07_1_lettuce.Rmd

---
title: "Exercise 7.1: ANOVA on the lettuce dataset"
author: "Lieven Clement and Jeroen Gilis"
date: "statOmics, Ghent University (https://statomics.github.io)"
---

# Background

In agriculture, it is important to have a high yield of crops. For lettuce
plants, plants with many leaves are known to be preferred by the consumers.

One way to increase the number of leaves (or better, total
leaf weight) is by using a fertilizer. Recently, there has been
a tendency to rely more on natural fertilizers, such as compost.
Near Ghent, the institute of research for agriculture and fishery is testing
new, natural fertilization methods. One of these new fertilizers is called
biochar. Biochar is a residual product from pyrolysis, a process in which
biomass is burned under specific conditions (such as high pressure) in order
to produce energy. Biochar is similar to charcoal, but has some very useful
properties, such as retaining water in the soil. It also has a positive
influence on the soil microbiome.

# The lettuce dataset

The researchers hypothesize that biochar, compost and
a combination of both biochar and compost can have a different influence
on the growth of lettuce plants. To this end, they grew up
lettuce plants in a greenhouse. The pots were filled with
one of four soil types;

1. Soil only (control)
2. Soil supplemented with biochar (refoak)
3. Soil supplemented with compost (compost)
4. Soil supplemented with both biochar and compost (cobc)

The dataset `freshweight_lettuce.txt` contains the freshweight
(in grams) for 28 lettuce plants (7 per condition). The researchers
want to use an ANOVA test to assess if the treatments have a different effect
on the growth of lettuce plants. If so, they will use a post-hoc test
(Tuckey test) to discover which specific treatments have an effect.

Load the required libraries

```{r, message = FALSE, warning=FALSE}
library(tidyverse)
library(multcomp)
```

# Data import

```{r}
lettuce <- read_csv("https://raw.githubusercontent.com/statOmics/PSLSData/main/freshweight_lettuce.txt")
```

Take a glimpse at the data

```{r}
glimpse(lettuce)
```

```{r}
## treatment to factor
lettuce <- lettuce %>%
  mutate(treatment = as.factor(treatment))
```

# Data exploration

```{r}
## Count the number of observations per treatment
lettuce %>%
  count(treatment)
```

Make plots to explore the data
```{r}
# ...
```

Interpret the boxplots!

# Questions and assignments

1. How will you model the data.
2. Translate the research question into parameters of the model.
3. Check the assumptions.
4. If the assumptions are fulfilled you can fit model
5. Further assess differences between the treatments in a post-hoc analysis
if applicable.
6. Question: can we extrapolate these results to another leaf vegetable,
for instance, spinache?
7. Question: Imaagine that all of the control and refoak plants were grown in 1
greenhouse and the other two conditions were grown in another greenhouse? How
would this affect the model assumptions of linear ANOVA?