FORTRAN 856 SOME USEFUL FUNCTIONS 86 † DEBUGGING FUNCTIONS 861 DEBUGGING FUNCTIONS IN PURE R 862 ERROR IN R CODE 863 ERROR IN THE C/C++ OR FORTRAN CODE 864 DEBUGGING WITH GDB 8641 DEBUGGING WITH EMACS 8642 DEBUGGING WITH DDD 8643 DEBUGGING WITH INSIGHT 8644 DETECTING MEMORY LEAKS 87 PARALLEL COMPUTING AND COMPUTATION ON GRAPHICAL CARDS 871 PARALLEL COMPUTING 872 COMPUTATION ON GRAPHICAL CARDS 9 MANAGING SESSIONS 91 R COMMANDS, OBJECTS AND STORAGE 92 WORKSPACE: RDATA FILES 93 COMMAND HISTORY: RHISTORY FILES 94 SAVING PLOTS 95 MANAGING PACKAGES 96 MANAGING ACCESS PATHS TO R OBJECTS 97 † OTHER USEFUL COMMANDS 98 † PROBLEMS IN MEMORY MANAGEMENT 981 ORGANIZATION OF RAM 982 ACCESSING THE MEMORY 9821 PROBLEMS CAUSED BY MEMORY MANAGEMENT OF INTEGERS 9822 SUCCESSIVE ALLOCATION OF MEMORY 983 OBJECT SIZE IN R 984 TOTAL MEMORY USED BY R 985 A FEW RECOMMENDATIONS 99 † USING R IN BATCH MODE 910 † CREATING A SIMPLE R PACKAGE PART III ELEMENTARY MATHEMATICS AND STATISTICS 10 BASIC MATHEMATICS: MATRIX OPERATIONS, INTEGRATION,OPTIMIZATION 101 BASIC MATHEMATICAL FUNCTIONS 102 MATRIX OPERATIONS 1021 BASIC MATRIX OPERATIONS 1022 OUTER PRODUCT 1023 KRONECKER PRODUCT 1024 TRIANGULAR MATRICES 1025 OPERATORS VEC AND HALF VEC 1026 DETERMINANT, TRACE AND CONDITION NUMBER 1027 SCALING AND CENTRING DATA 1028 EIGENVALUES AND EIGENVECTORS 1029 SQUARE ROOT OF A HERMITIAN POSITIVE-DEFINITE MATRIX 10210 SINGULAR VALUE DECOMPOSITION 10211 CHOLESKY DECOMPOSITION 10212 QR DECOMPOSITION 103 NUMERICAL INTEGRATION 104 DIFFERENTIATION 1041 SYMBOLIC DIFFERENTIATION 1042 NUMERICAL DIFFERENTIATION 105 OPTIMIZATION 1051 OPTIMIZATION FUNCTIONS 1052 ROOTS OF A FUNCTION 11 DESCRIPTIVE STATISTICS 111 INTRODUCTION 112 STRUCTURING VARIABLES ACCORDING TO TYPE 1121 STRUCTURING QUALITATIVE VARIABLES 1122 STRUCTURING ORDINAL VARIABLES 1123 STRUCTURING DISCRETE QUANTITATIVE DATA 1124 STRUCTURING CONTINUOUS QUANTITATIVE VARIABLES 113 DATA TABLES 1131 INDIVIDUAL DATA TABLES 1132 TABLES OF COUNTS AND FREQUENCY TABLES 1133 TABLES OF GROUPED DATA 1134 CROSS TABULATION 11341 CONTINGENCY TABLES 11342 JOINT DISTRIBUTION 11343 MARGINAL DISTRIBUTIONS 11344 CONDITIONAL DISTRIBUTIONS 114 NUMERICAL SUMMARIES 1141 SUMMARIES OF THE LOCATION OF A DISTRIBUTION 11411 MODES 11412 MEDIAN 11413 MEAN 11414 QUANTILES 1142 SUMMARIES OF THE DISPERSION OF A DISTRIBUTION 1143 SUMMARIES OF THE SHAPE OF A DISTRIBUTION 115 MEASURES OF ASSOCIATION 1151 MEASURES OF ASSOCIATION BETWEEN TWO QUALITATIVE VARIABLES 11511 PEARSON'S 2 STATISTIC 11512 2, CRAMÉR'S V AND PEARSON'S CONTINGENCY COEFFICIENT 1152 MEASURES OF ASSOCIATION BETWEEN ORDINAL VARIABLES(OR RANKS) 11521 KENDALL'S AND B 11522 SPEARMAN'S RANK CORRELATION COEFFICIENT 1153 MEASURES OF ASSOCIATION BETWEEN TWO QUANTITATIVE VARIABLES 11531 COVARIANCE AND PEARSON'S CORRELATION COEFFICIENT 1154 MEASURES OF ASSOCIATION BETWEEN A QUANTITATIVE VARIABLE AND A QUALITATIVE VARIABLE 11541 CORRELATION RATIO 2Y|X 116 GRAPHICAL REPRESENTATIONS 1161 PLOTTING QUALITATIVE VARIABLES 11611 CROSS CHART 11612 BAR CHARTS 11613 PARETO CHART 11614 STACKED BAR CHART 11615 PIE CHART 1162 PLOTTING ORDINAL VARIABLES 11621 BAR CHART WITH CUMULATIVE FREQUENCIESLINE 1163 PLOTTING DISCRETE QUANTITATIVE VARIABLES 11631 CROSS CHART 11632 BAR CHART 11633 PLOTTING THE EMPIRICAL DISTRIBUTION FUNCTION 11634 STEMPLOT 11635 BOXPLOT 1164 PLOTTING CONTINUOUS QUANTITATIVE VARIABLES 11641 EMPIRICAL DISTRIBUTION FUNCTION 11642 STEMPLOT 11643 BOXPLOTS 11644 DENSITY HISTOGRAM WITH IDENTICAL OR DIFFERENT CLASS RANGES 11645 FREQUENCY POLYGON 11646 CUMULATIVE FREQUENCY POLYGON 1165 GRAPHICAL REPRESENTATIONS IN A BIVARIATE SETTING 11651 TWO-WAY PLOTS FOR TWO QUALITATIVE VARIABLES 11652 TWO-WAY PLOTS FOR TWO QUANTITATIVEVARIABLES 11653 TWO-WAY PLOTS FOR ONE QUALITATIVE AND ONE QUANTITATIVE VARIABLE 12 A BETTER UNDERSTANDING OF RANDOM VARIABLES, DISTRIBUTIONS AND SIMULATIONS USING R SPECIFICITIES 121 NOTIONS ON RANDOM NUMBER GENERATION 122 THE NOTION OF RANDOM VARIABLES 1221 REALIZATIONS OF A RANDOM VARIABLE AND FUNCTIONINGLAW 1222 IID RANDOM VARIABLES 1223 CHARACTERIZING THE DISTRIBUTION OF A RANDOM VARIABLE 12231 DENSITY FUNCTION, DISTRIBUTION FUNCTION AND QUANTILE FUNCTION 1224 PARAMETERS OF THE DISTRIBUTION OF A RANDOM DISTRIBUTION 123 LAW OF LARGE NUMBERS AND CENTRAL LIMIT THEOREM 1231 LAW OF LARGE NUMBERS 1232 CENTRAL LIMIT THEOREM 124 INFERENTIAL STATISTICS 1241 POINT ESTIMATE OF PARAMETERS 1242 EMPIRICAL CUMULATIVE DISTRIBUTION FUNCTION 1243 MAXIMUM LIKELIHOOD ESTIMATION 1244 SAMPLING VARIATION AND PROPERTIES OF AN ESTIMATOR 125 A FEW TECHNIQUES TO DRAW FROM A DISTRIBUTION 1251 SIMULATING FROM ANOTHER DISTRIBUTION 1252 INVERSE TRANSFORM METHOD 1253 REJECTION SAMPLING 1254 SIMULATION OF DISCRETE RANDOM VARIABLES 126 BOOTSTRAP 127 STANDARD AND LESS STANDARD DISTRIBUTIONS 1271 STANDARD DISTRIBUTIONS 1272 † LESS STANDARD DISTRIBUTIONS 128 MODELLING A PHENOMENON 13 CONFIDENCE INTERVALS AND HYPOTHESIS TESTING 131 NOTATIONS 132 CONFIDENCE INTERVALS 1321 CONFIDENCE INTERVALS FOR THE MEAN 1322 CONFIDENCE INTERVALS FOR A PROPORTION P 1323 CONFIDENCE INTERVALS FOR A VARIANCE 1324 CONFIDENCE INTERVALS FOR A MEDIAN 1325 CONFIDENCE INTERVALS FOR A CORRELATION COEFFICIENT 1326 SUMMARY TABLE FOR CONFIDENCE INTERVALS 133 STANDARD HYPOTHESIS TESTING 1331 PARAMETRIC TESTS 13311 TESTS OF THE MEAN 13312 TESTS OF VARIANCE 13313 TESTS OF PROPORTION 13314 TESTS OF CORRELATION 1332 INDEPENDENCE TESTS 13321 2 TEST FOR INDEPENDENCE 13322 YATES' 2 TEST 13323 FISHER'S EXACT TEST 1333 NON-PARAMETRIC TESTS 13331 GOODNESS-OF-FIT TESTS 13332 TESTS OF POSITION 1334 MEMORANDUM OF STANDARD TESTS 134 OTHER TESTS 14 SIMPLE AND MULTIPLE LINEAR REGRESSION 141 INTRODUCTION 142 SIMPLE LINEAR REGRESSION 1421 AIM AND MODEL 1422 FITTING DATA 1423 CONFIDENCE AND PREDICTION INTERVALS FOR A NEW VALUE 1424 ANALYSIS OF RESIDUALS 1425 STUDENT'S TESTS FOR MEANS AND LINEAR MODEL 1426 SUMMARY 143 MULTIPLE LINEAR REGRESSION 1431 AIM AND MODEL 1432 FITTING DATA 1433 CONFIDENCE AND PREDICTION INTERVALS FOR A NEW VALUE 1434 TESTING A LINEAR SUB-HYPOTHESIS: PARTIAL FISHER TEST 1435 QUALITATIVE VARIABLES WITH MORE THAN TWOMODALITIES 1436 INTERACTION BETWEEN VARIABLES 1437 ISSUES WITH COLLINEARITY 1438 VARIABLE SELECTION 1439 ANALYSIS OF RESIDUALS 14310 POLYNOMIAL REGRESSION 14311 SUMMARY 15 ELEMENTARY ANALYSIS OF VARIANCE 151 ANALYSIS OF VARIANCE WITH ONE FACTOR 1511 AIMS, DATA AND MODEL 1512 EXAMPLE AND GRAPHICAL INSPECTION 1513 ANOVA TABLE AND PARAMETER ESTIMATION 1514 VALIDATION OF ASSUMPTIONS 1515 MULTIPLE COMPARISONS AND CONTRASTS 1516 SUMMARY 152 ANALYSIS OF VARIANCE WITH TWO FACTORS 1521 AIMS, DATA AND MODEL 1522 EXAMPLE AND GRAPHICAL INSPECTION 1523 ANOVA TABLE, TESTS AND PARAMETER ESTIMATION 1524 VALIDATING ASSUMPTIONS 1525 CONTRASTS 1526 SUMMARY 153 REPEATED MEASURES ANALYSIS OF VARIANCE 1531 ONE-WAY REPEATED MEASURES ANOVA 1532 TWO-FACTOR MODEL WITH REPEATED MEASURES FOR BOTH FACTORS 1533 TWO-FACTOR MODEL WITH REPEATED MEASURES FOR ONE FACTOR APPENDIX: INSTALLING R AND R PACKAGES A1 INSTALLING R UNDER MICROSOFT WINDOWS A2 INSTALLING ADDITIONAL PACKAGES A21 INSTALLING FROM A FILE ON YOUR DISK A22 INSTALLING DIRECTLY FROM THE INTERNET A23 INSTALLING FROM THE COMMAND LINE A24 INSTALLING PACKAGES UNDER LINUX A3 LOADING INSTALLED PACKAGES