Statistical Inference - A Short Course

Informationen zum Autor MICHAEL J. PANIK, PhD , is Professor Emeritus in the Department of Economics at the University of Hartford. He has served as a consultant to the Connecticut Department of Motor Vehicles as well as a variety of healthcare organizations. Dr. Panik has published numerous journal articles in the areas of economics, mathematics, and applied econometrics. Klappentext A concise, easily accessible introduction to descriptive and inferential techniquesStatistical 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. Zusammenfassung This concise, easily accessible introduction to descriptive and inferential techniques presents the essentials of basic statistics for readers seeking to acquire a working knowledge of statistical concepts, measures, and procedures. Inhaltsverzeichnis Preface xv 1 The Nature of Statistics 1 1.1 Statistics Defined 1 1.2 The Population and the Sample 2 1.3 Selecting a Sample from a Population 3 1.4 Measurement Scales 4 1.5 Let us Add 6 Exercises 7 2 Analyzing Quantitative Data 9 2.1 Imposing Order 9 2.2 Tabular and Graphical Techniques: Ungrouped Data 9 2.3 Tabular and Graphical Techniques: Grouped Data 11 Exercises 16 Appendix 2.A Histograms with Classes of Different Lengths 18 3 Descriptive Characteristics of Quantitative Data 22 3.1 The Search for Summary Characteristics 22 3.2 The Arithmetic Mean 23 3.3 The Median 26 3.4 The Mode 27 3.5 The Range 27 3.6 The Standard Deviation 28 3.7 Relative Variation 33 3.8 Skewness 34 3.9 Quantiles 36 3.10 Kurtosis 38 3.11 Detection of Outliers 39 3.12 So What Do We Do with All This Stuff? 41 Exercises 47 Appendix 3.A Descriptive Characteristics of Grouped Data 51 3.A.1 The Arithmetic Mean 52 3.A.2 The Median 53 3.A.3 The Mode 55 3.A.4 The Standard Deviation 57 3.A.5 Quantiles (Quartiles, Deciles, and Percentiles) 58 4 Essentials of Probability 61 4.1 Set Notation 61 4.2 Events within the Sample Space 63

List of contents

Preface xv
 
1 The Nature of Statistics 1
 
1.1 Statistics Defined 1
 
1.2 The Population and the Sample 2
 
1.3 Selecting a Sample from a Population 3
 
1.4 Measurement Scales 4
 
1.5 Let us Add 6
 
Exercises 7
 
2 Analyzing Quantitative Data 9
 
2.1 Imposing Order 9
 
2.2 Tabular and Graphical Techniques: Ungrouped Data 9
 
2.3 Tabular and Graphical Techniques: Grouped Data 11
 
Exercises 16
 
Appendix 2.A Histograms with Classes of Different Lengths 18
 
3 Descriptive Characteristics of Quantitative Data 22
 
3.1 The Search for Summary Characteristics 22
 
3.2 The Arithmetic Mean 23
 
3.3 The Median 26
 
3.4 The Mode 27
 
3.5 The Range 27
 
3.6 The Standard Deviation 28
 
3.7 Relative Variation 33
 
3.8 Skewness 34
 
3.9 Quantiles 36
 
3.10 Kurtosis 38
 
3.11 Detection of Outliers 39
 
3.12 So What Do We Do with All This Stuff? 41
 
Exercises 47
 
Appendix 3.A Descriptive Characteristics of Grouped Data 51
 
3.A.1 The Arithmetic Mean 52
 
3.A.2 The Median 53
 
3.A.3 The Mode 55
 
3.A.4 The Standard Deviation 57
 
3.A.5 Quantiles (Quartiles, Deciles, and Percentiles) 58
 
4 Essentials of Probability 61
 
4.1 Set Notation 61
 
4.2 Events within the Sample Space 63
 
4.3 Basic Probability Calculations 64
 
4.4 Joint, Marginal, and Conditional Probability 68
 
4.5 Sources of Probabilities 73
 
Exercises 75
 
5 Discrete Probability Distributions and Their Properties 81
 
5.1 The Discrete Probability Distribution 81
 
5.2 The Mean, Variance, and Standard Deviation of a Discrete Random Variable 85
 
5.3 The Binomial Probability Distribution 89
 
5.3.1 Counting Issues 89
 
5.3.2 The Bernoulli Probability Distribution 91
 
5.3.3 The Binomial Probability Distribution 91
 
Exercises 96
 
6 The Normal Distribution 101
 
6.1 The Continuous Probability Distribution 101
 
6.2 The Normal Distribution 102
 
6.3 Probability as an Area Under the Normal Curve 104
 
6.4 Percentiles of the Standard Normal Distribution and Percentiles of the Random Variable X 114
 
Exercises 116
 
Appendix 6.A The Normal Approximation to Binomial Probabilities 120
 
7 Simple Random Sampling and the Sampling Distribution of the Mean 122
 
7.1 Simple Random Sampling 122
 
7.2 The Sampling Distribution of the Mean 123
 
7.3 Comments on the Sampling Distribution of the Mean 127
 
7.4 A Central Limit Theorem 130
 
Exercises 132
 
Appendix 7.A Using a Table of Random Numbers 133
 
Appendix 7.B Assessing Normality via the Normal Probability Plot 136
 
Appendix 7.C Randomness, Risk, and Uncertainty 139
 
7.C.1 Introduction to Randomness 139
 
7.C.2 Types of Randomness 142
 
7.C.2.1 Type I Randomness 142
 
7.C.2.2 Type II Randomness 143
 
7.C.2.3 Type III Randomness 143
 
7.C.3 Pseudo-Random Numbers 144
 
7.C.4 Chaotic Behavior 145
 
7.C.5 Risk and Uncertainty 146
 
8 Confidence Interval Estimation of m 152
 
8.1 The Error Bound on X as an Estimator of m 152
 
8.2 A Confidence Interval for the Population Mean m (s Known) 154
 
8.3 A Sample Size Requirements Formula 159
 
8.4 A Confidence Interval for the Population Mean m (s Unknown) 160
 
Exercises 165
 
Appendix 8.A A Confidence Interval for the Population Median MED

Report

"The book is addressed to courses on probability, mathematical statistics, and statistical inference at the upper-undergraduate and graduate levels. It also serves as a valuable reference for researchers and practitioners who would like to develop further insights into essential statistical tools." ( Zentralblatt Math , 1 August 2013)

"If an undergraduate student seeks a guide that will introduce the basic ideas of statistics, or a lecturer wants interesting life examples and a source of valid intuitions to improve his teaching skills, then this book is a great place to start. . . This book, with its explanations of basic intuitions, its many examples, the easy language, and a minimal requirement for mathematical training, is a good self-contained starting point to prepare one for the jump into those heavier works." ( Computing Reviews , 30 September 2013)

Product details

• Authors: M. Panik, Michael J Panik, Michael J. Panik, Michael J. (University of Hartford) Panik, MJ Panik, Panik Michael J.
• Publisher: Wiley, John and Sons Ltd
• Languages: English
• Product format: Hardback
• Released: 26.07.2012
• EAN: 9781118229408
• ISBN: 978-1-118-22940-8
• No. of pages: 400
• Subjects: Natural sciences, medicine, IT, technology > Mathematics > Probability theory, stochastic theory, mathematical statistics; Statistik, Statistics, Wahrscheinlichkeitsrechnung u. mathematische Statistik, Probability & Mathematical Statistics, Statistics for Social Sciences, Statistik in den Sozialwissenschaften, Nichtparametrische Verfahren, Nonparametric Analysis, Statistische Inferenz