Note: You are responsible for ensuring that you submit the right file type, and to the correct link.  A failure to do so may become subject to late penalties and/or attract a mark of zero.  If you

experience any issues with your submission, please contact the Student Experience Team as soon as

possible viaenvsci@liverpool.ac.uk.

You should produce a report of approximately 2 pages (including figures, but excluding your R code, which should be included as an appendix, as described below).

Background

We want to know whether biomass of wetland plants can be determined from the height of the stems, and whether these plants have greater biomass for their height in elevated CO2 environments.

Coastal marshes provide several important ecological services, including sequestering carbon among many others. One of the most important contributors to these habitats in terms of ecosystem function is the plants themselves, and therefore determining plant biomass is critical to evaluate the services generated by these systems. Traditional methods of sampling can be destructive and would require removal of plants to measure biomass directly; instead, we can use our understanding of allometric relationships to collect relevant data without harming the habitat. Allometry describes the conserved relationships between different dimensions of an organism and therefore, if we know one dimension, we can calculate another without measuring it directly. Of course, the confidence in our calculated data is dependent on the natural variability in these measurements.

In this assessment you will examine data from a study by Lu et al. (2016) where data were collected from three long term experiments at the Smithsonian Global Change Research Wetland, a marsh in The Chesapeake Bay. For the plant Schoenoplectus americanus, measurements of stem height and  dry mass were taken across 8430 individuals, of which 3642 were exposed to elevated CO2 . The researchers were interested in being able to predict dry mass from stem height and to determine    whether mass dependent on CO2  exposure.

Data

The data were downloaded from the repository as a comma-delimited file named GCReW_Allom_SCAM_Data.csv (available on the Week 11 page on Canvas). Download this file. Each row contains the data from a single plant. There are three variables of interest: total_height (the height of the plant in centimetres), total_mass (the mass of the plant in    grams), and CO2, (0 for ambient or 1 for elevated). To read these data into R you need to save the data as a tab-delimited text file, with a name of your choice, and use read.table (XXX)where XXX refers to your filename.

N.B. The data I am providing you has already been slightly adjusted to remove some rows which did  not contain data. This was a clean-up step I did so you can focus on the analysis. However, this is still an authentic data-set from a published study and contains many elements not pertinent to the question you must answer. It may be important to explore the data yourself before beginning analysis to understand what’s there and what you need to use.

Analysis and report

You should use R for analysis. Your reports should be written up individually. Whilst you now have a wider repertoire of statistical tools at your disposal and lots of practise, we have still broken this report down into sections and explained what is required. The report will be marked out of 32 with marks as listed below. See the mark scheme on Canvas for more information about how the marks  are broken down within each step. Please do not hesitate to make use of workshops and the Discussion Board for help.

1.   You will need to load the packages ggplot2, ggfortify, and car. There are a couple of alterations you need to make to the data set before you conduct your analysis:

a.    The variable CO2 is a number; you need to convert it into a categorical variable as otherwise R would treat it as quantitative.

b.    In the original study the researchers determined that the model most closely meeting     the assumptions of their test required total_massto be cube root transformed. the  easiest way to calculate a cube root in R is to raise a value to the power of 1/3 e.g.           var^ (1/3) where “var” refers to the variable which requires transformation. You     should create a new column in your data frame containing values for the transformation of the variable total_mass.

You have performed similar tasks previously in assignment 1 so revisit the handout to remind yourself how to do these tasks.

This step does not carry any marks, but will set you up for the next steps.

2.    Provide a graphical summary of the relationship between total_height and transformed       total_mass and how this may vary at different levels of CO2, including appropriate axis labels with units where appropriate and a numbered legend underneath (6 marks).

3.    Suggest a statistical test to investigate the scientific hypotheses that the cube root of total_mass is linearly related to total_height and that such a relationship may depend upon exposure to CO2. Provide a brief (one-sentence) justification. Looking through materials  from Week 9“"Experimental Design” may be of use (3 marks).

4.    List the assumptions of this test. Where appropriate, explain how you checked each one, and what the outcome was. consider what you understand about sample size and violations of assumptions when explaining the outcome (7 marks).

5.    Carry out the test and provide a written summary of your findings. Remember to use an         appropriate level of precision and describe the relationship. Referencing a figure such as that