APPLIED STATISTICS USING SPSS, STATISTICA, MATLAB, AND R

By F. JOARA

CONTENTS 1 INTRODUCTION DETERMINISTIC DATA AND RANDOM DATA POPULATION, SAMPLE AND STATISTICS RANDOM VARIABLES PROBABILITIES AND DISTRIBUTIONS DISCRETE VARIABLES CONTINUOUS VARIABLES BEYOND A REASONABLE DOUBT STATISTICAL SIGNIFICANCE AND OTHER SIGNIFICANCES DATASETS SOFTWARE TOOLS SPSS AND STATISTICA MATLAB AND R 2 PRESENTING AND SUMMARISING THE DATA PRELIMINARIES READING IN THE DATA OPERATING WITH THE DATA PRESENTING THE DATA COUNTS AND BAR GRAPHS FREQUENCIES AND HISTOGRAMS MULTIVARIATE TABLES, SCATTER PLOTS AND 3D PLOTS CATEGORISED PLOTS SUMMARISING THE DATA MEASURES OF LOCATION MEASURES OF SPREAD MEASURES OF SHAPE MEASURES OF ASSOCIATION FOR CONTINUOUS VARIABLES MEASURES OF ASSOCIATION FOR ORDINAL VARIABLES MEASURES OF ASSOCIATION FOR NOMINAL VARIABLES EXERCISES 3 ESTIMATING DATA PARAMETERS POINT ESTIMATION AND INTERVAL ESTIMATION ESTIMATING A MEAN ESTIMATING A PROPORTION ESTIMATING A VARIANCE ESTIMATING A VARIANCE RATIO BOOTSTRAP ESTIMATION 4 PARAMETRIC TESTS OF HYPOTHESES HYPOTHESIS TEST PROCEDURE TEST ERRORS AND TEST POWER INFERENCE ON ONE POPULATION TESTING A MEAN TESTING A VARIANCE INFERENCE ON TWO POPULATIONS TESTING A CORRELATION COMPARING TWO VARIANCES COMPARING TWO MEANS INFERENCE ON MORE THAN TWO POPULATIONS INTRODUCTION TO THE ANALYSIS OF VARIANCE ONE-WAY ANOVA TWO-WAY ANOVA 5 NON-PARAMETRIC TESTS OF HYPOTHESES THE RUNS TEST THE BINOMIAL TEST THE CHI-SQUARE GOODNESS OF FIT TEST THE KOLMOGOROV-SMIRNOV GOODNESS OF FIT TEST THE LILLIEFORS TEST FOR NORMALITY THE SHAPIRO-WILK TEST FOR NORMALITY CONTINGENCY TABLES THE 2×2 CONTINGENCY TABLE THE RXC CONTINGENCY TABLE THE CHI-SQUARE TEST OF INDEPENDENCE MEASURES OF ASSOCIATION REVISITED TESTS FOR TWO INDEPENDENT SAMPLES TESTS FOR TWO PAIRED SAMPLES INFERENCE ON MORE THAN TWO POPULATIONS THE KRUSKAL-WALLIS TEST FOR INDEPENDENT SAMPLES THE FRIEDMANN TEST FOR PAIRED SAMPLES THE COCHRAN Q TEST 6 STATISTICAL CLASSIFICATION DECISION REGIONS AND FUNCTIONS LINEAR DISCRIMINANTS MINIMUM EUCLIDIAN DISTANCE DISCRIMINANT MINIMUM MAHALANOBIS DISTANCE DISCRIMINANT BAYESIAN CLASSIFICATION BAYES RULE FOR MINIMUM RISK NORMAL BAYESIAN CLASSIFICATION DIMENSIONALITY RATIO AND ERROR ESTIMATION THE ROC CURVE FEATURE SELECTION CLASSIFIER EVALUATION TREE CLASSIFIERS 7 DATA REGRESSION SIMPLE LINEAR REGRESSION SIMPLE LINEAR REGRESSION MODEL ESTIMATING THE REGRESSION FUNCTION INFERENCES IN REGRESSION ANALYSIS ANOVA TESTS MULTIPLE REGRESSION GENERAL LINEAR REGRESSION MODEL GENERAL LINEAR REGRESSION IN MATRIX TERMS MULTIPLE CORRELATION INFERENCES ON REGRESSION PARAMETERS ANOVA AND EXTRA SUMS OF SQUARES POLYNOMIAL REGRESSION AND OTHER MODELS BUILDING AND EVALUATING THE REGRESSION MODEL BUILDING THE MODEL EVALUATING THE MODEL CASE STUDY REGRESSION THROUGH THE ORIGIN RIDGE REGRESSION LOGIT AND PROBIT MODELS 8 DATA STRUCTURE ANALYSIS PRINCIPAL COMPONENTS DIMENSIONAL REDUCTION PRINCIPAL COMPONENTS OF CORRELATION MATRICES FACTOR ANALYSIS 9 SURVIVAL ANALYSIS SURVIVOR FUNCTION AND HAZARD FUNCTION NON-PARAMETRIC ANALYSIS OF SURVIVAL DATA THE LIFE TABLE ANALYSIS THE KAPLAN-MEIER ANALYSIS STATISTICS FOR NON-PARAMETRIC ANALYSIS COMPARING TWO GROUPS OF SURVIVAL DATA MODELS FOR SURVIVAL DATA THE EXPONENTIAL MODEL THE WEIBULL MODEL THE COX REGRESSION MODEL 10 DIRECTIONAL DATA REPRESENTING DIRECTIONAL DATA DESCRIPTIVE STATISTICS THE VON MISES DISTRIBUTIONS ASSESSING THE DISTRIBUTION OF DIRECTIONAL DATA 10 4 1 GRAPHICAL ASSESSMENT OF UNIFORMITY 10 4 2 THE RAYLEIGH TEST OF UNIFORMITY 10 4 3 THE WATSON GOODNESS OF FIT TEST 10 4 4 ASSESSING THE VON MISESNESS OF SPHERICAL DISTRIBUTIONS TESTS ON VON MISES DISTRIBUTIONS 10 5 1 ONE-SAMPLE MEAN TEST 10 5 2 MEAN TEST FOR TWO INDEPENDENT SAMPLES NON-PARAMETRIC TESTS 10 6 1 THE UNIFORM SCORES TEST FOR CIRCULAR DATA 10 6 2 THE WATSON TEST FOR SPHERICAL DATA 10 6 3 TESTING TWO PAIRED SAMPLES 1 INTRODUCTION 1 1 DETERMINISTIC DATA AND RANDOM DATA OUR DAILY EXPERIENCE TEACHES US THAT SOME DATA ARE GENERATED IN ACCORDANCE TO KNOWN AND PRECISE LAWS, WHILE OTHER DATA SEEM TO OCCUR IN A PURELY HAPHAZARD WAY DATA GENERATED IN ACCORDANCE TO KNOWN AND PRECISE LAWS ARE CALLED DETERMINISTIC GRAVITY WHEN THE BODY IS RELEASED AT A HEIGHT H, WE CAN CALCULATE PRECISELY WHERE THE BODY STANDS AT EACH TIME T THE PHYSICAL LAW, ASSUMING THAT THE FALL TAKES PLACE IN AN EMPTY SPACE, IS EXPRESSED AS ½GT H H ? = , WHERE H0 IS THE INITIAL HEIGHT AND G IS THE EARTH S GRAVITY ACCELERATION AT THE POINT WHERE THE BODY FALLS FIGURE 1 1 SHOWS THE BEHAVIOUR OF H WITH T, ASSUMING AN INITIAL HEIGHT OF METERS