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Take Home Project II Solution
You are allowed to work by yourself (one person total) or with one other person (two people total). No matter how many people you have in your group, you must answer one question.
Your report (including both topics) can be no longer than 12 pages total, including gures. This page limit does not include the cover page, or the code appendix..
Read all instructions carefully. You may only ask the TA, your group member (if you have one) or Dr. Melcon questions.
Out of the following questions, you (or your group) will choose one from each topic as your particular questions of interest, for two questions total.
Topic I: Transformation of Variables
Question 1 - Helicopter.csv
This data is over the period of a year, and is interested in if di erent times of day see di erent amount of helicopters requested for a sheri ’s o ce.
Column 1: Count: The number of times a helicopter was called to an emergency in one year.
Column 2: Shift: The shift, with I (between 2AM and 8AM), II (between 8AM and 2PM), III (between 2PM to 8PM), and IV (between 8PM to 2AM).
Question 2 - NewHawk.csv
This data is a random sample of hawks from the larger dataset used in Homework 2. It has columns
Column 1: Wing: Length (in mm) of primary wing feather from tip to wrist it attaches to
Column 2: Species: CH=Cooper’s, RT=Red-tailed, SS=Sharp-Shinned
Topic II: Two Factor ANOVA
Question 1 - Salary.csv
This data is taken from a random sample of \technology workers" from Seattle and San Francisco. Note, this data was scraped from the web, but from what website and what year was not disclosed.
Column 1: Annual: The subjects annual salary in thousands of dollars.
Column 2: Prof: The subjects title, with values DS (\Data Scientist"), SE (\Software Engineer"), and BE (\Bioinformatics Engineer").
Column 3: Region: SF for San Francisco, S for Seattle.
For this question, you should consider 6 con dence intervals total, 4 of which are pairwise, and two of which are contrasts (but are not pairwise). You get to pick which pairwise and contrasts you are interested in.
Question 2 - Scores.csv
This data is taken from a \high risk" population, who is undergoing treatment for psychological problems. A random sample was taken.
Column 1: Beck: The BECK depression score of the subject, with higher values indicating more at risk for depression. The scale is 0 to 75.
Column 2: Drug: The subjects’ history of drug use, with values Recent (they have recently used recreational drugs), Never (they have never used recreational drugs), and Previous (they have previously, but not recently, used recreational drugs).
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Column 3: Treatment: The length they have been receiving treatment, with values Long (a year or more), Short (less than a year).
For this question, you should consider 6 con dence intervals total, 4 of which are pairwise, and two of which are contrasts (but are not pairwise). You get to pick which pairwise and contrasts you are interested in.
The Report Format (by topic)
Transformation of Variables
For this topic, the report will have very little interpretation. The goal for this topic is to transform the data given so that it best ts the ANOVA model. This report should be fairly short. The sections of the report should include:
a. A small introduction. A sentence or two is ne.
write down the regression equation of original model?
Plot your original data and the diagnostic plots/tests for the original data. Report the model t of the original model.
You should consider removing outliers, transforming Y , or both. You should report back appropriate values (or plots) for every combination of transformations and removing outliers you considered. You should pick your \best" combination of transformed variables.
Discuss your results. Did transforming the data help? What are the downsides? Do you believe the transformed data is a better t? What would you suggest for a client who wants to use this data set for ANOVA (which transformations / removal of outliers would you use, if any)?
Two Factor ANOVA
You or your team will turn in a short report. This means you should write in full sentences, and have the following sections for each question, while being as speci c as you can about your results:
Introduction. State the question you are trying to answer, why it is a question of interest (why might we be interested in the answer), and what approach you are going to take (just the name of the approach).
Should I plot boxplot with model AB?
Summary of your data. This should include things like plots (histograms, boxplots) including the interpretation of the plots, and summary values such as sample means and standard deviations. You should have an idea about the trend of the data from this section.
Same interpretation as SFA?
Diagnostics. You should discuss your assumptions here, and if you believe they are violated. Perform diagnostics for the model. If you believe assumptions are violated, note this and continue with the project. Do not consider transformation of variables for this topic.
IV. Analysis. Report back the \best" model (and how you chose that as the best), con dence intervals, test-statistic/s, and p-value/s, nulls and alternatives, etc. You may use tables here, but be sure that you organize your work. Remember to write your results in full sentences where possible.
Interpretation. State your conclusion, and what inference you may draw from your corresponding tests or con dence intervals, and any other useful statistics you may have calculated. These should all be interpreted in terms of your problem.
VI. Conclusion. Summarize brie y your ndings. Here you do not have to re-iterate your numeric values, but summarize all relevant conclusions.
Details
Your report should be the following format:
Typed.
A title page including your name/s, the name of the class, and the name of your instructor (me).
Double-sided pages.
An appendix of your R code used to produce the results. Do not include in R code, or unformatted output from R in the body of your report.
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Please have the following format:
Cover Page
Report for Topic I Report for Topic II Code Appendix
Small Notes
\Model t" refers to estimated values of your parameters, and this will be based on what model formation you used. Feel free to make your cover page \unique" so that it is easy to nd when I hand them back.
You may combine the Analysis/Interpretation section if you so choose.
Notice: your project will be graded as a group e ort (if you have two people). This means that you are responsible for your own work, and your partner’s work. I will not assign two di erent grades to one project.
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