Book description
A concise, easily accessible introduction to descriptive and inferential techniques
Statistical Inference: A Short Course offers a concise presentation of the essentials of basic statistics for readers seeking to acquire a working knowledge of statistical concepts, measures, and procedures.
The author conducts tests on the assumption of randomness and normality, provides nonparametric methods when parametric approaches might not work. The book also explores how to determine a confidence interval for a population median while also providing coverage of ratio estimation, randomness, and causality. To ensure a thorough understanding of all key concepts, Statistical Inference provides numerous examples and solutions along with complete and precise answers to many fundamental questions, including:
How do we determine that a given dataset is actually a random sample?
With what level of precision and reliability can a population sample be estimated?
How are probabilities determined and are they the same thing as odds?
How can we predict the level of one variable from that of another?
What is the strength of the relationship between two variables?
The book is organized to present fundamental statistical concepts first, with later chapters exploring more advanced topics and additional statistical tests such as Distributional Hypotheses, Multinomial Chi-Square Statistics, and the Chi-Square Distribution. Each chapter includes appendices and exercises, allowing readers to test their comprehension of the presented material.
Statistical Inference: A Short Course is an excellent book for courses on probability, mathematical statistics, and statistical inference at the upper-undergraduate and graduate levels. The book also serves as a valuable reference for researchers and practitioners who would like to develop further insights into essential statistical tools.
Table of contents
- Cover
- Title Page
- Copyright
- Dedication
- Preface
- Chapter 1: The Nature of Statistics
- Chapter 2: Analyzing Quantitative Data
-
Chapter 3: Descriptive Characteristics of Quantitative Data
- 3.1 The Search for Summary Characteristics
- 3.2 The Arithmetic Mean
- 3.3 The Median
- 3.4 The Mode
- 3.5 The Range
- 3.6 The Standard Deviation
- 3.7 Relative Variation
- 3.8 Skewness
- 3.9 Quantiles
- 3.10 Kurtosis
- 3.11 Detection of Outliers
- 3.12 So What do We do with All this Stuff?
- Exercises
- Appendix 3.A Descriptive Characteristics of Grouped Data
- Chapter 4: Essentials of Probability
- Chapter 5: Discrete Probability Distributions And Their Properties
- Chapter 6: The Normal Distribution
-
Chapter 7: Simple Random Sampling and the Sampling Distribution of the Mean
- 7.1 Simple Random Sampling
- 7.2 The Sampling Distribution of The Mean
- 7.3 Comments on the Sampling Distribution of the Mean
- 7.4 A Central Limit Theorem
- Exercises
- Appendix 7.A Using a Table of Random Numbers
- Appendix 7.B Assessing Normality Via the Normal probability Plot
- Appendix 7.C Randomness, Risk, and Uncertainty
- Chapter 8: Confidence Interval Estimation Of μ
- Chapter 9: The Sampling Distribution of a Proportion and Its Confidence Interval Estimation
-
Chapter 10: Testing Statistical Hypotheses
- 10.1 What is a Statistical Hypothesis?
- 10.2 Errors in Testing
- 10.3 The Contextual Framework of Hypothesis Testing
- 10.4 Selecting A Test Statistic
- 10.5 The Classical Approach to Hypothesis Testing
- 10.6 Types of Hypothesis Tests
- 10.7 Hypothesis Tests for μ (σ Known)
- 10.8 Hypothesis Tests for μ (σ Unknown And n Small)
- 10.9 Reporting The Results of Statistical Hypothesis Tests
- 10.10 Hypothesis Tests for The Population Proportion (of Successes) p
- Exercises
- Appendix 10.A Assessing The Randomness of A Sample
- Appendix 10.B Wilcoxon Signed Rank Test (of a Median)
- Appendix 10.C Lilliefors Goodness-of-Fit Test for Normality
-
Chapter 11: Comparing Two Population Means and Two Population Proportions
- 11.1 Confidence Intervals for the Difference of Means when Sampling from Two Independent Normal Populations
- 11.2 Confidence Intervals for the Difference of Means When Sampling from Two Dependent Populations: Paired Comparisons
- 11.3 Confidence Intervals for the Difference of Proportions When Sampling from Two Independent Binomial Populations
- 11.4 Statistical Hypothesis Tests for the Difference of Means When Sampling from Two Independent Normal Populations
- 11.5 Hypothesis Tests for the Difference of Means When Sampling From Two Dependent Populations: Paired Comparisons
- 11.6 Hypothesis Tests for the Difference of Proportions when Sampling from Two Independent Binomial Populations
- Exercises
- Appendix 11.A Runs Test for Two Independent Samples
- Appendix 11.B Mann–Whitney (Rank Sum) Test for Two Independent Populations
- Appendix 11.C Wilcoxon Signed Rank Test When Sampling from Two Dependent Populations: Paired Comparisons
-
Chapter 12: Bivariate Regression and Correlation
- 12.1 Introducing an Additional Dimension to our Statistical Analysis
- 12.2 Linear Relationships
- 12.3 Estimating the Slope and Intercept of the Population Regression Line
- 12.4 Decomposition of the Sample Variation in Y
- 12.5 Mean, Variance, and Sampling Distribution of the Least Squares Estimators β and β
- 12.6 Confidence Intervals for β and β
- 12.7 Testing Hypotheses about β and β
- 12.8 Predicting the Average Value of Y given X
- 12.9 The Prediction of a Particular Value of Y given X
- 12.10 Correlation Analysis
- Exercises
- Appendix 12.A Assessing Normality (Appendix 7.B Continued)
- Appendix 12.B On Making Causal Inferences
-
Chapter 13: An Assortment of Additional Statistical Tests
- 13.1 Distributional Hypotheses
- 13.2 The Multinomial Chi-Square Statistic
- 13.3 The Chi-Square Distribution
- 13.4 Testing Goodness Of Fit
- 13.5 Testing Independence
- 13.6 Testing k Proportions
- 13.7 A Measure of Strength of Association in a Contingency Table
- 13.8 A Confidence Interval for σ2 Under Random Sampling from a Normal Population
- 13.9 The F Distribution
- 13.10 Applications of the F Statistic to Regression Analysis
- Exercises
- Appendix A
- Solutions to Exercises
- References
- Index
Product information
- Title: Statistical Inference: A Short Course
- Author(s):
- Release date: July 2012
- Publisher(s): Wiley
- ISBN: 9781118229408
You might also like
book
Essential Statistics for Non-STEM Data Analysts
Reinforce your understanding of data science and data analysis from a statistical perspective to extract meaningful …
book
Statistical Intervals, 2nd Edition
Describes statistical intervals to quantify sampling uncertainty,focusing on key application needs and recently developed methodology in …
book
Examples and Problems in Mathematical Statistics
Provides the necessary skills to solve problems in mathematical statistics through theory, concrete examples, and exercises …
book
Nonparametric Statistics: A Step-by-Step Approach, 2nd Edition
"...a very useful resource for courses in nonparametric statistics in which the emphasis is on applications …