13  Task Six - Interaction models

13.1 Objective:

In the previous exercise {Chapter 12}, you conducted an ANOVA

In this workshop, you will test whether two experimental factors — Light and Fertiliser — interact to affect plant biomass. You’ll use a factorial dataset and compare two models:

  • Additive model – assumes effects of Light and Fertiliser simply add together

  • Interaction model – allows the effect of one variable to depend on the other

13.2 Learning Outcomes

By completing this assignment, you will:

  • Fit factorial ANOVA models in R using lm().

  • Test for an interaction term with anova().

  • Interpret model summaries and visualise predicted means.

  • Decide when an interaction term is warranted.

13.2.1 Set up your Quarto document

  • Create a new .qmd file with a clear title, author, and date.
---
title: "My Report"
author: "Your Name"
format: pdf
execute:
  echo: false
  warning: false
  message: false

---

  • Load packages

  • Read in the dataset

  • Complete the following sections

```{r}
#| include: false

library(tidyverse)
library(here)
library(rstatix)     # simple t-tests with tidy output
library(broom)       # tidy model summaries (optional)
library(sandwich)    # robust (heteroskedasticity-consistent) variance estimators
library(lmtest)      # coeftest/coefci for robust inference
library(performance) # easy model checks

biomass <- read_csv(here("data", "biomass.csv"))

## The data

## Visualisation

## Additive model

## Interaction model

## Model predictions

## Visualise model predictions

```

13.3 The data

The dataset records biomass production (g/m²) for grassland plots treated with combinations of Fertiliser and Light.

Download and read the data

How many observations are there, and what are the three variables in the dataset?

13.4 Visualise treatment effects

Create a boxplot to explore how biomass varies with Fertiliser and Light.

What pattern do you notice? Does the combined (F+ L+) treatment appear additive or possibly interactive?

13.5 Fit an additive model

Now test whether each treatment affects biomass independently.

model_add <- lm(Biomass.m2 ~ Fert + Light, data = biomass)
summary(model_add)

Which treatments are significant predictors of biomass?

What does the intercept represent in this model?

13.6 Fit an interaction model

Add an interaction term and compare models.

model_int <- lm(Biomass.m2 ~ Fert + Light +
                  Fert:Light, # interaction term
                data = biomass)
summary(model_int)

anova(model_add, model_int)

Does the interaction term improve model fit (look at the F-test)?

What does a significant interaction mean in this context?

13.7 Visualise model predictions

  • Use emmeans

  • Plot predicted means and 95% confidence intervals

Describe what the plot shows.

Does Light increase biomass more when Fertiliser is present or absent?

13.8 Check model assumptions

check_model(model_int,
            detrend = FALSE)

Do the residuals appear normally distributed and homoscedastic?

Would you keep this model based on the diagnostics?

13.9 Summarise your findings

In 4–6 sentences, interpret your analysis:

  • Write a short results summary - it should include estimates of difference, uncertainty values, test statistics and p-values.

  • Which model (additive or interaction) fits the data better?

  • Summarise the biological conclusion in two sentences.

13.10 Rendering your Quarto doc

After completing your analysis, render your .qmd file to Pdf to produce a polished report. Check the following:

  • Code runs top to bottom – all chunks execute without errors.

  • Figures and tables appear correctly – plots are visible, captions make sense.

  • Formatting is clear – headers, text, and code chunks are readable.

  • Interpretation is included – your narrative explains results, not just code output.

    • Include a figure
    • Include a short results section (with a model write-up and correlation test)

If the document doesn’t render, check that all packages are loaded and all objects are created in previous chunks.

Check out {Chapter 20} for more help.