MBiol2 2025 TT: Nature Recovery in the UK

Lecturer: Dr Tin Hang (Henry) Hung 洪天恒 [email protected] Fulford Fellow in Biology, Somerville College Lecturer in Biology, St Hilda’s College

<aside> ❗ Make sure you have downloaded and installed R (and R Studio) in your laptop.

</aside>

Before the session

• [ ] These are the R libraries we need to use today. Load these libraries into your R session.

library(tidyverse)
library(ggplot2)
library(lme4)
library(car)

• [ ] If you have not, you can install them by install.packages(”library_name”), such as install.packages("tidyverse").

Analysis of variance (ANOVA)

⌛ 15 min

• $H_0$: Population means $\mu_i$ are the same for all groups
• $H_1$: Population means $\mu_i$ are not the same for all groups (at least one is different from the others)
• Even $H_0$ is true, sample means $\bar Y_i$ still differ from each other solely because of sampling error
  • Taking a random sample from each population is equivalent to taking the same number of samples from a single population
• If $H_0$ is not true, variation in sample means attributable to chance still exists, but there is an additional component caused by real variation among population means

Partitioning the sum of squares

$$ Y_{ij}-\bar Y=(Y_{ij}-\bar Y_i)+(\bar Y_i-\bar Y) $$