Statistical Analysis for Dairy Cattle Milk Production, Vegetation Distribution, and House Prices

Assignment Task

Introduction

Answer all questions.

• Read questions carefully and only answer what I ask. If I say to present as you would for a journal, then please follow the guidelines you have been given during taught sessions – include graph captions
• When asked to suggest which test you should use, you might find it helpful to present graphs or test outputs. These do not need to be presented as you would for a journal – but make sure they are clear
• I provide a template to help you organise your answers.
• Provide an appendix (e.g. ANOVA table outputs) but do not stress about it. This is just as a check if things go wrong. You do not get marks specifically for this, but it might allow me to give you some you would otherwise miss
• You do not need to understand anything about cows or plants or house sales to answer these questions. The variables could be anything.
• I am not trying to catch you out, I want to give you marks. Try to enjoy the learning. I’m on your side!

Extra guidance

• With stats there is not always one way to analyse the data. The important thing is that you can justify what you did if asked. If you do a different test from what I think is best, you will still get credit, unless it is completely inappropriate, so don’t sweat too much.
• For instance: if you have two groups you want to compare means for, then you can use ANOVA or t-test if the data are parametric. This year I did not teach you t-test, because why teach you a test that you don’t need? Sometimes, even if the data don’t obviously meet the requirements for parametric tests, they can be justified
• You might need to look something up – e.g. you might find the package I gave you does not run on your computer. Don’t be scared to do so, I will notice and give you credit

Part A

You are a scientist interested in analysing milk production performance in dairy cattle. You used 10 cows from 3 breeds (Friesian, Ayrshire and Shorthorn) and recorded: parity (number of times the cow calved), milk yield (kg/day) for the current lactation, milk yield (kg/day) for the previous lactation, milk butterfat for the current lactation (%), history of mastitis (udder infection) and history of metritis (uterine infection). Raw data are given in the Excel spreadsheet, “PtA animal”

The numbers in bold are NOT marks, but they give you an idea of the relative importance of each section.

Question 1

• You want to assess the association between “history of mastitis” and “history of metritis”.
• Which test should you use? Justify your answer
• Carry out the analysis and present the results in the form of a summary table and descriptive sentence 

Question 2

• You want to test if there is a difference in parity between Friesian, Ayrshire and Shorthorn
• Which test should you use? Justify your answer
• Carry out the test and produce a short report of your statistical method and results (as would appear in a scientific journal article). (

Question 3

• Do the breeds and the production systems affect the means of “milk yield (kg/day) for actual lactation”?
• Which test should you use? Justify your answer
• Write a short method and results (including graph if appropriate) for your statistical test as it would appear in a journal article.

Part B

For the following tasks you will need to load ‘vegan’ package. You are not required to understand the significance of this in terms of the vegetation distribution nor understand what the species are – in fact they could be anything you like e.g. species of bacteria, soil, water or blood properties. The data for this are provided on the sheet “PtB plant”.

Question 4

• The data represent percent cover of 13 variables (species) and 24 sites (quadrats). No method is required here – simply present the graphs with a legend if necessary and a caption.
• Carry out a PCA with Heilinger transformation on the data. Try it with scaling set as TRUE and then as FALSE. Then try a CA. Create a plot for each analysis to shows sites and species. Try scaling of sites, species and symmetric. I realise you cannot make an ecological decision on the TRUE or FALSE scaling, but present the clearest one or two graphs from the PCA and one from the CA and say how you think the PCA and CA compare in terms of describing the data. (I’m only looking for a couple of sentences here to see if you understand what we are looking for in an ordination graph. There will not be one clear, correct answer necessarily – but only a justified opinion.
• Carry out a cluster analysis on the vegetation data Create 3 then 4 groups and present a cluster diagram with caption to show your results.
• Use colour, ellipse or polygon or other means to identify the 3 cluster groups onto your best of the plots produced in section 5a. Repeat for the 4 cluster. Add a legend. Which looks better, 3 or 4? (Again your justified opinion is what I am interested in. You do not have to agree with me.) 

Part C

The “Pt C House” data are factors potentially affecting prices of houses in the USA – taken from internet but I have tweaked the data to make them more manageable. The meaning of the columns is not important though it is semi-guessable. I do not require you to present this output as you would for a journal

Question 5

• Use backwards regression to determine which factors affect house prices.
• Present the model (equation) that you think best reflects the factors)
• Justify your decision – (present your reasoning) using concise bullet points and table(s)
• Check the validity of the model in terms of met assumptions e.g. qqplot. Comment on what you find.

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