Homework answers / question archive / STAT*2040 DE Fall 2020 Data Analysis Assignment #2 This assignment has an official deadline of Wednesday November 25 at 11:59 pm, but I will give you an extra week and accept submissions without penalty until Wednesday December 2 at 11:59 pm

STAT*2040 DE Fall 2020 Data Analysis Assignment #2 This assignment has an official deadline of Wednesday November 25 at 11:59 pm, but I will give you an extra week and accept submissions without penalty until Wednesday December 2 at 11:59 pm

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STAT*2040 DE

Fall 2020

Data Analysis Assignment #2

This assignment has an official deadline of Wednesday November 25 at 11:59 pm, but I will give you an extra week and accept submissions without penalty until Wednesday December 2 at 11:59 pm. You must submit one pdf document for each part of this assignment (4 pdfs in total). Submissions must be made to Crowdmark, using the personalized link that will be sent to your email address.

You may complete this assignment individually, or in groups of 2 or 3.

There are 4 parts to this assignment:

1. Data analysis and write-up of conclusions for a two-sample problem. (10 marks)
2. Data analysis and write-up of conclusions for one-sample problem (well, it’s a paired-difference procedure in its nature). (10 marks)
3. Reading parts of a two journal articles, and giving interpretations of the results of the statistical inference procedures used in the articles. (8 marks)
4. Data analysis and write-up of a data set that you find. (10 marks)

This assignment involves creating various plots in R, and using R to calculate some summary statistics. Any plot or output that is done in software other than R (e.g. Excel) will receive a grade of 0. This is an R assignment.

On at least one of the parts, you will need to look up journal articles. The journal articles are available from the University of Guelph library website. If you are off-campus, then you must use the off-campus sign on (top right of the page) before proceeding to the journal article. One way to find the articles is to go to http://www.lib.uoguelph.ca, hover over Find and click on E-Journals, then search for the journal title. You can also search for the article title in Omni (on the library site).

This assignment is worth 12.5% of your final grade. You will be marked on: 1) Getting the proper R output and plots, 2) Validity of your statistical conclusions and interpretations, 3) Writing style

(grammar and clear concise language count!), 4) Presentation. (I don’t have a specific presentation

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style in mind, but make it clean and easy to read. Sloppy work won’t earn full marks.) Note that you must use R to complete this assignmen. My “Intro to R” document is available on the Courselink site.

You will have to do some thinking in this assignment. I am not going to tell you exactly what to do, and I would be negligent in my duties as a professor if I were to do so. You are most welcome to ask me questions, and post questions or comments on the discussion board (but refrain from posting specific answers or code that could simply be copied). If you’re holding up your end of the bargain, and giving these questions an honest go, then I’m very willing to help when you have questions or concerns. I am not always looking for one specific method of analysis – for some of these questions, there is more than one path to perfect marks.

1. Part I: Impulsivity in adult ADHD patients with and without cocaine dependence

Crunelle et al. (2013) investigated impulsivity in adult ADHD patients with and without cocaine dependence. The authors investigated a number of characteristics, but here we restrict ourselves to only the results of a “stop completion task” (see Section 2.3.1 in the paper for more information). In the end, a stop signal reaction time (SSRT) was recorded for each individual. The authors state “a high SSRT reflecting low response inhibition, and indicating higher motor impulsivity” (but state your conclusions and interpretations in terms of SSRT).

The SSRT times (ms) for the 17 ADHD patients without cocaine dependence (labelled ADHD) and the 11 ADHD patients with cocaine dependence (labelled ADHDC in the file) are contained in the file s2040DE_F20_ADHD, which has been sent to the class in an email. You must import this data into R to carry out the analysis. (This data is simulated data based on information in Table 2 of the article. You must use the data in the file to carry out the analysis. The authors also used a control group in the study, but we will ignore that group for the purposes of this analysis.) For your write-up to be complete, you must:

• Give the hypotheses of the appropriate hypothesis test, in both words and symbols.
• Plot side-by-side box plots of the data (in one plot). Label the plot appropriately.
• Plot normal quantile-quantile plots for the two groups separately. Include the line in your normal QQ plots.
• Comment on the normality assumption of the two-sample t procedures in this setting (i.e. is it reasonable to use the t procedures here?). You should make reference to the plots.
• Choose either the the pooled-variance t procedure or the Welch procedure to analyze the data, and justify your choice of procedure.
• Give the R output for your choice of t procedure.
• Interpret the results, including commenting on the results of the test of the null hypothesis that the true mean stop signal reaction is the same for both groups, and an appropriate interpretation of a relevant confidence interval. Interpretations must relate to the problem at hand.

Your submission must include the boxplots, normal QQ plots, and the R output, in addition to your comments and interpretation. Your submission for this part should only be two pages, but can be three pages if you feel that is necessary.

2. Part II: Melatonin Phase Shift Due to Blue Light Exposure

Various studies have shown that exposure to certain types of light near bedtime can delay the onset of the hormone melatonin, and this can impact a person’s circadian rhythm and sleep cycle.

Figueiro (2015) investigated a possible effect of exposure to blue and green light through closed eyelids on melatonin suppression. (This article is also available at https://www.ncbi.nlm.nih.gov/ pmc/articles/PMC4790124/) In the study, subjects had their dim light melatonin onset ( DLMO ) measured in dark conditions one night, and after being exposed to bombardment of light through closed eyelids each night for a week. (See the article for details.) The phase shift was recorded.^[1] A negative phase shift indicates a delay in melatonin onset after light exposure. The authors investigated both flashing red and flashing blue light in their study, but we will look only at the data involving flashing blue light.

The authors studied 17 normal sleepers and 8 insomniacs, but we will restrict our analysis to the normal sleepers. The data contained in s2040DE_F20_DLMO_phaseshift contains the 17 phase shifts. (The phase shifts are the same as the values given in the last column of table 1.) For this part of the assignment:

• Set up the most appropriate hypothesis test, the one that addresses the research question of interest. Give the null and alternative hypotheses, in words and symbols.
• Plot a normal quantile-quantile plot and boxplot of the phase shifts. Include the line in your normal QQ plot. Properly label the axes (you can use the default labelling for the normal QQ plot).
• In the next step you will use the t procedures to construct a 95% confidence interval for the population mean and carry out an appropriate hypothesis test. One of the assumptions of this procedure is a normally distributed population. Based on the plots, comment on whether the phase shifts appear to be roughly normally distributed.
• Assume the phase shifts are normally distributed. Using the t.test procedure, get R to carry out the calculations for the hypothesis test and the 95% confidence interval for µ. Include the output of the procedure in your submission.
• Give an appropriate interpretation of the 95% confidence interval in the output. Your interpretation must relate to the problem at hand.
• Interpret the results, including commenting on the results of the most appropriate test, and giving an appropriate interpretation of the most appropriate confidence interval. Interpretations must relate to the problem at hand.

Your submission must include the boxplot, normal QQ plot, and the R output, as well as your comments and interpretation. It must all be on a single page.

3. Interpreting some values in journal articles

(2 marks for each part, 6 marks total)

Answer the following questions clearly and concisely. Your submission for this part should be a single page.

1. Taylor et al. (1998) investigated various characteristics of Megarcys signata, a type of stonefly. These researchers collected samples at two streams in Colorado, and investigated relationships between a number of variables. Just above Figure 1 in their paper, on page 497, the authors report a t statistic of 8.164 and a p-value of less than 0.001. Give the null hypothesis associated with this hypothesis test and an appropriate conclusion.
2. In many journals, when the authors report a result such as 16.8±1.4, the 1.4 is the standard error of the statistic and not the margin of error. Consider again Taylor et al. (1998). At the bottom right of page 496, the authors report summary statistics of 159.8±5.49. Explain, in casual terms as if you were explaining to a layperson, the meaning of 5.49 in this situation. Do not refer to a confidence interval in your explanation. You do not need to be technically perfect, but you should give the “truthful gist” of what that number represents.
3. Consider again Table 2 of Crunelle et al. (2013). The authors run one-way ANOVA and various other procedures on the 3 groups. In table 2, they report a p-value of 0.274 for one of the tests. Give an appropriate conclusion to the hypothesis test that resulted in this p-value (it’s from a one-way ANOVA). Your conclusion must relate to the problem at hand.

4. Answering a research question of your choosing

In this section you will need to find some data, carry out some statistical analysis in R, and write up your results. You need to:

1. Clearly state the problem you are investigating. (Why are you doing what you are doing? What are you hoping to achieve?)
2. Find some data that will help to answer your research question(s). Be sure to cite your source. (You can collect some data on your own, or you can use some you find online or elsewhere.)
3. Illustrate and analyze the data in R. Your submission must include at least one plot that illustrates the data and illuminates the question of interest. The plot cannot be a normal quantile-quantile plot; it must be something that provides some insight into the question at hand. The plot and statistical analysis must be done in R, and must include at least one relevant confidence interval and relevant hypothesis test based on the methods of this course (that help to answer to the question(s) of interest). The statistical methods could be one or two sample t procedures on means, inference for proportions, or material covered later in the course such as chi-square tests, ANOVA, or regression. Include the R output for your choice of procedure.
4. Give a summary of the results of your analysis.

To get a good mark, your submission needs to:

1. Address a reasonable and reasonably interesting question. It needs to be something that somebody might care about. (See some examples below.) I’ll give you a fair bit of leeway here, but don’t be silly.
2. Use data that can help to address the question of interest.
3. Carry out a reasonable method of analysis.
4. Be well written and presented, and properly explain the results.
5. Be your own work. (Simply copying somebody else’s analysis is academic misconduct.) Examples of reasonable questions:

• Does Pfizer’s preliminary data show evidence of the effectiveness of their candidate vaccine?
• Is there evidence of a difference in mean driving distance between right-handed and left-handed PGA tour players?
• Do right-leaning Twitter accounts tend to have more followers than left leaning ones?
• Does using a fertilizer change the growth rate of peas in my garden?
• Is there a relationship between temperature and incubation period for painted turtle eggs?
• Is blood type related to severity of Covid-19 symptoms?

Examples of unreasonable questions:

• Does my brother tend to pick his nose more in the morning or the evening?
• Does this sample of 10 coin tosses show that the coin is biased toward heads?
• Do the toes on my left foot have the same average length as the toes on my right?

Note that I’m not suggesting anyone address one of the “reasonable” questions above, I’m simply saying that you should address a reasonable question of interest and not phone it in. I’m open to all sorts of possibilities here, but don’t do anything silly like toss a coin 5 times and then estimate the true proportion of heads based on that.

Your submission for this part cannot be longer than 2 pages.

References

Crunelle et al. (2013). Impulsivity in adult ADHD patients with and without cocaine dependence.

Drug and Alcohol Dependence, 129:18–24.

Figueiro, M. (2015). Individually tailored light intervention through closed eyelids to promote circadian alignment and sleep health. Sleep Health, 1(1):75 – 82.

Taylor et al. (1998). Effects of size at metamorphosis on stonefly fecundity, longevity, and reproductive success. Oecologia, 114:494–502.