PROBABILITY THEORY AND MATHEMATICAL STATISTICS

By RICHARD JOHNSON

CONTENTS THE ROLE OF STATISTICS THE BASIC STATISTICAL PROCEDURE THE SCIENTI?C METHOD EXPERIMENTAL DATA AND SURVEY DATA COMPUTER USAGE REVIEW EXERCISES SELECTED READINGS POPULATIONS, SAMPLES, AND PROBABILITY DISTRIBUTIONS POPULATIONS AND SAMPLES RANDOM SAMPLING LEVELS OF MEASUREMENT RANDOM VARIABLES AND PROBABILITY DISTRIBUTIONS EXPECTED VALUE AND VARIANCE OF A PROBABILITY DISTRIBUTION BINOMIAL DISTRIBUTIONS THE NATURE OF BINOMIAL DISTRIBUTIONS TESTING HYPOTHESES ESTIMATION NONPARAMETRIC STATISTICS: MEDIAN TEST POISSON DISTRIBUTIONS THE NATURE OF POISSON DISTRIBUTIONS POISSON DISTRIBUTIONS AND BINOMIAL DISTRIBUTIONS CHI-SQUARE DISTRIBUTIONS THE NATURE OF CHI-SQUARE DISTRIBUTIONS GOODNESS-OF-FIT TESTS CONTINGENCY TABLE ANALYSIS RELATIVE RISKS AND ODDS RATIOS NONPARAMETRIC STATISTICS: MEDIAN TEST FOR SEVERAL SAMPLES SAMPLING DISTRIBUTION OF AVERAGES POPULATION MEAN AND SAMPLE AVERAGE POPULATION VARIANCE AND SAMPLE VARIANCE THE MEAN AND VARIANCE OF THE SAMPLING DISTRIBUTION OF AVERAGES SAMPLING WITHOUT REPLACEMENT NORMAL DISTRIBUTIONS THE STANDARD NORMAL DISTRIBUTION INFERENCE FROM A SINGLE OBSERVATION THE CENTRAL LIMIT THEOREM INFERENCES ABOUT A POPULATION MEAN AND VARIANCE USING A NORMAL DISTRIBUTION TO APPROXIMATE OTHER DISTRIBUTIONS NONPARAMETRIC STATISTICS: A TEST BASED ON RANKS STUDENT’S T DISTRIBUTION THE NATURE OF T DISTRIBUTIONS INFERENCE ABOUT A SINGLE MEAN INFERENCE ABOUT TWO MEANS INFERENCE ABOUT TWO VARIANCES NONPARAMETRIC STATISTICS: MATCHED-PAIR AND TWO-SAMPLE RANK TESTS DISTRIBUTIONS OF TWO VARIABLES SIMPLE LINEAR REGRESSION MODEL TESTING INFERENCES RELATED TO REGRESSION CORRELATION NONPARAMETRIC STATISTICS: RANK CORRELATION ESTIMATING ONLY ONE LINEAR TREND PARAMETER TECHNIQUES FOR ONE-WAY ANALYSIS OF VARIANCE THE ADDITIVE MODEL ONE-WAY ANALYSIS-OF-VARIANCE PROCEDURE MULTIPLE-COMPARISON PROCEDURES ONE-DEGREE-OF-FREEDOM COMPARISONS BONFERRONI PROCEDURES NONPARAMETRIC STATISTICS: KRUSKAL–WALLIS ANOVA FOR RANKS THE ANALYSIS-OF-VARIANCE MODEL RANDOM EFFECTS AND FIXED EFFECTS TESTING THE ASSUMPTIONS FOR ANOVA TRANSFORMATIONS OTHER ANALYSIS-OF-VARIANCE DESIGNS NESTED DESIGN RANDOMIZED COMPLETE BLOCK DESIGN LATIN SQUARE DESIGN A B FACTORIAL DESIGN A B C FACTORIAL DESIGN SPLIT-PLOT DESIGN SPLIT PLOT WITH REPEATED MEASURES ANALYSIS OF COVARIANCE COMBINING REGRESSION WITH ANOVA ONE-WAY ANALYSIS OF COVARIANCE TESTING THE ASSUMPTIONS FOR ANALYSIS OF COVARIANCE MULTIPLE REGRESSION AND CORRELATION MATRIX PROCEDURES ANOVA PROCEDURES FOR MULTIPLE REGRESSION AND CORRELATION INFERENCES ABOUT EFFECTS OF INDEPENDENT VARIABLES MODEL FITTING LOGARITHMIC TRANSFORMATIONS POLYNOMIAL REGRESSION LOGISTIC REGRESSION