Lecture notes. Written from the material of GTPB Psls20, licensed CC BY 4.0. These are notes, not a transcript: the material has been reorganised and rewritten. This adaptation carries the same licence, and the original is linked above.

19. ANOVA on the Lettuce Dataset

What this covers

This chapter works through a single applied exercise: testing, with a one-way ANOVA, whether soil treatment affects the growth of lettuce plants in a fertiliser trial. It assumes the reader already knows what a one-way ANOVA tests — whether the mean of a continuous outcome differs across more than two groups defined by one categorical factor — since the source is a hands-on tutorial script, not a theory lecture. The chapter follows the tutorial as far as it goes: setting up the applied question, loading and preparing the data, and laying out the steps of the analysis. It stops where the tutorial itself stops, at the point where the student is asked to do the modelling, the assumption checks and the test.

The fertiliser trial

Higher crop yield is a persistent goal in agriculture, and for lettuce, plants with more leaves — or, more precisely, a higher total leaf weight — are what growers and consumers want. One route to that is fertiliser, and there is a growing preference for natural fertilisers such as compost over synthetic ones. Near Ghent, an agricultural and fisheries research institute has been testing a newer natural fertiliser called biochar: a residual product of pyrolysis, the process of burning biomass under controlled conditions (such as high pressure) to produce energy. Biochar behaves similarly to charcoal but has some useful extra properties — it helps soil retain water, and it has a positive effect on the soil microbiome.

The researchers wanted to know whether biochar, compost, or a combination of the two changes how lettuce plants grow, relative to untreated soil. They grew lettuce in a greenhouse in pots filled with one of four soil treatments:

1. soil only (control)
2. soil supplemented with biochar (labelled refoak in the data)
3. soil supplemented with compost (compost)
4. soil supplemented with both biochar and compost (cobc)

The response variable is freshweight, in grams, recorded for 28 lettuce plants — 7 under each of the four treatments, so the design is balanced. Because there are four groups rather than two, the natural first test is an omnibus one-way ANOVA: does treatment have any effect at all, before asking which specific treatments differ. If the ANOVA says yes, the plan is to follow it with a post-hoc test (Tukey's test) to work out which pairs of treatments are actually different from each other.

Loading and preparing the data

The tutorial's own code loads the data straight from the course's dataset repository and does two small but necessary pieces of housekeeping before any modelling can happen.

library(tidyverse)

lettuce <- read_csv("https://raw.githubusercontent.com/GTPB/PSLS20/master/data/freshweight_lettuce.txt")

glimpse(lettuce)

glimpse is there to check that the import worked as expected — the right number of rows and columns, and each column read as a sensible type. That check matters here in particular because treatment is a categorical grouping variable, and read_csv has no way of knowing that: left alone, it will read the treatment labels as plain character strings. R's modelling functions need the grouping variable encoded as a factor to treat the four labels as group levels rather than as arbitrary text, so the tutorial converts it explicitly:

lettuce <- lettuce %>%
  mutate(treatment = as.factor(treatment))

With that done, a quick tally checks that the design really is balanced as described:

lettuce %>%
  count(treatment)

This should return seven plants per treatment; if it does not, that is a sign either the import went wrong or the trial was not run as described, and either way it changes how the later ANOVA should be interpreted — an unbalanced design is more sensitive to violations of the equal-variance assumption than a balanced one.

Before modelling: look at the data

Before fitting anything, the tutorial asks for a plot of freshweight by treatment — boxplots are the natural choice for a continuous outcome split by a categorical group — and for that plot to be interpreted before moving on. That step is worth taking seriously rather than skipping past: a boxplot gives an informal first look at whether the group medians look different, how much the groups overlap, and whether the spread of freshweight looks roughly similar across the four treatments — a rough, visual preview of the homogeneity-of-variance assumption that the formal ANOVA will need checked properly before its result can be trusted.

Exercises

Using lettuce as prepared above (freshweight in grams for 28 lettuce plants, 7 per treatment: control, biochar, compost, and biochar-plus-compost):

1. Make a plot of freshweight against treatment and interpret it: do the groups look different, and does the spread of freshweight look similar across treatments?
2. Decide how to model these data — what statistical model fits this design of one continuous response and one categorical factor with four levels?
3. Translate the research question ("does soil treatment change lettuce growth?") into a statement about the parameters of that model.
4. Check whatever assumptions the model chosen in (2) requires before it can be trusted.
5. If those assumptions are satisfied, fit the model.
6. If the model shows an overall treatment effect, follow up with a post-hoc test (Tukey's test) to work out which specific treatments differ from each other.

Sources

• Notes: ANOVA_lettuce_plants_half.md, the tutorial exercise script "Tutorial 7.1: ANOVA in the lettuce dataset" from GTPB "Practical Statistics for the Life Sciences" (2020) — source, CC BY 4.0. All of the applied motivation, the data-loading code, and the numbered task list above come from this script.
• No slide deck and no lecture transcript were supplied for this chapter.
• The dataset file itself, freshweight_lettuce.txt, is referenced and loaded by URL in the script but was not included in the supplied material, so no actual results, plots, model fit, or test outcome appear in this chapter — the source is a "half" version of the tutorial, meant to be completed by the student, and the chapter follows it exactly that far.

---

← 18. One-Way ANOVA on Cuckoo Eggs · Contents · 20. ANOVA on the NHANES Dataset →