STAT 205

Introduction to Mathematical Statistics

Author

Affiliation

Dr. Irene Vrbik

University of British Columbia Okanagan

Welcome!

This is the official course website for STAT 205. Here, you’ll find:

• The course syllabus.
• Weekly lecture slides (see links in Table 1)
• About the instructor.

All other course material (e.g. assignments and grades) can also be accessed through Canvas. The syllabus can be found in the Syllabus tab in the Navigation bar.

Use the navigation bar above to explore the content.

Lectures

Lectures will be uploaded here. These slides were built using Quarto and includes a built in version of the reveal.js-menu plugin. You can access the navigation menu using the button located in the bottom left corner of the presentation¹. Clicking the button opens a slide navigation menu that enables you to easily jump to any slide.

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Tentative Schedule

Table 1: Tentative lecture schedule: Supplementary materials are optional and provide additional, in-depth coverage related to the slides. Practice problems are recommended but not mandatory.

Lecture: Topic	Supplementary Material	Practice Problems
Introduction [slides]	📘 Diez et al. (2016) Section 1.2, 1.3	Diez et al. (2016): Exercises: 1.1, 1.9, 1.13, 1.15, 1.17, 1.27, 1.39, 1.43
Summarizing Data [slides]	📘 Diez et al. (2016) Sections 2.1 and 2.2 (can skip special topics) 📈 R: Irene’s tutorial: R basics	Diez et al. (2016) Exercises: 2.1, 2.5, 2.11, 2.13, 2.15, 2.17, 2.27, 2.33 JB exercises3 Ch 3 Exercises: 10, 20, 21, 22, 23, 31, 32, 34, 39, 36, 37, 39, 40, 41, 45, 46, 48, 49, 50
📝 Assignment 1 (see Canvas)	📘 Wickham et al. (2023) Chapter 28 📈 R: Quarto tutorial: Hello, Quarto 📈 R:Irene’s tutorial: Quarto documents 📊 – data: cheer.csv 💡 – demo: (rendered: stat205demo.html source: stat205demo.qmd)	Wickham et al. (2023) 28.3.1: 1, 2, 3; 28.5.5: 1, 2; 28.6.3: 1, 2, 3
Sampling Distribution for the mean [slides]	📘 Ross - Ch 6 📘 Balka 4.1, 4.2, 4.3, 4.4, 4.5 🎬 What is the CLT 📘 StatKey: Sampling Distribution for a Mean	JB exercises4 Ch 7: 1, 6, 7, 8, 9, 10, 11, 12, 13, 19, 20, 21, 24, 25
Confidence Intervals for the mean (known \(\sigma\)) [slides]	📘(Balka, n.d.) Ch 5: 5.1 – 5.6 📘(Illowsky and Dean 2022) Ch 8: 8.1, 8.4 📘 (Diez et al. 2016) Ch 4.1, 4.2	JB exercises Ch 8.2 🧮 calculations: 1, 2 🧠interpretation 3, 4, 5, 6, 7 JB exercises Ch 8.5 📏 CI \(\sigma\) unknown: 20
Finite Population Correction and Choosing a Sample Size [slides]	📘 Illowsky and Dean (2022) 7.4	Illowsky and Dean (2022) Ch 7: Practice 41-48 JB exercises Ch 8.4 🧮 calculations: 14
Confidence Intervals for the mean (unknown \(\sigma\)) [slides]	🎬 JB Online 5.7 (unknown \(\sigma\) method) 🎬 JB Online 5.8 (t-distribution) 🎬 JB Online 5.8 (Finding \(p\)-value5 )	JB exercises Ch 8.3-8.5 🧮 calculations: 8, 14, 15, 16, 21 🧠 9, 10, 11, 12, 13, 18, 19, 21, 24, 25, 35 📏 CI \(\sigma\) unknown: 17, 26, 27, 29, 31, 32, 34, 42
Hypothesis Testing for one-sample mean (critical value approach) [slides]	Devore et al. (2021) 9.1, 🎬 JB Online 6.1 (Intro to Hypothesis Testing) 🎬 JB online 6.2 (Tests for One Mean) 🎬 JB online 6.8 (One-Sided Test or Two-Sided Test?) 🎬 JB online 6.9 (The Relationship Between Confidence Intervals and Hypothesis Tests)	JB exercises Ch 9:6 🛠️ concepts and setup: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 23, 26, 27, 53, 59, 60   |  | 🧪 applied: 12, 13 |
Hypothesis Testing for one-sample mean (\(p\)-value approach + t.test()) [slides]	Diez et al. (2016) Chapter 6 and 7, Balka (n.d.) Section 9.10 🎬 JB online 6.4 (Z Tests for One Mean: The p-value) 🎬 JB online 6.5 (Z Tests for One Mean: An Example) 🎬 JB online 6.6 (What is a p-value?) 🎬 JB online 6.16 (t Tests for One Mean: An Example) 🎬 JB Online 6.17 (t-tests for One Mean: Investigating the Normality Assumption) 🎬 JB Online 6.18 (Hypothesis tests on one mean: t or z?)	JB exercises Ch 8 Extra Ex: 📈 R: 36, 39 JB exercises Ch 9 🛠️ concepts and setup: 28, 29, 33, 34, 36, 37, 38, 39, 40, 52  |  | 🧪 applied: 30, 31, 32, 43, 46, 47, 56  | 📈 R: 35, 44, 62f, 63f, 64f, 67f, 71
Type I/II errors and power [slides]	🌐 StatSig 🌐 Stats By Jim	JB exercises Ch 9: 16-19, 20, 21, 22, 47, 51, 54, 55, 57, 58, Ch 10: 15
✂✂✂✂	Midterm 1 material cut off	✂✂✂✂
Inference for Proportions [slides]	Devore et al. (2021) 9.4, Diez et al. (2016) 5.3 (Illowsky and Dean 2022) 8.3, 8.5 JB statistics: Ch 8. Inference for Proportions (Ramachandran and Tsokos 2020) Ch 5.4-5.5 Khan: Sampling Distribution for proportions	Confidence Intervals: JB exercises Ch 10: 📈 R: 14, 18, 19, 30 Diez et al. (2016) Ch 6: 6.1, 6.5, 6.7, 6.9, 6.10, 6.11, 6.13, 6.15 Hypothesis Tests: 🛠️ concepts and setup:   | JB exercises Ch 11: 1, 2, 4, 5, 6  | Diez et al. (2016) Ch 6: 6.1, 6.5, 6.9, 6.13  | 🧪 applied: 7, 19, 20, 21
Chi-squared tests (contingency table analysis) [slides]	Balka (n.d.) Chapter 13, Penn Stat STAT 500 Lesson 8, Diez et al. (2016) 6.3, 6.4	JB exercises Ch 13: 1, 2, 3, 8, 11, 12, 13, 14, 17, 18, 19, 22, 23, 28
Inference for two proportions [slides]	Balka (n.d.) chapter 11.3, Diez et al. (2016) 6.2	JB exercises Ch 11: 🛠️ Concepts: 8, 9, 10, 11, 12, 13, 14, 15, 17, 18  |  | 🧪 Applied: 22, 23, 24-26  |
Inference of two means [slides] Examples: [slides]	Balka (n.d.) chapter 10, Diez et al. (2016) 7.2, 7.3	JB exercises Ch 10: 🛠️ Concepts: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 18, 19, 20, 22, 23, 24, 25   |  | 🧪 Applied: 26, 27, 28, 29, 30, 31 | | |
Analysis of Variance (ANOVA) [slides]	Lesson 10 Penn Stat 500, Chapter 14 Balka text	JB exercises Ch 14: 1, 2, 3, 5, 12, 14–23, 25–30
ANOVA post-hoc tests [slides]
✂✂✂✂	Midterm 2 material cut off	✂✂✂✂
Linear Regression [slides]
	✅ above is all adapted current material 👆
	⛔️ below is old material that will likely change 👇
Maximum Likelihood Estimation [slides]	(Ramachandran and Tsokos 2020) - Ch 5.1-5.3; Ross - Ch 6	JB exercises (solutions found here) Ch 7: 14, 15 Rice (2007) Section 8.10: 4, 5, 6, 7 (excluding part d), 16, 21, 27, 47, 50, 52, 60
	Midterm 2 Review
	Midterm 2	Practice Problems (Set 2), Suggested problems7, plus Review questions from JB exercises (solutions found here): Ch 9 62, 63, 64, 65, 66, 67 Extra Practice: Ch 9:68 - 75 Ch 10: 32-41 Ch 11: 27-33
Chi-squared tests for one variance [slides]	Balka (n.d.) 12.1 – 12.3 (Ramachandran and Tsokos 2020) 4.2

14: Type I/II errors and power

16: Contingency Table Analysis

15: Analysis of Variance (ANOVA) 17: Linear Regression and Correlation

10: Inference for difference of Two Means

11: Examples involving two-populations 5: Likelihood and Parameter Estimation

References

Balka, Jeremy. n.d. “Making Statistics Make Sense.” Accessed January 6, 2024. https://www.jbstatistics.com/.

Devore, J. L., K. N. Berk, and M. A. Carlton. 2021. Modern Mathematical Statistics with Applications. Springer Texts in Statistics. Springer International Publishing. https://books.google.ca/books?id=ghcsEAAAQBAJ.

Diez, D. M., C. D. Barr, and M. Çetinkaya-Rundel. 2016. OpenIntro Statistics. OpenIntro, Incorporated. https://books.google.ca/books?id=wfcPswEACAAJ.

Illowsky, B., and S. Dean. 2022. Introductory Statistics. Open Stax Textbooks. https://books.google.ca/books?id=-GQIzwEACAAJ.

Ramachandran, K. M., and C. P. Tsokos. 2020. Mathematical Statistics with Applications in r. Elsevier Science. https://books.google.ca/books?id=t3bLDwAAQBAJ.

Rice, J. A. 2007. Mathematical Statistics and Data Analysis. Advanced Series. Cengage Learning. https://books.google.ca/books?id=KfkYAQAAIAAJ.

Wickham, H., M. Çetinkaya-Rundel, and G. Grolemund. 2023. R for Data Science: Import, Tidy, Transform, Visualize, and Model Data. O’Reilly. https://books.google.ca/books?id=xU-gzwEACAAJ.

Footnotes

1. You can also open the navigation menu by pressing the M key.

2. Note: This feature has only been confirmed to work in Google Chrome and Chromium.

3. solutions found here

4. note that the exercise chapters don’t match up with the website.

5. we will cover \(p\)-values later, for now you can just think of \(p\)-values as generic probabilities

6. I would priorities the questions in bold

7. the listed practice problems from this column of the table for the appropriate Lectures