HLTH7008 Introduction to Biostatistics

Please answer each question in the template document provided and submit via Turnitin on or before the due date. The marks allocated to each question are shown in the assignment. A total of 30 marks are available and this assignment is worth 30% of your overall grade.

All of the questions in this assignment ask you to analyse the data set assigned to you for assignments. This is the same data set which you used for Assignment 1. Read ‘Description of your data set.docx’ for the descriptions of the variables.

This assignment is assessing your skills, not the skills of the computer. You will need to copy and paste graphs from R Commander into your answers, but all other R Commander output will attract 0 marks and is discouraged. It is your task to identify the relevant results in the R Commander output and write these up in your assignment.

Some of the assignment questions ask you to show working or justify your answer. Answers without these requested workings or justifications will be awarded 0 marks.

Question 1 (12 marks)

Research question: Does average protein consumed in a day differ between male and female adults in the USA?

In the following analyses, use R Commander and the NHANES data set assigned to you. Assume that your sample of adult NHANES respondents represents a random sample of US adults. The variables you will use are ‘sex’, ‘protein’ and ‘log_protein’. Each student will get different answers as the data sets differ.

• Using appropriate graphs and statistics from R Commander and the NHANES data set assigned to you, compare the shape of the distribution of estimate daily protein consumption (variable 'protein') with the shape of the distribution of logarithm of protein consumption (variable 'log_protein') for males. Do the same for females. (3 marks)
• The research question could be addressed by conducting either a two-sided independent samples t-test on the difference in mean daily protein consumption between males and females or a two-sided independent samples t-test on the difference in mean logarithms of daily protein consumed between males and females. Which of these two alternatives would you chose? Justify your choice. (1 marks)
• Using R Commander and the NHANES data set assigned to you, implement the analysis you chose in b) and use the results to answer the above research question. The analysis must be an independent samples t-test. Present your analyses using the 5-step method and define any symbols you use. (5 marks)
• The logarithm transformation changes the numeric values of the data but does not change the order of data values. Therefore, a non-parametric hypothesis test (which ranks the data) will give the same answer whether conducted on ‘protein’ or ‘log-protein’. Using R Commander and the NHANES data set assigned to you, complete an appropriate non-parametric test and use the results to answer the above research question. Present your answer following the 5-step method. (3 marks)

Question 2 (9 marks)

Research question: What is the average estimated daily fat consumption for US adults?

In the following analyses, use R Commander and the assignment data set assigned to you. Assume that your sample of adult NHANES respondents represents a random sample of US adults. The variable you will use is ‘fats’. Each student will get different answers as the data sets differ.

• Using R Commander and the NHANES data set assigned to you, calculate the point estimate of the mean daily fat consumption for US adults. (1 mark)
• Using R Commander and the assignment data set assigned to you, calculate a 95% confidence interval for the mean daily fat consumption for US adults. (Don’t forget to check any assumptions.) (1 mark)
• Using your results from part b) write a sentence which answers the research question above as fully as possible. (2 marks)

Sample size question: What is the minimum sample size required to produce a 95% confidence interval for mean daily fat consumption for US adults which has a margin of error of 2 grams?

• Estimate the required sample size using and information from the NHANES assignment data set assigned to you and the excel calculation sheet provided. Present your answer as a sentence which specifies the required sample size and under what conditions. (3 marks)
• Suppose each of the 571 respondents in your data set had had their consumption of fats recorded on a weekday and each had their consumption of fats recorded on a weekend day. Consider the research question: "Is the average consumption of fats in US adults lower on weekdays than weekends." Name the statistical test you would use to address this research question. Explain why this test would be appropriate. (2 marks)

Question 3 (9 marks)

Research question: Is there a relationship between marital status and the choice of using English or Spanish to answer surveys among US adults?

In the following analyses, use R Commander and the assignment data set assigned to you. Assume that your sample of adult NHANES respondents represents a random sample of US adults. The variables you will use are ‘lang’ and ‘ms’. Each student will get different answers as the data sets differ.

• Describe the relationship the between language used when completing the survey and current marital status in the NHANES data set assigned to you. Use R Commander to produce frequency counts and row or column percentages, but present these results in a Word table with appropriate title and headings. Then describe the relationship in a sentence or two. (2 marks)
• Assuming that the NHANES data set assigned to you represents a random sample of US adults, would it be appropriate to address the research question above using a Chi-square test of independence on these data? Explain why or why not. (1 mark)
• Irrespective of your answer in b), using R Commander and the NHANES data set assigned to you, address the above research question using a Chi-Square test. Please use R Commander for all calculations but format your answer following the 5-step method. (3 marks)

Sample size question: Assuming equal numbers per group, what is the minimum sample size required to determining whether 'Never Married' survey respondents were more likely to choose to respond in Spanish than 'everyone else' in the US adult population with 80% power at the 0.05 significance level?

• To address this question, consider 2 groups: one group contains survey respondents classified as 'never married' and the second group contains everyone else. Assuming that the NHANES data set assigned to you represents a random sample of US adults, you can use these data to obtain a point estimate of the proportion of 'never married' respondents who choose to use Spanish in the wider US adult population. Suppose the proportion of 'everyone else' respondents who choose to use Spanish needs to be 5 percentages points lower (i.e. the proportion would be 0.05 lower than the proportion in the 'never married' group) than this value to be of any practical significance. Using the information from the NHANES assignment data set assigned and an appropriate online sample size calculator, calculate the minimum sample size required to detect this 5 percentage point difference between these two populations, with 80% power at the significance level and assuming there will be equal numbers of patients in the two groups. Present your answer as a sentence which specifies the required sample size and under what conditions.(3 marks)