This book offers a modern and accessible introduction to Statistical Inference, the science of inferring key information from data. Aimed at beginning undergraduate students in mathematics, it presents the concepts underpinning frequentist statistical theory. Written in a conversational and informal style, this concise text concentrates on ideas and concepts, with key theorems stated and proved. Detailed worked examples are included and each chapter ends with a set of exercises, with full solutions given at the back of the book. Examples using R are provided throughout the book, with a brief guide to the software included. Topics covered in the book include: sampling distributions, properties of estimators, confidence intervals, hypothesis testing, ANOVA, and fitting a straight line to paired data. Based on the author’s extensive teaching experience, the material of the book has been honed by student feedback for over a decade. Assuming only some familiarity with elementary probability, this textbook has been devised for a one semester first course in statistics.
Author(s): Jonathan Gillard
Series: Springer Undergraduate Mathematics Series
Edition: 1st Edition
Publisher: Springer
Year: 2020
Language: English
Pages: 167
Tags: Statistical Theory And Methods
Aim......Page 7
Use of R......Page 8
Contents......Page 9
1.2.1 Discrete and Continuous Random Variables......Page 11
1.2.2 Probability Mass/Density Functions......Page 13
1.3 Exercises......Page 19
2.1 Introduction......Page 20
2.2 Sampling Distributions......Page 22
2.3 Key Results on the Sample Mean, Sample Variance, Sample Minimum, and Sample Maximum......Page 25
2.4.1 Normal Distribution......Page 31
2.4.2 Student's t-Distribution......Page 34
2.4.3 Chi-Squared Distribution......Page 35
2.4.4 F-Distribution......Page 37
2.5 Central Limit Theorem......Page 38
2.6 Exercises......Page 41
3.2 Bias and Variance......Page 43
3.3 Mean Square Error......Page 46
3.4 Exercises......Page 50
4.1 Introduction......Page 52
4.2 Commonly Used Confidence Intervals......Page 54
4.2.1 Confidence Intervals for Unknown Means......Page 55
4.2.2 Confidence Intervals for Unknown Variances......Page 63
4.3 Exercises......Page 67
5.1 Introduction......Page 69
5.2 Power......Page 83
5.3 Categorical Data......Page 88
5.3.1 The Chi-Square Goodness-of-Fit Test......Page 89
5.3.2 Contingency Tables for Testing Independence......Page 92
5.4 Exercises......Page 94
6.2 Notation and Setup......Page 97
6.3 Possible Sources of Variation......Page 98
6.3.2 Between-Group Sum of Squares, SSG......Page 99
6.3.3 Within-Group Sum of Squares, SSerror......Page 100
6.3.4 ANOVA Table......Page 101
6.3.5 Multiple Comparison Tests......Page 102
6.4 Exercises......Page 106
7.1 Introduction......Page 108
7.2 Least Squares Regression......Page 109
7.3 Properties of the Least Squares Estimators: Distributions......Page 113
7.3.2 Mean and Variance of......Page 114
7.3.4 Distributional Results......Page 115
7.3.5 Estimating the Error Variance σ2......Page 117
7.4 Exercises......Page 121
A.2 What R Looks Like......Page 123
A.3 Dealing with Data......Page 127
B.1 Problems of Chap. 1摥映數爠eflinkprobl11......Page 129
B.2 Problems of Chap. 2摥映數爠eflinkchap:sampling22......Page 132
B.3 Problems of Chap. 3摥映數爠eflinkchap:est33......Page 136
B.4 Problems of Chap. 4摥映數爠eflinkchap:ci44......Page 140
B.5 Problems of Chap. 5摥映數爠eflinkchap:ht55......Page 142
B.6 Problems of Chap. 6摥映數爠eflinkchap:ANOVA66......Page 146
B.7 Problems of Chap. 7摥映數爠eflinkchap:reg77......Page 149
C.1 The Normal Distribution Function......Page 151
C.3 Percentage Points of the Chi-Squared Distribution......Page 154
C.4 Percentage Points of the Student's t-Distribution......Page 156
C.5 Percentage Points of the F-Distribution......Page 157
Index......Page 166
