Hypothesis testing to correlation
This worksheet will help you practice the key ideas behind hypothesis testing — including the null hypothesis, p-values, test selection, and interpretation — using real data and R code.
You’ll apply tests to different types of data (continuous and categorical), interpret p-values, and connect statistical decisions with biological questions.
BIOL65161 students
Please upload your saved .R script to Canvas before 5PM on the day of the practical.
In your own words, what does the null hypothesis (H₀) represent?
Suppose you’re testing whether a new antibiotic reduces bacterial growth compared with a control.
Write out suitable null (H₀) and alternative (H₁) hypotheses.
We’ll use simulated data to explore how p-values behave.
library(tidyverse)
# Simulate bacterial growth under control vs antibiotic
set.seed(42)
growth <- tibble(
treatment = rep(c("Control", "Antibiotic"), each = 15),
OD600 = c(rnorm(15, mean = 0.8, sd = 0.05),
rnorm(15, mean = 0.7, sd = 0.05))
)
growth |> head()# A tibble: 6 × 2
treatment OD600
<chr> <dbl>
1 Control 0.869
2 Control 0.772
3 Control 0.818
4 Control 0.832
5 Control 0.820
6 Control 0.795Make a boxplot showing mean growth (OD600) by treatment group.
Use a t-test to test whether the mean growth differs between treatments.
If the p-value is 0.012, what does that mean in context?
We might instead ask whether the antibiotic specifically reduces growth.
Re-run the t-test using a one-tailed test (hint: use alternative = "less").
Now suppose we have counts of resistant and sensitive isolates from two species.
microbiology <- tibble(
Species = c(rep("E. coli", 100), rep("P. aeruginosa", 100)),
Resistance = c(rep(c("Resistant", "Sensitive"), times = c(45, 55)),
rep(c("Resistant", "Sensitive"), times = c(70, 30)))
)
table(microbiology) Resistance
Species Resistant Sensitive
E. coli 45 55
P. aeruginosa 70 30Use table() to summarise the counts by Species and Resistance.
Run a χ² test to check if resistance is associated with species.
Run a Fisher’s exact test on the same data. Does the outcome differ? When should you use Fisher’s exact test?
We’ll now explore relationships between two continuous variables using the Palmer Penguins dataset.
install.packages("palmerpenguins") # If not already installed
library(palmerpenguins)
penguins |> glimpse()Rows: 344
Columns: 8
$ species <fct> Adelie, Adelie, Adelie, Adelie, Adelie, Adelie, Adel…
$ island <fct> Torgersen, Torgersen, Torgersen, Torgersen, Torgerse…
$ bill_length_mm <dbl> 39.1, 39.5, 40.3, NA, 36.7, 39.3, 38.9, 39.2, 34.1, …
$ bill_depth_mm <dbl> 18.7, 17.4, 18.0, NA, 19.3, 20.6, 17.8, 19.6, 18.1, …
$ flipper_length_mm <int> 181, 186, 195, NA, 193, 190, 181, 195, 193, 190, 186…
$ body_mass_g <int> 3750, 3800, 3250, NA, 3450, 3650, 3625, 4675, 3475, …
$ sex <fct> male, female, female, NA, female, male, female, male…
$ year <int> 2007, 2007, 2007, 2007, 2007, 2007, 2007, 2007, 2007…Make a scatter plot of bill_length_mm vs flipper_length_mm coloured by species using ggplot() and geom_point()
Use cor() to find the correlation between bill length and flipper length for Adélie penguins only.
Use cor.test() to determine if the correlation is statistically significant.
What does it mean if a result is statistically significant but not biologically meaningful?
Why do we say we “fail to reject” H₀ instead of “accepting” it?
Why is correlation not the same thing as causation?
When might a one-tailed test be more appropriate than a two-tailed test?
What kind of data are suitable for a t-test compared with a chi-squared test?
What does a p-value actually represent in hypothesis testing?
Why should we check assumptions (like normality or independence) before running a test?
What kind of biological question would be best addressed using a correlation analysis?