STATS 1000 / STATS 1004 / STATS 1504
Statistical Practice 1
Assignment 5 (Report)
DEADLINE:
• Friday of Week 11 at 5:00pm
PART I : Statistical Analysis (Matched pairs t-test in R)
1. In practical 8 you were shown how to complete a matched pairs t-test. Now you have to re-produce the analysis for "Maths_Marks" data in the first part of this assignment and answer the questions below. Following is the background of this data.
Background
The data, Maths Marks, was collected by a Maths lecturer at the University of Adelaide and consists of marks for the first two assignments their students completed in their course. The lecturer is worried that their assignments may not be consistently difficult so is interested in whether there is a difference in the marks received between the two assignments. Students who got zero for either or both assignments have been removed from this data set by the lecturer. Both assignments were out of 50 marks in total.
This data is given in "Maths_Marks.xlsx" on MyUni and it has two variables:
• A1: Student’s math marks for the first assignment
• A2: Student’s math marks for the second assignment
In your Word document, include the following:
(a) A table of summary statistics for each assignment marks. The summary statistics needed are the sample mean, sample standard deviation, sam- ple median and the sample IQR. [2 marks]
(b) Produce a histogram in R of the marks for the two assignments and include in your document. [1 mark]
(c) According to the above histograms and table answer the following ques- tions.
i. Describe the shape of the distributions of the marks for each as- signment. [2 marks]
ii. Which summary statistics are the most appropriate to summarize the location and spread of the two distributions ? Why? [3 marks]
iii. Compare the distribution of the marks for each assignment using the summary statistics you have selected for location and spread? [2 marks]
(d) Following is a side-by-side box-plot of the marks for each assignment. Looking at these boxplots, do you have any strong evidence to assume that there are errors in data? Explain? [2 marks]
Figure 2: Side-by-side boxplot of marks for each assignment.
(e) Perform a matched pairs t-test in R for the difference of marks be- tween Assignment 1 and Assignment 2 and include the output in your document. [1 mark]
i. Why a matched pairs t-test is appropriate for this case? [1 mark]
ii. Write down appropriate null and alternative hypotheses for the
Matched pairs t-test. Remember to define any parameters used. [2 marks]
iii. What is the observed value of the test-statistic to 3 decimal places? [1 mark]
iv. What is the distribution of the test statistic if the null hypothesis is true? [2 marks]
v. What is the P-value to 3 decimal places? [1 mark]
vi. Do you reject or retain the null hypothesis at the 5% significance level? Why? [2 marks]
vii. Write down the confidence interval for the mean difference and interpret the results in context. [3 marks]
(f) Produce a normal QQ plot for the differences between the marks on assignments 1 and 2 and include in your document. [1 mark]
i. Which assumption can be checked using the above Q-Q plot ? De-cide if this assumption is reasonable for the data? [2 marks]
(g) A Challenging question
The lecturer doubts that if we observe a difference between the marks, it might not be purely because of the difficulty of the assignment. As every student completed the assignments in the same order, there may be carry over effect or order effects present. It could be the case that students approached assignment 2 differently because of their feedback on assignment 1. This may mean our findings are showing the effect of this ordering, rather than the effect of a change in assignment difficulty.
i. What is this phenomenon called in Statistics? [1 mark]
ii. What can be done to avoid this issue? [1 mark]
(h) Presentation marks (1 for word, 1 for informative table captions, 1 for informative figure captions.) Note: consider your R output for t-test as a table. [3 marks]
[Total: 33]
PART II : Communicating Statistics - Executive Summary
This part of the assignment requires you to complete a exectutive summary to accompany the analysis you have done in Part I and present it in the form of a statistical report. This aims to extend your abilities from understanding the tests and how to do them, to being able to explain the outcome to a wider audi- ence.
As such, the part II will not be in the usual form of your assignments, but in a report form; with a plain English exectutive summary which explains your findings to go with the statistical analysis you have done in part I. Following includes a template, with instructions, on how to complete the executive summary and there will be a sample, Executive Summary for you to see on MyUni.
• Instructions
Given the background above in part I, identify the research question and, using the statistical analysis, report your findings using the template on the following pages.
1. The following will detail the elements you need to include in your executive summary.
(a) Title - The title should not be “Assignment 5” or “Math Marks Assign-ment”, but rather the title of the report you have created. For example, a report on the diving behaviour of seals might read “The Diving Be-haviour of Seals in Antarctica”. [1 mark]
(b) Aims - The aim of the Report, not the assignment. For example, “To ascertain how deep seals dive and the how far they travel from shore on those dives”. [1 mark]
(c) Background - Where the data came from. That is, everything you were told about the data before you started analysing it (copy-paste from the assignment instructions is totally ok here). [1 mark]
(d) Findings - Feel free to use dot points for this section
i. Prioritise your findings! Make sure the most important, most awe-some, most awe-inspiring finding comes first.
ii. Only talk about significant/important findings (unless you have been specifically asked to do otherwise). You don’t want to lose your audience in a sea of irrelevance.
iii. Be CONCISE. Short, sharp and accurate is what we want to see.
iv. Reference every finding with a table/figure (figure 1) from the anal-ysis in Part I. [4 marks]
(e) Discussion - Do not just repeat your findings here.
Any issues in your experimental design or the findings that needs to be explored further or retested should be discussed here.
The whole executive summary in Part II, should only take 1 to 1.5 pages. [3 marks]
(f) Formatting
There will be five marks assigned for the five following elements of the exectutive summary:
i. The summary is clear and easy to read.
ii. The summary is concise and gets straight to the point.
iii. The summary is completely unambiguous and does not use statis- tical terminology.
iv. There are a reasonable number of decimal places presented.
v. No misleading statements beyond the reach of analysis have been made. [5 marks]
[Total: 15]
[[Assignment total: 48]]