1. What Is Statistics?
Introduction. Characterizing a Set of Measurements: Graphical
Methods. Characterizing a Set of Measurements: Numerical Methods.
How Inferences Are Made. Theory and Reality. Summary.
2. Probability.
Introduction. Probability and Inference. A Review of Set Notation.
A Probabilistic Model for an Experiment: The Discrete Case.
Calculating the Probability of an Event: The Sample-Point Method.
Tools for Counting Sample Points. Conditional Probability and the
Independence of Events. Two Laws of Probability. Calculating the
Probability of an Event: The Event-Composition Methods. The Law of
Total Probability and Bayes''''s Rule. Numerical Events and Random
Variables. Random Sampling. Summary.
3. Discrete Random Variables and Their Probability
Distributions.
Basic Definition. The Probability Distribution for Discrete Random
Variable. The Expected Value of Random Variable or a Function of
Random Variable. The Binomial Probability Distribution. The
Geometric Probability Distribution. The Negative Binomial
Probability Distribution (Optional). The Hypergeometric Probability
Distribution. Moments and Moment-Generating Functions.
Probability-Generating Functions (Optional). Tchebysheff''''s
Theorem. Summary.
4. Continuous Random Variables and Their Probability
Distributions.
Introduction. The Probability Distribution for Continuous Random
Variable. The Expected Value for Continuous Random Variable. The
Uniform Probability Distribution. The Normal Probability
Distribution. The Gamma Probability Distribution. The Beta
Probability Distribution. Some General Comments. Other Expected
Values. Tchebysheff''''s Theorem. Expectations of Discontinuous
Functions and Mixed Probability Distributions (Optional).
Summary.
5. Multivariate Probability Distributions.
Introduction. Bivariate and Multivariate Probability Distributions.
Independent Random Variables. The Expected Value of a Function of
Random Variables. Special Theorems. The Covariance of Two Random
Variables. The Expected Value and Variance of Linear Functions of
Random Variables. The Multinomial Probability Distribution. The
Bivariate Normal Distribution (Optional). Conditional Expectations.
Summary.
6. Functions of Random Variables.
Introductions. Finding the Probability Distribution of a Function
of Random Variables. The Method of Distribution Functions. The
Methods of Transformations. Multivariable Transformations Using
Jacobians. Order Statistics. Summary.
7. Sampling Distributions and the Central Limit Theorem.
Introduction. Sampling Distributions Related to the Normal
Distribution. The Central Limit Theorem. A Proof of the Central
Limit Theorem (Optional). The Normal Approximation to the Binomial
Distributions. Summary.
8. Estimation.
Introduction. The Bias and Mean Square Error of Point Estimators.
Some Common Unbiased Point Estimators. Evaluating the Goodness of
Point Estimator. Confidence Intervals. Large-Sample Confidence
Intervals Selecting the Sample Size. Small-Sample Confidence
Intervals for u and u1-u2. Confidence Intervals for o2.
Summary.
9. Properties of Point Estimators and Methods of Estimation.
Introduction. Relative Efficiency. Consistency. Sufficiency. The
Rao-Blackwell Theorem and Minimum-Variance Unbiased Estimation. The
Method of Moments. The Method of Maximum Likelihood. Some
Large-Sample Properties of MLEs (Optional). Summary.
10. Hypothesis Testing.
Introduction. Elements of a Statistical Test. Common Large-Sample
Tests. Calculating Type II Error Probabilities and Finding the
Sample Size for the Z Test. Relationships Between Hypothesis
Testing Procedures and Confidence Intervals. Another Way to Report
the Results of a Statistical Test: Attained Significance Levels or
p-Values. Some Comments on the Theory of Hypothesis Testing.
Small-Sample Hypothesis Testing for u and u1-u2. Testing Hypotheses
Concerning Variances. Power of Test and the Neyman-Pearson Lemma.
Likelihood Ration Test. Summary.
11. Linear Models and Estimation by Least Squares.
Introduction. Linear Statistical Models. The Method of Least
Squares. Properties of the Least Squares Estimators for the Simple
Linear Regression Model. Inference Concerning the Parameters BI.
Inferences Concerning Linear Functions of the Model Parameters:
Simple Linear Regression. Predicting a Particular Value of Y Using
Simple Linear Regression. Correlation. Some Practical Examples.
Fitting the Linear Model by Using Matrices. Properties of the Least
Squares Estimators for the Multiple Linear Regression Model.
Inferences Concerning Linear Functions of the Model Parameters:
Multiple Linear Regression. Prediction a Particular Value of Y
Using Multiple Regression. A Test for H0: Bg+1 + Bg+2 = . = Bk = 0.
Summary and Concluding Remarks.
12. Considerations in Designing Experiments.
The Elements Affecting the Information in a Sample. Designing
Experiment to Increase Accuracy. The Matched Pairs Experiment. Some
Elementary Experimental Designs. Summary.
13. The Analysis of Variance.
Introduction. The Analysis of Variance Procedure. Comparison of
More than Two Means: Analysis of Variance for a One-way Layout. An
Analysis of Variance Table for a One-Way Layout. A Statistical
Model of the One-Way Layout. Proof of Additivity of the Sums of
Squares and E (MST) for a One-Way Layout (Optional). Estimation in
the One-Way Layout. A Statistical Model for the Randomized Block
Design. The Analysis of Variance for a Randomized Block Design.
Estimation in the Randomized Block Design. Selecting the Sample
Size. Simultaneous Confidence Intervals for More than One
Parameter. Analysis of Variance Using Linear Models. Summary.
14. Analysis of Categorical Data.
A Description of the Experiment. The Chi-Square Test. A Test of
Hypothesis Concerning Specified Cell Probabilities: A
Goodness-of-Fit Test. Contingency Tables. r x c Tables with Fixed
Row or Column Totals. Other Applications. Summary and Concluding
Remarks.
15. Nonparametric Statistics.
Introduction. A General Two-Sampling Shift Model. A Sign Test for a
Matched Pairs Experiment. The Wilcoxon Signed-Rank Test for a
Matched Pairs Experiment. The Use of Ranks for Comparing Two
Population Distributions: Independent Random Samples. The
Mann-Whitney U Test: Independent Random Samples. The Kruskal-Wallis
Test for One-Way Layout. The Friedman Test for Randomized Block
Designs. The Runs Test: A Test for Randomness. Rank Correlation
Coefficient. Some General Comments on Nonparametric Statistical
Test.
16. Introduction to Bayesian Methods for Inference.
Introduction. Bayesian Priors, Posteriors and Estimators. Bayesian
Credible Intervals. Bayesian Tests of Hypotheses. Summary and
Additional Comments.
Appendix 1. Matrices and Other Useful Mathematical Results.
Matrices and Matrix Algebra. Addition of Matrices. Multiplication
of a Matrix by a Real Number. Matrix Multiplication. Identity
Elements. The Inverse of a Matrix. The Transpose of a Matrix. A
Matrix Expression for a System of Simultaneous Linear Equations.
Inverting a Matrix. Solving a System of Simultaneous Linear
Equations. Other Useful Mathematical Results.
Appendix 2. Common Probability Distributions, Means, Variances, and
Moment-Generating Functions. Discrete Distributions. Continuous
Distributions.
Appendix 3. Tables. Binomial Probabilities. Table of e-x. Poisson
Probabilities. Normal Curve Areas. Percentage Points of the t
Distributions. Percentage Points of the F Distributions.
Distribution of Function U. Critical Values of T in the Wilcoxon
Matched-Pairs, Signed-Ranks Test. Distribution of the Total Number
of Runs R in Sample Size (n1,n2); P(R < a). Critical Values of
Pearman''s Rank Correlation Coefficient. Random Numbers. Answer to
Exercises. Index.
The late Dr. Mendenhall served in the Navy in the Korean War and obtained a Ph.D. in Statistics at North Carolina State University. After receiving his Ph.D , he was a professor in the Mathematics Department at Bucknell University in Pennsylvania before moving to Gainesville in 1963 where he was the first chairman of the Department of Statistics at the University of Florida. Dr. Mendenhall published articles in some of the top statistics journals, such as Biometika and Technometrics; however, he is more widely known for his prolific textbook career. He authored or co-authored approximately 13 Statistics textbooks and several books about his childhood. Richard L. Scheaffer, Professor Emeritus of Statistics, University of Florida, received his Ph.D. in statistics from Florida State University. Accompanying a career of teaching, research and administration, Dr. Scheaffer has led efforts on the improvement of statistics education throughout the school and college curriculum. Co-author of five textbooks, he was one of the developers of the Quantitative Literacy Project that formed the basis of the data analysis strand in the curriculum standards of the National Council of Teachers of Mathematics. He also led the task force that developed the AP Statistics Program, for which he served as Chief Faculty Consultant. Dr. Scheaffer is a Fellow and past president of the American Statistical Association, a past chair of the Conference Board of the Mathematical Sciences, and an advisor on numerous statistics education projects.
1. What Is Statistics? Introduction. Characterizing a Set of Measurements: Graphical Methods. Characterizing a Set of Measurements: Numerical Methods. How Inferences Are Made. Theory and Reality. Summary. 2. Probability. Introduction. Probability and Inference. A Review of Set Notation. A Probabilistic Model for an Experiment: The Discrete Case. Calculating the Probability of an Event: The Sample-Point Method. Tools for Counting Sample Points. Conditional Probability and the Independence of Events. Two Laws of Probability. Calculating the Probability of an Event: The Event-Composition Methods. The Law of Total Probability and Bayes"s Rule. Numerical Events and Random Variables. Random Sampling. Summary. 3. Discrete Random Variables and Their Probability Distributions. Basic Definition. The Probability Distribution for Discrete Random Variable. The Expected Value of Random Variable or a Function of Random Variable. The Binomial Probability Distribution. The Geometric Probability Distribution. The Negative Binomial Probability Distribution (Optional). The Hypergeometric Probability Distribution. Moments and Moment-Generating Functions. Probability-Generating Functions (Optional). Tchebysheff"s Theorem. Summary. 4. Continuous Random Variables and Their Probability Distributions. Introduction. The Probability Distribution for Continuous Random Variable. The Expected Value for Continuous Random Variable. The Uniform Probability Distribution. The Normal Probability Distribution. The Gamma Probability Distribution. The Beta Probability Distribution. Some General Comments. Other Expected Values. Tchebysheff"s Theorem. Expectations of Discontinuous Functions and Mixed Probability Distributions (Optional). Summary. 5. Multivariate Probability Distributions. Introduction. Bivariate and Multivariate Probability Distributions. Independent Random Variables. The Expected Value of a Function of Random Variables. Special Theorems. The Covariance of Two Random Variables. The Expected Value and Variance of Linear Functions of Random Variables. The Multinomial Probability Distribution. The Bivariate Normal Distribution (Optional). Conditional Expectations. Summary. 6. Functions of Random Variables. Introductions. Finding the Probability Distribution of a Function of Random Variables. The Method of Distribution Functions. The Methods of Transformations. Multivariable Transformations Using Jacobians. Order Statistics. Summary. 7. Sampling Distributions and the Central Limit Theorem. Introduction. Sampling Distributions Related to the Normal Distribution. The Central Limit Theorem. A Proof of the Central Limit Theorem (Optional). The Normal Approximation to the Binomial Distributions. Summary. 8. Estimation. Introduction. The Bias and Mean Square Error of Point Estimators. Some Common Unbiased Point Estimators. Evaluating the Goodness of Point Estimator. Confidence Intervals. Large-Sample Confidence Intervals Selecting the Sample Size. Small-Sample Confidence Intervals for u and u1-u2. Confidence Intervals for o2. Summary. 9. Properties of Point Estimators and Methods of Estimation. Introduction. Relative Efficiency. Consistency. Sufficiency. The Rao-Blackwell Theorem and Minimum-Variance Unbiased Estimation. The Method of Moments. The Method of Maximum Likelihood. Some Large-Sample Properties of MLEs (Optional). Summary. 10. Hypothesis Testing. Introduction. Elements of a Statistical Test. Common Large-Sample Tests. Calculating Type II Error Probabilities and Finding the Sample Size for the Z Test. Relationships Between Hypothesis Testing Procedures and Confidence Intervals. Another Way to Report the Results of a Statistical Test: Attained Significance Levels or p-Values. Some Comments on the Theory of Hypothesis Testing. Small-Sample Hypothesis Testing for u and u1-u2. Testing Hypotheses Concerning Variances. Power of Test and the Neyman-Pearson Lemma. Likelihood Ration Test. Summary. 11. Linear Models and Estimation by Least Squares. Introduction. Linear Statistical Models. The Method of Least Squares. Properties of the Least Squares Estimators for the Simple Linear Regression Model. Inference Concerning the Parameters BI. Inferences Concerning Linear Functions of the Model Parameters: Simple Linear Regression. Predicting a Particular Value of Y Using Simple Linear Regression. Correlation. Some Practical Examples. Fitting the Linear Model by Using Matrices. Properties of the Least Squares Estimators for the Multiple Linear Regression Model. Inferences Concerning Linear Functions of the Model Parameters: Multiple Linear Regression. Prediction a Particular Value of Y Using Multiple Regression. A Test for H0: Bg+1 + Bg+2 = . = Bk = 0. Summary and Concluding Remarks. 12. Considerations in Designing Experiments. The Elements Affecting the Information in a Sample. Designing Experiment to Increase Accuracy. The Matched Pairs Experiment. Some Elementary Experimental Designs. Summary. 13. The Analysis of Variance. Introduction. The Analysis of Variance Procedure. Comparison of More than Two Means: Analysis of Variance for a One-way Layout. An Analysis of Variance Table for a One-Way Layout. A Statistical Model of the One-Way Layout. Proof of Additivity of the Sums of Squares and E (MST) for a One-Way Layout (Optional). Estimation in the One-Way Layout. A Statistical Model for the Randomized Block Design. The Analysis of Variance for a Randomized Block Design. Estimation in the Randomized Block Design. Selecting the Sample Size. Simultaneous Confidence Intervals for More than One Parameter. Analysis of Variance Using Linear Models. Summary. 14. Analysis of Categorical Data. A Description of the Experiment. The Chi-Square Test. A Test of Hypothesis Concerning Specified Cell Probabilities: A Goodness-of-Fit Test. Contingency Tables. r x c Tables with Fixed Row or Column Totals. Other Applications. Summary and Concluding Remarks. 15. Nonparametric Statistics. Introduction. A General Two-Sampling Shift Model. A Sign Test for a Matched Pairs Experiment. The Wilcoxon Signed-Rank Test for a Matched Pairs Experiment. The Use of Ranks for Comparing Two Population Distributions: Independent Random Samples. The Mann-Whitney U Test: Independent Random Samples. The Kruskal-Wallis Test for One-Way Layout. The Friedman Test for Randomized Block Designs. The Runs Test: A Test for Randomness. Rank Correlation Coefficient. Some General Comments on Nonparametric Statistical Test. 16. Introduction to Bayesian Methods for Inference. Introduction. Bayesian Priors, Posteriors and Estimators. Bayesian Credible Intervals. Bayesian Tests of Hypotheses. Summary and Additional Comments. Appendix 1. Matrices and Other Useful Mathematical Results. Matrices and Matrix Algebra. Addition of Matrices. Multiplication of a Matrix by a Real Number. Matrix Multiplication. Identity Elements. The Inverse of a Matrix. The Transpose of a Matrix. A Matrix Expression for a System of Simultaneous Linear Equations. Inverting a Matrix. Solving a System of Simultaneous Linear Equations. Other Useful Mathematical Results. Appendix 2. Common Probability Distributions, Means, Variances, and Moment-Generating Functions. Discrete Distributions. Continuous Distributions. Appendix 3. Tables. Binomial Probabilities. Table of e-x. Poisson Probabilities. Normal Curve Areas. Percentage Points of the t Distributions. Percentage Points of the F Distributions. Distribution of Function U. Critical Values of T in the Wilcoxon Matched-Pairs, Signed-Ranks Test. Distribution of the Total Number of Runs R in Sample Size (n1,n2); P(R < a). Critical Values of Pearman's Rank Correlation Coefficient. Random Numbers. Answer to Exercises. Index.
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