Assignment 02 [50 marks in total]
For this assignment you will be designing & running an experiment as well as collecting & analyzing your own tomato growth data. Don’t worry I’m not expecting you to carry out an IRL (in real life) experiment to grow real tomatoes; rather you will be doing this virtually using an online environment I created (see below for a screen shot from Farm Rescue The Tomato Trials)!
To run your experiment head to Farm Rescue The Tomato Trials Notes:
• I strongly encourage you to write your assignment using RMarkdown. This ensures that your code is reproducible and that your text will be seamlessly integrated. Knit your work to either a PDF or HTML document.
• Include all relevant code and output in the final document. Please do not include any irrelevant or overly verbose output that has not been requested (e.g., DO NOT print out your raw data in full); this makes it difficult to find and therefore award the relevant components!
• Please keep your code tidy and your plots neat and professional. For example, it’s very useful for the reader if you use informative, readable axis labels rather than allowing the default behaviour of printing the R object name.
Question 01 [12 marks]
Design and run an experiment using the Farm Rescue The Tomato Trials ( this and Q2 both assume a single run of the experiment).
This assignment is designed to give you the freedom to conduct your own virtual experiment; there is no restriction on what tomato variety you use, or how you set/choose/apply treatment variables. The key thing is that your experiment is valid and is designed in such a way as to reliably answer your chosen hypothesis. You should justify your choices at each step.
Write up your experimental design strategy justifying your choices and including appropriate levels of detail such that your experiment is reproducible.
You should
1. clearly state the goal(s)/objective(s) of the experiment,
2. clearly state the hypothesis,
3. specify what will be measured as well as the experimental units and observational units,
4. list treatment variables as well as any potential sources of nuisance variation,
5. outline the experimental procedure clearly, including how you abided by the principles of experimental design, and
6. discuss any limitations your experiment may have/has.
Any code used to create your design (e.g., from the R package edibble or similar) should be included in your write-up and be fully reproducible.
There is no specific template you need to follow for this question. However, you should take care that your design is clear and that your justification/choices are easy to follow. All justifications should be relevant and specific to your experiment. Note that you should aim for concise & detailed writing rather than overly verbose text, which can be difficult to follow. TLDR keep things clear and as consice as possible.
Question 02 [13 marks]
Using your data from Q1 ( again, this question assumes a single run of the experiment)
1. Perform a pairwise comparisons of means for your treatment(s) using Fisher’s LSD with α = 0.05 level of significance,
2. Summarise and present these results in a table with the following column names Comparison, Calculated difference (in means), SED (standard error of the difference), LSDs, Lower 95% CI & Upper 95% CI (lower & upper 95% confidence interval), t-statistic, P-value, and
3. Calculate the scale factor (i.e., critical value of the assumed distribution) using
a. Bonferroni’s correction method and
b. Tukey’s HSD method
for all pairwise comparison 95% CI from 2. Discuss what effect the multipliers might have on inference and produce a plot that compares the three multiple comparisons methods above.
Question 03 [20 marks]
Model your data from Q1 and report your findings ( again, this question assumes a single run of the experiment).
You may want to consider one or more of the following
• the distribution of your response variable,
• if you employed a blocking technique in your design form Q1, how might this be appropriately be accounted for in your model,
• whether a transformation of a variable may be appropriate,
• which variables might be considered fixed effects or random effects, and/or
• whether a linear relationship between these effects and your expected value is appropriate.
Any relevant model fitting code should be included in your answer to this question, you may assume prior knowledge of the data structure obtained from Q1. When reporting on your chosen model(s) you should write out the fitted model(s) in full and interpret any coefficients. In addition, you should create an informative plot of your fitted model(s). You should also discuss any limitations of your chosen models(s) and employ appropriate model diagnostic techniques. If you choose to compare two or more competing models then you should make sure to report on each and use an appropriate model comparison technique.
Using your chosen model(s) state what conditions lead to the maximum yield (either of mature fruit or total yield). You should show your derivation/working here.
Again, there is no specific template you need to follow for this question. You should take care that your inference is clear and that your fitted model(s) is/are clearly detailed. TLDR keep things clear and as consice as possible.
Question 04 [5 marks]
Create an informative visualization that illustrates the partition of variance (e.g., residual error variance, variance accounted for by fixed and/or random effects etc.) of your fitted model(s) from Q3.