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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.
About the Author
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.
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Remember, folks: mathematical statistics is much deeper and more conceptual than the plug-and-play that is sophomore-level intro statistics. If you don't have a mathematical background, then this book (and in all honesty, a mathematical statistics course) is NOT for you.
I first encountered this book while working at the Federal Trade Commission (i.e., not in an academic setting), and found it so clear and easy to understand that I bought a copy for myself. I will concede that you can't come at this book without an understanding of at least integral calculus (and since so many people get turned off by Algebra, well...), so I suspect a lot of the negative reviews here are written by people who jumped in the deep end of the pool without having a few swimming lessons. If you know the calculus and basic set theory, the book is exceedingly easy to follow.
I wholly recommend this book, provided you have the prerequisite skills necessary to use it.
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31 of 37 people found the following review helpful
The numbering of the end of chapter exercises in the Kindle edition is NOT the same as the numbering of the exercises in the hardcover book. This has cost me several points on assignments for having completed and turned in the wrong problems. I have to make copies of the end of chapter problems from someone else's book. This is time consuming, irritating, and increases the functional cost of the Kindle edition.
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23 of 28 people found the following review helpful
I appreciate that the authors have tried to write an easy-to-read text. In fact, its clarity might be the only good characteristic, as it's marred by the following problems:
(1) Shallowness. The text is shallow. The extraordinarily easy problems fail to challenge the reader's mind, and the descriptions/lessons, while easy to read, aren't as informing as random Google search results for similar topics. That is, you'd get more simply googling statistics lessons rather than buying this book.
(2) It's an international version. This might not be a problem if you're learning statistics on your own, but if you're buying this book for class, double check the problems with the same text your professor has. I've lost points on my homework because the problems didn't match up, despite the fact that the professor listed this very same book on the syllabus.
(3) It's expensive. Not worth anything *near* the used prices you see. $180? $190? I wouldn't pay $100 for a book this shallow.
I know my opinion sounds harsh, but it's only so that others don't make the same mistake in buying the book I bought.
I hope this helps... please comment if you have any questions/comments/suggestions.
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10 of 13 people found the following review helpful
The examples are insufficient and do not show what formulas the results are derived from or the mathematical or statistical steps that are needed. The proofs also do not tell you the necessary formulas and often tell you to refer to sections that tell you to refer to other sections. Worst of all are the problems, which do not give you any hints and so you won't know if you are doing them with a completely wrong method. The book also does not give some of the necessary formulas to solve many forms of the problems. The distributions and estimators that you will need to work with are usually not given. If your class requires this book, you are going to be pulling your hair out in frustration and you'll need significant amounts of help for about half of the problems.
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I think the book clearly outlines the proofs, and the examples are pretty good. Some of them recur throughout a chapter - that can be good and bad. Good in that once you learn more material you can do more with the question, but bad in that in might limit variety and you will see some of the same pdf's over and over again - probably because they are easy to work with.
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If you're like me, you'll be stuck with a professor who insists on using this book, and you're out of luck. If you have the choice though, I strongly recommend avoiding this book at all costs.
The authors, while they might be great statisticians, display no knowledge of what actually helps students learn. There is little continuity between explanations, examples and problems. The explanations while sometimes good are generally counterintuitive and certainly don't foster a deep understanding of the material.
Particularly frustrating is the answers - even if you splash out the considerable sum for the Student Solutions Manual, it only answers half the questions, often with little to no explanation (which I would have thought was the point....) and even then the answers are riddled with errors.
Basically, this is the prototypical lazy textbook, written by people who have no incentive to produce a great work, because they are guaranteed an audience of students forced to use it. Do your best to avoid it.
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Book is horrendous. Author's do not explain where any of the theories come from and do not prove anything. This is the most dry and uninformative math book I have every encountered. If you have to take a class and this is the book I would look around if a different class uses a different book and try to take that one. The author's do not explain ANYTHING conceptually and use the most impenetrable terminology rather than just the standard phrases.
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This item: Mathematical Statistics with Applications