A First Course in Statistical Inference

1. Front Matter

   Pages i-x

   PDF

2. Recap of Probability Fundamentals

   • Jonathan Gillard

   Pages 1-9

3. Sampling and Sampling Distributions

   • Jonathan Gillard

   Pages 11-33

4. Toward Estimation

   • Jonathan Gillard

   Pages 35-43

5. Confidence Intervals

   • Jonathan Gillard

   Pages 45-61

6. Hypothesis Testing

   • Jonathan Gillard

   Pages 63-90

7. One-Way Analysis of Variance (ANOVA)

   • Jonathan Gillard

   Pages 91-101

8. Regression: Fitting a Straight Line

   • Jonathan Gillard

   Pages 103-117

9. Back Matter

   Pages 119-164

   PDF

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.

• Statistical inference
• confidence interval
• hypothesis testing
• distribution theory
• data science
• R

• School of Mathematics, Cardiff University, Cardiff, UK

  Jonathan Gillard

Dr Jonathan Gillard is a Reader in Statistics at Cardiff University, Senior Fellow of the Higher Education Academy, and a member of the Statistics Interest Group of sigma: the UK network for excellence in mathematics and statistics support. He has taught statistical inference to mathematics undergraduates and postgraduates for over 10 years. Jonathan maintains a strong interest in innovative teaching methods, being an editorial board member of MSOR Connections. He is an active researcher of the theory of statistics and is currently working on a number of collaborative projects with the Office for National Statistics and National Health Service. His recent publications have included work on using regression in large dimensions, novel methods for forecasting, and new approaches for learning about the performance of machine learning algorithms.

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