For this week you should read all of Chapter 12 of the textbook. When you read the text that involves running R script you are expected to run the code by yourself on your computer, in parallel to reading it in the textbook, and compare what you get with the output presented in the textbook.
In statistical thinking there is a tenancy towards conservatism. The investigators, enthusiastic to obtain positive results, may prefer favorable conclusions and may tend to over-interpret the data. It is the statistician’s role to add objectivity to the interpretation of the data and to advocate caution.
On the other hand, the investigators may say that conservatism and science are incompatible. If one is too cautious, if one is always protecting oneself against the worst-case scenario, then one will not be able to make bold new discoveries.
Which of the two approach do you prefer?
When you formulate your answer to this question it may be useful to recall cases in your past in which you where required to analyze data or you were exposed to other people’s analysis. Could the analysis benefit or be harmed by either of the approaches?
For example, many scientific journal will tend to reject a research paper unless the main discoveries are statistically significant (p-value < 5%). Should one not publish also results that show a significance level of 10%?
In this assignment we consider data that examines the effect of two soporific drugs, drugs that induce sleep. These two drugs were tested on a group of 10 patients. For each of the patients the increase in hours of sleep was measured both for drug 1 and for drug 2. The source of the data is the R dataset “sleep”, which quotes the paper by Cushny, A.R. and Peebles, A.R. (1905). (The action of optical isomers. II. Hyoscines. J. Physiol. 32, 501–510.) The files “sleep_paired.csv” and “sleep_unpaired.csv” contain the same data in two different formats. The first format will be used in the first part of the assignment and the second format will be used in th second part. You may download the files sleep_paired.csv and sleep_unpaired.csv using the links.
For the assignment you should complete the following 8 tasks. Tasks 1-5 refer to the the paired design and Tasks 6-8 refer to the unpaired design. Your answers should be short and clear. We recommend that you copy and paste the tasks below into the form titled “Submit your Assignment using this Form”. You can then write you answers to the tasks in the designated positions that are marked in the text:TasksA Paired Design:1. The number of outlier observations in the difference between the response to drug 1 and the response to drug 2 is: _____.Explain each step in the computation of the number of outlier observations:2. The percentile of the t-distribution that should be used in order to compute an 80%-confidence interval for the expectation of the difference between the responses to the two drugs is (write the numerical value): _____.Attach the R code for conducting the computation:3. The 80%-confidence interval for the expectation of the difference between the responses to the two drugs is:Lower end = _____, Upper end = _____.Explain each step in the computation of the confidence interval:4. The p-value for testing the null hypothesis that the expected difference is equal to 0 versus the two-sided alternative is equal to: _____.Attach the R code for computing the p-value:5. Do you reject the null hypothesis with a significance level of 5%? __Yes __No.Explain your choice:An Unpaired Design:6. The test statistic for the permutation test is the absolute value of the difference between the average of the first 10 observations and the average of the last 10 observations. The value of the test statistic is:_____.Attach the R code for computing the test statistic:7. Run a simulation to compute the p-value of the permutation test. The p-value is:_____.Attach the R code for computing the p-value:8. Do you reject the null hypothesis with a significance level of 5%? __Yes __No.Explain your choice:
The Learning Journal is a tool for self-reflection on the learning process. In addition to completing directed tasks, you should use the Learning Journal to document your activities, record problems you may have encountered and to draft answers for Discussion Forums and Assignments.
The Learning Journal should be updated regularly (on a weekly basis), as the learning journals will be assessed by your instructor as part of your Final Grade.
Your learning journal entry must be a reflective statement that considers the following questions:
1. Describe what you did. This does not mean that you copy and paste from what you have posted or the assignments you have prepared. You need to describe what you did and how you did it.
2. Describe your reactions to what you did.
3. Describe any feedback you received or any specific interactions you had. Discuss how they were helpful.
4. Describe your feelings and attitudes.
5. Describe what you learned.
Another set of questions to consider in your learning journal statement include:
1. What surprised me or caused me to wonder?
2. What happened that felt particularly challenging? Why was it challenging to me?
3. What skills and knowledge do I recognize that I am gaining?
4. What am I realizing about myself as a learner?
5. In what ways am I able to apply the ideas and concepts gained to my own experience?
Finally, describe one important thing that you are thinking about in relation to the activity.
Your Learning Journal should be a minimum of 500 words.