Week 4 Overview
| Dates | 10 February 2025 - 14 February 2025 |
| Reading | Required: SCIU4T4 Workbook chapters 14 and 15 |
| Recommended: Navarro and Foxcroft (2022) Chapter 7 | |
| Suggested: Rowntree (2018) Chapter 4 | |
| Advanced: None | |
| Lectures | 4.1: What is probability? (16:07 min; Video) |
| 4.2: Adding and multiplying probabilities (16:18 min; Video) | |
| 4.3: Probability distributions (15:30 min; Video) | |
| 4.4: The normal distribution (15:15 min; Video) | |
| 4.5: z-scores (5:12 min; Video) | |
| 4.6: Examples using z-scores (13:22 min; Video) | |
| 4.7: More examples using z-scores (9:52 min; Video) | |
| 4.8: The binomial distribution (16:34 min; Video) | |
| 4.9: The Poisson distribution (12:57 min; Video) | |
| 4.10: The central limit theorem (5:21 min; Video) | |
| 4.11: z-score tables (14:32 min; Video) | |
| Lecture | Lecture: 12 FEB 2025 (WED) 09:00-10:00 Cottrell LT B4 |
| Practical | Probability and simulation (Chapter 17) |
| Room: Cottrell 2A15 | |
| Group A: 12 FEB 2025 (WED) 10:00-13:00 | |
| Group B: 13 FEB 2025 (THU) 15:00-18:00 | |
| Help hours | Brad Duthie |
| Room: Cottrell 2Y8 | |
| 14 FEB 2025 (FRI) 14:00-16:00 | |
| Assessments | Week 4 Practice quiz on Canvas |
Week 4 focuses on probability and the central limit theorem.
Chapter 15 introduces probability models and how to interpret them. The chapter also provides some examples of probability distributions that are especially relevant to biological and environmental sciences. It leads with an instructive example of coin flipping to explain the concept of independent trials and when to multiply versus add probabilities. Notation for expressing probabilities is introduced. From the simple coin flipping example, biological applications are provided to illustrate how probability is applied in science. Sampling with versus without replacement is then explained using playing cards. Lastly, probability distributions are introduced. These probability distributions include the binomial distribution, the Poisson distribution, the uniform distribution, and the normal distribution. Figures are used to show the shapes of each distribution, and the parameter values for each are introduced. The section clarifies the discrete distributions described by a probability mass function (binomial and Poisson) versus the continuous distributions described by a probability density function (uniform and normal).
Chapter 16 the introduces the central limit theorem (CLT). It focuses on what the CLT is and why it is so important in statistics. As with most topics in this book, the goal here is conceptual understanding. The key idea is that the distribution of sample means is always expected to be normally distributed, and this chapter demonstrates this principle using the distributions introduced in Chapter 15. For the binomial, Poisson, and uniform distributions, data are simulated and the distribution of means from multiple sets simulated data are presented side-by-side the distribution to demonstrate the CLT. Chapter 16 also introduces standard normal deviates (z-scores) and how they relate to probability. It explains how total probability under the curve of a normal distribution equals 1, and that variables can be standardised to a standard normal distribution by subtracting the mean of the distribution and dividing by the standard deviation.
Chapter 17 guides the reader through applying the ideas from Chapter 15 and Chapter 16 in jamovi to predict probabilities from a real dataset. This chapter includes 3 exercises, which focus on calculating probabilities from a dataset and the normal distribution, and demonstrating the CLT with simulated data. It also introduces modules in jamovi, and how they can be downloaded and used. Jamovi modules include the distrACTION and Rj Editor modules. The first two exercises in this chapter use a hypothetical dataset collected from a mobile game about decision-making in sustainable development. This dataset includes game player decisions on dam construction and subsequent development on the game landscape, and the scores of players at the end of the game. Probabilities of different player decisions are inferred from the data, and probabilities of player scores are predicted from a normal distribution using the distrACTION module. In the final exercise, some code is used in the Rj Editor to simulate data and illustrate the central limit theorem.