1.9: Practice problems

In each chapter, the last section contains some questions for you to complete to make sure you understood the material. You can download the code to answer questions 1.1 to 1.5 below at http://www.math.montana.edu/courses/s217/documents/Ch1.Rmd. But to practice learning R, it would be most useful for you to try to accomplish the requested tasks yourself and then only refer to the provided R code if/when you struggle. These questions provide a great venue to check your learning, often to see the methods applied to another data set, and for something to discuss in study groups, with your instructor, and at the Math Learning Center.

1.1. Open RStudio and go to File -> New File -> R Markdown… to create a .Rmd. Click on the “Knit” button and see what happens. Try to complete the following questions in that document, clicking on the Knit button after you add a code chunk with code to complete each question. Part of the assignment on this question is to not get frustrated the first time you are trying this and seek out help to answer questions you have when practicing.

1.2. Read in the treadmill data set discussed previously and find the mean and SD of the Ages (Age variable) and Body Weights (BodyWeight variable). In studies involving human subjects, it is common to report a summary of characteristics of the subjects. Why does this matter? Think about how your interpretation of any study of the fitness of subjects would change if the mean age (same spread) had been 20 years older or 35 years younger.

1.3. How does knowing about the distribution of results for Age and BodyWeight help you understand the results for the Run Times discussed previously?

1.4. The mean and SD are most useful as summary statistics only if the distribution is relatively symmetric. Make a histogram of Age responses and discuss the shape of the distribution (is it skewed right, skewed left, approximately symmetric?; are there outliers?). Approximately what range of ages does this study pertain to?

1.5. The weight responses are in kilograms and you might prefer to see them in pounds. The conversion is lbs = 2.205*kgs. Create a new variable in the treadmill tibble called BWlb using this code:

treadmill$BWlb <- 2.205*treadmill$BodyWeight

and find the mean and SD of the new variable (BWlb).

1.6. Make histograms and boxplots of the original BodyWeight and new BWlb variables, both using base R plots and using ggplot2. Discuss aspects of the distributions that changed and those that remained the same with the transformation from kilograms to pounds. What does this tell you about changing the units of a variable in terms of its distribution?

References

Arnold, Jeffrey B. 2021. Ggthemes: Extra Themes, Scales and Geoms for Ggplot2. https://github.com/jrnold/ggthemes.

Gandrud, Christopher. 2015. Reproducible Research with R and R Studio, Second Edition. Chapman Hall, CRC.

Pruim, Randall, Daniel T. Kaplan, and Nicholas J. Horton. 2021a. Mosaic: Project MOSAIC Statistics and Mathematics Teaching Utilities. https://CRAN.R-project.org/package=mosaic.

R Core Team. 2022. R: A Language and Environment for Statistical Computing. Vienna, Austria: R Foundation for Statistical Computing. https://www.R-project.org/.

RStudio Team. 2022. RStudio: Integrated Development Environment for R. Boston, MA: RStudio, PBC. http://www.rstudio.com/.

Westfall, Peter H., and S. Stanley Young. 1993. Resampling-Based Multiple Testing: Examples and Methods for p-Value Adjustment. New York: Wiley.

Wickham, Hadley, Winston Chang, Lionel Henry, Thomas Lin Pedersen, Kohske Takahashi, Claus Wilke, Kara Woo, Hiroaki Yutani, and Dewey Dunnington. 2022. Ggplot2: Create Elegant Data Visualisations Using the Grammar of Graphics. https://CRAN.R-project.org/package=ggplot2.

Wickham, Hadley, Jim Hester, and Jennifer Bryan. 2022. Readr: Read Rectangular Text Data. https://CRAN.R-project.org/package=readr.

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1. A placebo is a treatment level designed to mimic the potentially efficacious level(s) but that can have no actual effect. The placebo effect is the effect that thinking that an effective treatment was received has on subjects. There are other related issues in performing experiments like the Hawthorne or observer effect where subjects modify behavior because they are being observed.↩︎
2. We will reserve the term “effect” for situations where we could potentially infer causal impacts on the response of the explanatory variable which occurs in situations where the levels of the explanatory variable are randomly assigned to the subjects.↩︎
3. There is a cloud version of R Studio available at https://rstudio.cloud/ that is free for limited usage and some institutions have locally hosted versions that you can use with a web-browser (check with your instructor for those options). We recommend following the steps to be able to work locally but try this option if you have issues with the installation process and need to complete an assignment or two until you get the installation sorted out.↩︎
4. I created this interactive website (https://rconnect.math.montana.edu/InstallDemo/) that contains discussions and activities related to installing and using R and RStudio.↩︎
5. The need to keep the code up-to-date as R continues to evolve is one reason that this book is locally published and that this is the 9^th time it has been revised in nine years…↩︎
6. There are ways to read “.xls” and “.xlsx” files directly into R that we will explore later so you can also use that format if you prefer.↩︎
7. If you are having trouble getting the file converted and read into R, copy and run the following code: treadmill <- read_csv("http://www.math.montana.edu/courses/s217/documents/treadmill.csv").↩︎
8. You can also use Ctrl+Enter if you like hot keys (Command+Enter on Mac OS).↩︎
9. Tibbles are R objects that can contain both categorical and quantitative variables on your \(n\) subjects with a name for each variable that is also the name of each column in a matrix. Each subject is a row of the data set. The name (supposedly) is due to the way table sounds in the accent of a particularly influential developer at RStudio who is from New Zealand.↩︎
10. The median, quartiles and whiskers sometimes occur at the same values when there are many tied observations. If you can’t see all the components of the boxplot, produce the numerical summary to help you understand what happened.↩︎
11. I recently had to revisit some work from almost a decade ago (before I switched to using R Markdown) as we were working on a journal article submission that re-used some of that work and it was unclear where some results came from, so I had to do some new work that could have been avoided if I had worked in a reproducible fashion.↩︎
12. This discussion is based on materials developed for a data visualization workshop originally developed by Dr. Allison Theobold and related to the https://datacarpentry.org/ workshops.↩︎
13. Jittering typically involves adding random variability to each observation that is uniformly distributed in a range determined based on the spacing of the observations. The idea is to jitter just enough to see all the points but not too much. Because it is random noise being added, this also means that if you re-run the jitter function, the results will change if you do not set the random number seed using set.seed that is discussed more below. For more details, type help(geom_rug) in the console in RStudio. The code is unfortunately clumsy to add jittering to the rug, so a simpler option is to use geom_rug(alpha = 0.3) where the transparency is modified with the alpha option to help with identifying overplotting of lines in the rug.↩︎
14. This certainly could have waited until later, but I have now seen enough base ggplot graphs that I really like to change their overall look.↩︎