227.212: Animal Production 1

Statistics Assignment, 2023

General information

This assignment is assessed. Your work must be submitted by 11:59pm on April 24th 2023.

• All work should be done by altering the markdown file provided.
• Make sure you enter your name in the author field of the markdown document.
• All questions are worth equal marks.
• All graphs should have clear axis labelling and legends if needed.
• The answer alone will not give full marks; you should include explanation and/or descriptions of plots alongside your answers.
• Once done, ‘Knit’ your document to HTML and submit the HTML file to stream.

Dataset: Dairy production in New Zealand

All the exercises in this assignment are concerned with a dataset on dairy production in New Zealand, from the 2014/15 through to 2019/20 seasons. The following variables are measured.

Variable	Description
Region	Region of New Zealand.
Island	Which island the region is in (North, South).
Year	Year the season started. 2014–2019.
Month	Month number during the season. 1 (June) – 12 (May).
Milk	Milk per cow per day (litres).
Milkfat	Milk fat per cow per day (kg).
Protein	Protein per cow per day (kg).
SCC	Somatic cell count (000 cells/ml).

Start by downloading the project file by Right clicking and Save File As… here:

https://www.massey.ac.nz/~jcmarsha/227212/project.Rmd

Then loading it into RStudio.

Before you start, make sure you can Knit this document to produce an HTML file from it.

Exercise 1: Milk through time

1. In the first code block there is some code that produces a plot of milk per cow per day for each Month. Improve the axis labels on this plot and describe any observed trends. The MonthLabel column may be useful.

2. Produce a plot of milk per cow per day by Year. Is there evidence that milk yields are increasing?

3. In the plot of milk by month, you should have noticed a number of outliers in May. Which region are these from? Ensure you clearly describe how you found your answer.

4. Produce a plot showing milk per cow per day by Region. Ideally we’d also show which region is in which Island. Options might be colouring or you could facet_wrap to split by island. The scales parameter of facet_wrap might be useful should you choose to do a facetted plot.

Exercise 2: Somatic cell counts

1. Create a plot to show the distribution of somatic cell counts for North and South islands. Describe the distribution and comment on whether you think there is evidence for differences between the islands.

2. Try repeating the above using a log transformation of the somatic cell count. Describe what you see. Which graph do you prefer?

3. Produce 95% confidence intervals to summarise the average somatic cell count in North and South Islands. Is there evidence of a difference between the islands?

4. Produce plots to compare the distribution of somatic cell counts between North and South Islands and between months. Summarise what you see.

Exercise 3: Relationships with milk volume

1. Produce a plot to show the relationship between milk fat and milk volume. Does the relationship differ between the North and South Island?

2. Perform a statistical test to determine if the average milk volume per cow per day differs between North and South Island. Ensure you clearly state your conclusion, the hypothesis being tested and any P-values and that you quantify the magnitude of any difference.