Compare Several Means with ANOVA

Fit the model, check residual spread, then use Tukey’s HSD to see which groups differ

Everything on this page runs real R in your browser. You will practice Coding Assignment 4, Part C: one-way ANOVA with assumption checks and Tukey’s HSD post-hoc comparisons.

Assignment vs this activity

On DataHub, Assignment 4 uses BrittlebushNitrogen.csv with four nitrogen levels and biomass_g. Here we ask whether bill depth differs across the three penguin species. The workflow — aov(), residual plot, fligner.test(), TukeyHSD() — is the same.

ANOVA in one sentence

One-way ANOVA tests whether any group mean differs when you have one categorical factor with more than two levels and a continuous response. If the overall F-test is significant, use Tukey’s HSD (not a pile of uncorrected t-tests) to see which pairs differ.

With several groups, fit the model first, then check residuals — faceted histograms show each level; plot(model, which = 1) shows residual spread.

Research question: Does mean bill depth differ across Adelie, Chinstrap, and Gentoo penguins?

1. Load packages

2. Build the analysis table

Keep every penguin with non-missing bill_depth_mm — use filter(!is.na(bill_depth_mm)). Save as penguin_data.

3. Boxplot by species

Make a boxplot of bill_depth_mm by species. Save as box_species and display it.

Solution

box_species <- ggplot(penguin_data, aes(x = species, y = bill_depth_mm)) +
  geom_boxplot()
box_species

Gentoo bills look shallower than Adelie and Chinstrap — but is that difference significant?

4. Faceted histograms

Build a histogram of bill_depth_mm faceted by species so you can judge shape within each level (as in lecture A009’s facet_wrap(~ feed)). Save as hist_species and display it.

Hint

Add geom_histogram(), then facet_wrap(~ species) so each species gets its own panel.

Example:

ggplot(penguins, aes(x = bill_length_mm)) +
  geom_histogram() +
  facet_wrap(~ species)

Solution

hist_species <- ggplot(penguin_data, aes(x = bill_depth_mm)) +
  geom_histogram() +
  facet_wrap(~ species)
hist_species

Each species gets its own panel — easier to spot skew or outliers per group.

5. Fit one-way ANOVA

Fit aov(bill_depth_mm ~ species, data = penguin_data). Save as anova_model and print summary(anova_model).

6. Residuals vs fitted

Use plot(anova_model, which = 1) to display the residuals-versus-fitted plot. Use only which = 1 — do not interpret the normal Q–Q panel.

7. Fligner test for equal variance

Test homogeneity of variance across species with fligner.test(). Save as fligner_anova and print it.

8. Assumptions reasonably met?

Assign anova_assumptions_ok <- TRUE if the residual plot and Fligner test look acceptable.

9. Tukey’s HSD

Run TukeyHSD(anova_model). Save as tukey_result and print it.

10. Interpret Tukey contrasts

Which pair is not significantly different? Assign adelie_chinstrap_same <- TRUE if Adelie and Chinstrap bill depths do not differ after Tukey correction.

Solution

adelie_chinstrap_same <- TRUE
gentoo_shallower <- TRUE

Overall ANOVA was significant, but only Gentoo stands apart in bill depth — Adelie and Chinstrap are statistically similar.

11. Recap — functions you practiced

What does each function do?

Function	Role
`ggplot()` + `geom_boxplot()`	Compare a continuous response across factor levels
`geom_histogram()` + `facet_wrap(~ species)`	One distribution panel per level
`aov(y ~ x, data = ...)`	Fit one-way ANOVA
`summary(anova_model)`	Overall F-test — do any means differ?
`plot(model, which = 1)`	Residuals vs fitted — check spread
`fligner.test(y ~ x, data = ...)`	Test homogeneity of variances
`TukeyHSD(model)`	Pairwise comparisons with family-wise error control

If you can explain each row, you have covered Coding Assignment 4, Part C.

Keep playing

Try ANOVA on body_mass_g ~ species instead. Run fligner.test(body_mass_g ~ species, data = penguin_data) — does equal variance hold?

Fligner p ≈ 0.01 for body mass — variances differ across species. That is why this activity uses bill depth, where Fligner passes. Choosing a response where assumptions hold makes interpretation cleaner.