Week 5 Overview
| Dates | 17 February 2025 - 21 February 2025 |
| Reading | Required: SCIU4T4 Workbook chapters 17 and 18 |
| Recommended: None | |
| Suggested: Fedor-Freybergh and Mikulecký (2006) (Download) | |
| Advanced: None | |
| Lectures | 5.1: Some background for confidence intervals (6:36 min; Video) |
| 5.2: Recap of z-scores (10:47 min; Video) | |
| 5.3: Confidence interval for the population mean (14:08 min Video) | |
| 5.4: The t-interval (10:24 min; Video) | |
| 5.5: Confidence interval for the population proportion (6:37 min; Video) | |
| Lecture | Test Review: 19 FEB 2025 (WED) 09:00-10:00 Cottrell LT B4 |
| Practical | z- and t- intervals (Chapter 20) |
| Room: Cottrell 2A15 | |
| Group A: 19 FEB 2025 (WED) 14:00-17:00 | |
| Group B: 20 FEB 2025 (THU) 15:05-18:00 | |
| Help hours | Brad Duthie |
| Room: Cottrell 2Y8 | |
| 21 FEB 2025 (FRI) 14:00-16:00 | |
| Assessments | Week 5 Practice quiz on Canvas |
| Test 1F on Canvas (19 FEB 2025 at 11:00-13:00) |
Week 5 focuses making statistical inferences using confidence intervals (CIs) and and introduces the t-interval.
Chapter 18 introduces what confidence intervals are and how to calculate them for normally and binomially distributed variables. Understanding CIs builds on the concepts from Chapters 9-16, especially the standard error introduced in Chapter 12 and z-scores introduced in Chapter 16. Calculating CIs also requires an understanding of mathematical order of operations, which were first introduced in Chapter 1. Chapter 18 first explains what CIs are in general terms, with an example of resampling from a population. It then presents equations for calculating CIs for a normally distributed variable, then for binomial confidence intervals. The Wald interval is introduced as a way to calculate binomial confidence intervals, but its deficiencies are then pointed out in favour of the Clopper-Pearson CIs that jamovi uses.
Chapter 19 introduces the t-distribution and explains why this interval is usually necessary for calculating confidence intervals. The t-distribution makes it possible to adjust confidence intervals appropriately given a small sample size. The t-distribution also appears in multiple hypothesis tests that are introduced later in this book, most obviously the t-test, but also regression. An example from Chapter 17 is re-used to illustrate how confidence intervals change when using a normal distribution versus a t-distribution with the correct degrees of freedom, and the shape of how the t-distribution changes given different degrees of freedom is illustrated.
Chapter 20 guides the reader through how to calculate confidence intervals in jamovi. This chapter includes five exercises, all of which involve calculating confidence intervals. In addition to working through how to calculate confidence intervals in jamovi, this chapter includes an exercise that shows the importance of the t-distribution for small sample size. Exercises use a hypothetical dataset inspired by the Woodland Creation and Ecological Networks (WrEN) project. Data include measurements of tree diameters at breast height across different sites. The distrACTION module is used to find appropriate z-scores and t-scores for confidence intervals in a continuous distribution, and confidence intervals created with the two intervals are compared across different sample sizes. Two exercises focus on proportional confidence intervals, first using the Wald intervals calculated by hand, then using jamovi to calculated Clopper-Pearson confidence intervals with a comparison between the two methods.