ENVX2001 Applied Statistical Methods
Lecturer, SOLES
Apr 2026
In a partially migratory elk population in Alberta, Canada, researchers compared calf birth weights between resident and migrant herds.
elk <- read.csv("data/elk_calf_clean.csv")
elk$mig_status <- factor(elk$mig_status,
levels = c("Resident", "Eastern"),
labels = c("Resident", "Migrant")
)
ggplot(elk, aes(x = mig_status, y = birth_wt, fill = mig_status)) +
geom_boxplot(show.legend = FALSE) +
scale_fill_viridis_d(end = 0.9) +
labs(x = NULL, y = "Birth weight (kg)") +
theme_minimal(base_size = 18)You have already learnt to compare groups like this with t-tests (Weeks 1–3).
Eighteen pet dogs were exposed to odours from humans who were either relaxed or stressed. Researchers then measured how long each dog took to approach food bowls.
dogs <- read.csv("data/dog_odour_clean.csv")
dogs$treatment <- factor(dogs$treatment,
levels = c("Baseline", "Relaxed", "Stressed")
)
dog_means <- aggregate(latency ~ dog_id + treatment, data = dogs, FUN = mean)
ggplot(dog_means, aes(x = treatment, y = latency, fill = treatment)) +
geom_violin(alpha = 0.6) +
scale_fill_viridis_d(end = 0.9) +
labs(x = "Odour treatment", y = "Mean latency (s)") +
theme_minimal(base_size = 18) +
theme(legend.position = "none")What if there are more than 2 groups to compare? We use Analysis of Variances (ANOVA) (Weeks 3–6).
Heavier penguins tend to have longer flippers – but how strong is that relationship?
penguins <- palmerpenguins::penguins
ggplot(penguins, aes(x = flipper_length_mm, y = body_mass_g)) +
geom_point(aes(colour = species), alpha = 0.6) +
geom_smooth(method = "lm", se = FALSE, colour = "#e64626", aes(linetype = "Linear")) +
geom_smooth(method = "lm", formula = y ~ poly(x, 2), se = FALSE, colour = "#8f9ec9", aes(linetype = "Quadratic")) +
scale_colour_viridis_d(end = 0.9) +
scale_linetype_manual(values = c(Linear = "solid", Quadratic = "solid")) +
guides(linetype = guide_legend(override.aes = list(colour = c("#e64626", "#8f9ec9")))) +
labs(x = "Flipper length (mm)", y = "Body mass (g)", linetype = "Model") +
theme_minimal(base_size = 18)We can model this relationship with regression, but how do we validate this against other models? You will learn to do this with model selection (Weeks 7–9).
Researchers at Lake MacBride, Iowa trapped three hawk species over a decade and measured wing length, weight, culmen, and hallux on each bird.
hawks <- read.csv("data/hawks_clean.csv")
pca <- prcomp(hawks[, c("Wing", "Weight", "Culmen", "Hallux")], scale. = TRUE)
scores <- data.frame(pca$x, Species = hawks$Species)
ggplot(scores, aes(x = PC1, y = PC2, colour = Species)) +
geom_point(alpha = 0.5) +
stat_ellipse(linewidth = 1) +
scale_colour_viridis_d(end = 0.9) +
labs(x = "PC1", y = "PC2", colour = "Species") +
theme_minimal(base_size = 18)We can represent multivariate data in fewer dimensions using multivariate methods (Weeks 10–12).
Wednesdays 10am - 12pm, Chemistry Lecture Theatre 3 (CLT03)
Copyright The University of Sydney
Labs are held at the South Eveleigh Precinct
Credit: Michael Wheatland
