Week 9 Overview
| Dates | 17 March 2025 - 21 MAR 2025 |
| Reading | Required: SCIU4T4 Workbook chapters 28 and 29 |
| Recommended: Navarro and Foxcroft (2022) (Chapter 12.1 and 12.2) | |
| Suggested: Rowntree (2018) (Chapter 8) | |
| Advanced: Rodgers and Nicewander (1988) (Download) | |
| Lectures | 9.1: Frequency and count data (13:19 min; Video) |
| 9.2: Chi-squared goodness of fit test (16:34 min; Video) | |
| 9.3: Chi-squared test of association (16:03 min; Video) | |
| 9.4: Correlation key concepts (7:02 min; Video) | |
| 9.5: Correlation underlying mathematics (12:06 min; Video) | |
| 9.6: Correlation hypothesis testing (27:28 min; Video) | |
| Lecture | Lecture: 19 MAR 2025 (WED) 09:00-10:00 Cottrell LT B4 |
| Practical | Analysis of counts and correlations (Chapter 31) |
| Room: Cottrell 2A15 | |
| Group A: 19 MAR 2025 (WED) 10:00-13:00 | |
| Group B: 20 MAR 2025 (THU) 15:00-18:00 | |
| Help hours | Martina Quaggiotto and Brad Duthie |
| Room: Cottrell 2Y8 | |
| 21 MAR 2025 (FRI) 14:00-16:00 | |
| Assessments | Week 9 Practice quiz on Canvas |
Week 9 introduces count data and correlations, and how to interpret scatterplots.
Chapter 29 focuses on count data. Count data are defined by natural numbers of discrete entities (e.g., the number of trees or birds in a site). We can test statistical hypotheses on count data using a Chi-square (chi-square) distribution, which is introduced in the first part of the chapter. Like the t-distribution and F-distribution, the Chi-square distribution also appears in many places in statistics. In this chapter, applications of the Chi-squared distribution are the Chi-squared goodness of fit test, which tests if observed counts are significant different from some expectation, and the Chi-square test of association, which tests if counts of two different categories are associated. A simple example with real numbers introduces the Chi-square, followed by goodness of fit tests and tests of association using player decision-making data originally introduced in Chapter 17.
Chapter 30 focuses on continuous data. Continuous data can take any real value (e.g., body length or mass). Association between two continuous variables can be calculated as a correlation. This chapter introduces correlation, how it can be visualised using a scatterplot and defined mathematically as the correlation coefficient. Two different correlation coefficients are introduced, then a test is introduced to reject or not reject the null hypothesis that two variables are uncorrelated. This test of the correlation coefficient relies on the t-distribution, which was introduced in Chapter 19. Example data for this chapter include morphological measurements from two species of non-pollinating fig wasps. From these data, the chapter demonstraates how to calculate the Pearson product-moment correlation coefficient and the Spearman’s rank correlation coefficient. Jamovi output for a correlation matrix is shown with an explanation of how to correctly interpret it.
Chapter 31 demonstrates how to use jamovi to run and correctly interpret output for the Chi-square tests introduced in Chapter 29 and correlation tests introduced in Chapter 30. It includes six exercises, which focus on the Chi-square goodness of fit, the Chi-square test of association, and tests of the correlation coefficient. Exercises use a dataset that is inspired by experimental work testing the effects of radiation on bumblebee traits. The first exercise works through a very simple goodness of fit test by hand, demonstrating the calculations needed to obtain a Chi-square test statistic. Jamovi is then used to recreate the hand calculations, and this is followed by another goodness of fit exercise and a test of association between bumblebee colony and survival. How to make scatterplots is then illustrated in jamovi using bumblebee mass and carbon dioxide output. Exercises then demonstrate out to calculate Pearson product moment correlation coefficients and Spearman rank correlation coefficients in jamovi. The chapter ends with an example of how to run a goodness of fit test in a simplified way with data that are not in a tidy format.