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Statistics for Natural Scientists Assessment

Answer Sheet

Academic Year 2024/25, Semester 1

Instructions: This is the assessment for EART11200 Natural Scientists’ Toolkit: Statistics for Natural Scientists. The assessment includes the following files:

SFNS Assessment S1 2024.pdf: This document presents the questions that you will need to answer in this assessment.

SFNS Assessment S1 2024 answer sheet.docx: This is the document on which you will answer the assessment questions. You will need to consult “SFNS Assessment S1 2024.pdf” for a full explanation of the questions to be answered.

After you have answered the questions on “SFNS Assessment S1 2024 answer sheet.docx,” please save the document as a PDF. Name the file with your student number followed by “_stats_assessment.pdf” (for example, 123456789_stats_assessment.pdf) and submit the PDF via Blackboard by 9 January 2025 at 9:00 am.

The assessment is divided into three sections, each with several parts. In section 1, you will choose statistical tests to use, but you will not need to conduct the analyses. In section 2, you will interpret analyses where R output has been provided for you. In question 2.2.3 you will also provide a figure to illustrate your conclusion. All the information you need to answer the questions in section 2 can be found in the R output or in the questions themselves. In section 3, you will analyse datasets that have been provided for you, either in the text of the question (as in question 3.1) or in separate CSV files (questions 3.2 to 3.4).

You should attempt to answer all parts of all questions. The marks for each question are clearly indicated. You may use the unit handbook, your notes or completed practicals, starter code for practicals, code you have written during the semester, and the answer keys to completed practicals while completing this assessment. You may also use online resources or external handbooks/textbooks (but I hope you will not need to!). However, you must not collaborate with others while completing this assessment. Collaboration on this assessment is detectable, so please do not do it! If you have questions about the assessment, you can post them to the discussion board so I can answer publicly. This ensures that everyone has the same information about the assessment. You can find the discussion board here:

https://online.manchester.ac.uk/ultra/courses/_81724_1/cl/outline

If you have not done so already, I recommend that you subscribe to the discussion board so you get a message any time I post a new answer.

If you have a DASS plan that specifies an extension on coursework assessments, then you can apply that extension to this assessment. In practice, I recommend that you do not use your extension even if you are entitled to one. The assessment is designed so that everyone can complete it before the deadline. If you apply an extension to the standard deadline, then this assessment will drag into the exam period, and it may not be in your interest to allow that to happen. Please note that the discussion board will close at the standard submission deadline. This is important because it ensures that no new information about the assessment becomes available after some students have been required to submit. So, if you have a DASS extension and intend to use it, please make sure that you have asked any questions you need to ask before the standard submission deadline.

Section 1 (4 marks each)

For each question in section 1:

i) what is the predictor and is it numerical or categorical (if there is more than one predictor, answer this for all the predictors)?

ii) what is the response and is it numerical or categorical?

iii) what test would you use to answer the study question?

Section 2 (16 marks)

Each question in this section is followed by a block of R code and output. The output provided is sufficient to answer the questions. You may not need to use all the output.

Question 2.1

2.1.1 Controlling for the plot condition, is there evidence that the fertiliser brand affects the crop yield? If so, which brand(s) provide higher yields than which others? Report your results clearly and concisely.

2.1.2 Controlling for the fertiliser brand, is their evidence that the plot condition affects the crop yield? If so, in what way? Report your result clearly and concisely.

2.1.3  Is there evidence that the performance of the fertiliser brands depends on the condition of the field being fertilised? Report your result clearly and concisely.

2.1.4 Fertiliser brand A is running an advertising campaign to take market share from brand C. The company that produces brand A claims that constantly cropped fields fertilised with their brand yield as much winter wheat as recently fallowed fields fertilised with brand C. Does your study provide evidence to support or refute this claim? If so, what is that evidence?

Question 2.2 (12 marks)

2.2.1 Test the hypothesis that children at Park Street School have higher blood lead levels than children at Dana School. Report your results clearly and concisely.

2.2.2 Provide a figure to illustrate your results.

Section 3

In this section, data is provided in each question or datasets are provided separately. Analyse the data sets to answer each question.

Question 3.1 (4 marks)

3.1.1 Does your study provide evidence that car colour is non-randomly associated with speeding at the study site? Report your result clearly and concisely.

3.1.2 You show your results to a friend and they notice that the speeding rate is lowest among white cars. They sum up the red, blue, and black cars that were obeying the speed limit (88 cars) and those that were exceeding the speed limit (54 cars). They conduct a test comparing the numbers of white cars that were obeying or exceeding the speed limit to the numbers of all other cars combined that were obeying or exceeding the speed limit, and they obtain a p-value of 0.0381. They argue that this is evidence that the drivers of white cars are less likely than the drivers of other cars to exceed the limit. Is their conclusion valid? Why or why not?

Question 3.2 (20 marks)

3.2.1 Conduct an analysis to answer your question of interest. Report your results clearly and concisely. (Note: logged radii are unitless.)

3.2.2 Provide a figure to illustrate your result.

3.2.3 Is there evidence from your data that moon sizes differ among planets for reasons other than the size of the planet? If so, what proportion of the variability in moon size that is not explained by the size of the planet is explained by some other (unknown) attributes of the planet?

Question 3.3 (8 marks)

3.3.1 Does the probability that a breeding pair survived after release into the wild depend on the number of generations they were in captivity? If so, how? Report your results clearly and concisely.

3.3.2 A conservation organisation you work with has obtained a pair of birds that have been in captivity for 5 generations. They plan to release these birds into the wild, and they have asked you to predict the probability that the birds will survive for at least one year after reintroduction. What is your prediction?

3.3.3 If a breeding pair survived for at least one year, does the probability that the pair bred successfully in the wild depend on the number of generations for which the birds had been in captivity? If so, how? Report your result clearly and concisely.

Question 3.4 (20 marks)

3.4.1 Controlling for population, is there a relationship between the concentration of PBDEs in a female house sparrow’s blood and the thickness of the shells of the eggs she lays? If so, what that relationship? Report your results clearly and concisely.

3.4.2 Is there a difference in eggshell thickness in the two study populations that cannot be attributed to the concentration of PBDEs in the mothers’ blood? Report your results clearly and concisely.

3.4.3 Does the effect of PDBE concentration in the mothers’ blood affect eggshell thickness differently in the two populations? Report your results clearly and concisely.

3.4.4 Provide a figure to illustrate your results.

3.4.5 You sample a female house sparrow and find she has a PBDE concentration of 4.6 ng/g in her blood. How thick would you expect her eggshells to be if she comes from the Brooklyn population? How thick would you expect her eggshells to be if she comes from the Castleton population?