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Responsible applied statistics in R for behavioral and health data

Information and Reference

Welcome to HE-902 at MGH Institute of Health Professions! Please watch the following welcome video:

This video can be viewed externally at https://youtu.be/XUMwNmyGhh0.

Please additionally read the following items:

This textbook accompanies the course HE-902—Advanced Statistical Modeling for Health Professions Education—in the PhD in HPEd program at MGH Institute of Health Professions. HE-902 is a statistics course that equips students to analyze healthcare and/or behavioral data in R. This online textbook is the main resource to guide you through the course.
The purpose of this textbook is to prepare users to responsibly apply data analysis methods to their work. Beyond just making a regression model and interpreting its results, it is important to know when we can and cannot trust these results. It is critical to know which claims you can and cannot make based on results that the computer gives you. The goal of this textbook is to equip you with many of the tools you need to responsibly apply and interpret regression models.
My name is Anshul Kumar and I am the author/preparer of this textbook. You can reach me at akumar@mghihp.edu with any questions, comments, and/or suggestions for modifications to this textbook. I co-teach HE-902 with Nicole Danaher-Garcia.
All of the materials here are available online for anybody to use. Those who are not part of the course HE-902 are welcome to use this textbook if it is useful. Please e-mail me any feedback you have.
I use a lot of footnotes like the one after this sentence.¹ You can read the footnote by clicking on the small-but-tall number in between this sentence and the previous one. Footnotes contain comments from me or extra information that might be helpful. But footnotes in this textbook are never required for you to read. It is fine for you to skip the footnotes and not read them.
Please note that many of the examples of data and research that you will encounter in this textbook use a binary, inappropriately narrow, and/or potentially problematic conceptualization of sex, gender, and other individual-level characteristics. My personal view is that this is often not the best way to organize data or present examples. Furthermore, our collective understanding of sex, gender, race, ethnicity, and other individual characteristics is constantly changing, and it is critical for all of us as data analysts and researchers to engage in related discussions and initiatives. I am always looking for materials that represent a more inclusive framework and I do update materials when possible. I welcome your input and suggested alternatives.²
At IHP, we recognize that students who observe religious and cultural holidays may not be able to complete their assignments or study for exams during these holidays. We will do our best to be flexible and accommodate your schedule related to your observation of holidays. Please just let us know about your expected schedule as soon as possible.

0.1 Course calendar 2025

Everything you need to do in each week of this course can be found a) in the calendar below and b) in the chapter of this textbook corresponding to each week. Keep in mind that this calendar might change during the semester.

Each week starts on a Monday and ends on a Sunday.

Week of	Week/Chapter #	Assignment/Activities
Jan 13	1	Assignment in R. 15 flashcards.
Jan 20	2	Assignment in R. 15 flashcards.
Jan 27	3	Assignment in R. 15 flashcards.
Feb 3	4	Assignment in R. 15 flashcards.
Feb 10	5	Assignment in R. 15 flashcards. Schedule oral exam #1.
Feb 17	6	Assignment in R. 15 flashcards. Do oral exam #1.
Feb 24	7	Assignment in R. 15 flashcards. Do oral exam #1 (if not already complete).
Mar 3	8	Assignment in R. 15 flashcards. Schedule oral exam #2.
Mar 10	9	Assignment in R. 15 flashcards. Do oral exam #2.
Mar 17	-	Spring break. No new work.
Mar 24	10	Assignment in R. 15 flashcards. Do oral exam #2 (if not already complete).
Mar 31	11	Assignment in R. 15 flashcards.
Apr 7	12	Assignment in R. 15 flashcards. Schedule oral exam #3.
Apr 14	None	No new reading. Final project is due April 18 2025.

Optional clarifications:

Note that the week of April 7 2025 (Week 12) will be the final week in which there is new material given.
How do I schedule oral exams? Students are responsible for scheduling their three oral exams on or near the scheduled weeks in the calendar, by e-mailing all course instructors.
When are assignments due? All assignments are due on the Sunday at the end of each week. For example, Week 3 of the class starts on Monday January 27 2025; the assignment for that week is due on Sunday February 2 2025. Assignments can be submitted at any time on the day they are due.

0.2 Useful links

Link to this HE-902 course textbook: https://bookdown.org/anshul302/HE902-MGHIHP-Spring2020/ or http://tinyurl.com/he902stats.
MGHIHP Academic Calendar
D2L site for HE-902 in spring 2025 at MGH Institute of Health Professions. You can find assignment submission drop boxes by clicking on: Assessments -> Assignments.
Adaptive Learner App: https://educ-app-2.vercel.app/
Chat GPT: http://chat.openai.com

0.3 Course curriculum

0.3.1 Grade calculation

Your grade will be calculated as shown in the table below.

Type of Work	% of Grade
Weekly homework assignments	35
Weekly flashcard practice completion	15
Oral exams	30
Final project	20

0.3.2 Interaction with instructors

Here are the main ways that you can interact with us (the instructors):

Regularly scheduled office hours on Zoom: You should receive calendar invitations by email to at least two office hour sessions each week. If you have any questions about an assignment, want to see what others are asking, or want to work together on an assignment or project, you can join one of these sessions. It is fine to arrive late to and leave early from these sessions. If you do not receive invitations to office hours, please email all instructors.
Email: You can email us at any time with questions and comments. Please send a second message if we don’t reply within 24 hours. When you email us, please email ALL course instructors.
One-on-one Zoom meetings: If you cannot attend office hours or if it would be more productive for you to learn, you can schedule a one-on-one Zoom meeting with an instructor. Just email all instructors with some times that might work for you (or look in our calendars and send an invitation). We can often meet with you within 24 hours of your request.

Since ours is an asynchronous online course, all of these forms of interaction are optional (not required). You can choose which of these, if any, are best for you, or suggest something else to us.

0.3.3 Learning activities

Here are descriptions of the activities you will do in this course:

Weekly homework assignments: These assignments will involve applying/practicing the statistical techniques taught each week week using a provided dataset. Because of the cumulative nature of the course, these assignments may also involve applying skills and knowledge from previous weeks. Some assignments will help you prepare for your final project. Assignments will be posted within the online textbook and students will submit completed assignments in D2L. Note that if you have data of your own that you are interested in analyzing, you can often use your own data instead of the provided data for the weekly assignments. Please discuss this with the instructors as desired. As long as you are adequately practicing the new skills each week, it doesn’t matter which data you use. If you find yourself spending too much time on an assignment or spending more than 30 minutes on a single task in an assignment, please do not hesitate to contact us so that we can assist you in finishing each task. The purpose of weekly assignments is to discuss or practice skills. Coding assignments are mostly graded based on your completion of the work. An instructor will look at your submitted work for each assignment, but might not give you any feedback on it if you have fulfilled the requirements. If you ask a question or we notice any omissions or errors, then we will give you feedback accordingly.
Weekly flashcard practice: During the orientation process for this course, you will sign up for the online Adaptive Learner App.³ This App has a section specifically for students in HE-902. The App contains flashcards with practice quiz questions for you to answer each week. You are required to answer at least 15 flashcard questions each week (with the option of answering more if you wish). This requirement might change during the course. The goals of this formative assessment activity are to a) build and retain knowledge about quantitative analysis topics and b) identify content and skill areas that require additional practice or attention. Your actual score on the flashcard quiz questions will NOT impact your final grade. You are only required to complete the flashcards each week, but your score doesn’t matter for your grade. Please provide any feedback on this learning activity and associated technology to Anshul at akumar@mghihp.edu .
Oral exams: You must take three oral exams, each occurring approximately during the weeks specified in the calendar. Each exam will be a one-on-one Zoom (online video) meeting between a student and an instructor. During the exam, you will be asked to show your understanding of the concepts we cover and you will be asked to demonstrate data analysis tasks on your own computer while sharing your screen on Zoom. The exams are “open-book,” meaning that you can refer to any notes or course materials during the exam. You are allowed to re-take an exam as many times as you would like, if you are not satisfied with your initial performance. If you want to get your exam dates on the calendar early, just e-mail the instructors and we can definitely do that.
Final project: You will develop and execute an abbreviated version of a full quantitative research study and submit it as a final project at the end of the term. This project will include research questions, study hypotheses, sample size/power, gathering or finding the necessary data (this can be instructor-provided if you prefer), and identifying analyses necessary to test hypotheses. Students will then conduct and interpret a full data analysis and write up results, including tables or figures, as appropriate. Some of the homework assignments will help you complete this project. Students who turn in their final project early can receive feedback and then resubmit the project after incorporating the feedback (with the grade of the resubmission being recorded as the final project grade). Details about this project will be posted within the online textbook and students will submit completed projects in D2L.

0.4 Oral exams information

Note that information for each exam might be modified or updated in the few weeks prior to when it occurs in our course schedule.

0.4.1 Skills covered in the exams

Here are some notes about what to focus on as you prepare for each Oral Exam in this course:

Oral Exam #1: Oral Exam #1 relates to content up to and including Chapter 5. Please come to Oral Exam #1 prepared to run (in R) and interpret the results of OLS linear regression models, as well as run (in R) and interpret the results of diagnostic tests of OLS assumptions. This is the primary focus of Oral Exam #1. A few other questions will also be asked, but they are secondary to the primary focus. You should also be ready to create and interpret a two-way table and import data into R from an Excel file. If you do not feel ready to demonstrate these skills by the scheduled day of your exam, you should postpone your exam to a later date, which is completely acceptable (and use the additional time to ask any questions and/or review content). I recommend that you practice these skills on your own prior to the exam.
Oral Exam #2: Oral Exam #2 relates to content up to and including Chapter 8, with a primary focus on skills that were not covered in Oral Exam #1. Please come to Oral Exam #2 prepared to run (in R) and interpret the results of logistic regression models, regression models that model nonlinear data, and regression models that model interactions. This is the primary focus of Oral Exam #2. Questions about causal inference and model specification will also be asked, but they are secondary to the primary focus. You should also review and be prepared to interpret a two-way table. If you do not feel ready to demonstrate these skills by the scheduled day of your exam, you should postpone your exam to a later date, which is completely acceptable (and use the additional time to ask any questions and/or review content). I recommend that you practice these skills on your own prior to the exam.
Oral Exam #3: Oral Exam #3 relates to content up to and including Chapter 12, with a primary focus on skills that were not covered in Oral Exams #1 and #2. Please come to Oral Exam #3 prepared to run (in R) and interpret analyses related to multilevel and/or clustered data (this includes intra-class correlation, fixed effects, and random effects), and interpret the results of ordinal and multinomial logistic regression models. This is the primary focus of Oral Exam #3. A few other questions will also be asked, but they are secondary to the primary focus. If you do not feel ready to demonstrate these skills by the scheduled day of your exam, you should postpone your exam to a later date, which is completely acceptable (and use the additional time to ask any questions and/or review content). I recommend that you practice these skills on your own prior to the exam.

0.4.2 Details and tips about the exams

How should I prepare for an oral exam? What will it test?

The exam will test your knowledge of and skills related to the quantitative methods we have learned in the chapters corresponding to each exam.
The exam will test your ability to conduct some but not all of these methods in R.
You can refer to any materials you would like—course book, your notes and assignments, online sources, anything else—during the exam. Therefore, I suggest that you refresh your memory about where you can find R code that you need, so that you can copy and paste it easily. You can also copy and paste from your homework assignments during the exam. Beyond that, I recommend reviewing the statistical concepts and their interpretations more than R code.
More weight will be given to your knowledge and interpretation of statistical concepts than your ability to write R code.

What will happen during the exam?

There is no time limit. The exam will likely take 1–2 hours,⁴ depending on your level of familiarity with the required skills and content.
We will ask you a few theoretical questions.
We will ask you to open a dataset in R and run a few data preparation commands in it.
We will ask you to conduct a series of statistical tests in R and interpret the results.
We will tell you after each task/question if you were correct or not. You can re-try some tasks on the spot if you wish. Other items can be flagged for re-testing later.
If you need to have anything re-tested, we can schedule a separate time for that or you can re-test some topics during a subsequent exam (for example, if you miss any questions on Oral Exam #1, we can re-test you on those during your Oral Exam #2).
We will try to be efficient during the exam so that we don’t run out of time.
During the exams, there might occasionally be trick questions. An example of a trick question is: Is water blue or red? This is a trick question because none of the provided answer choices are correct, so the student answering the question must say: Water doesn’t have either of those colors. Water is actually transparent. Trick questions can help us determine if a student understands the broader context of a quantitative analysis scenario or a particular data analysis technique.

Why do we do oral exams in this course?

Since ours is an asynchronous course in which we do not have regular class meetings, we instructors do not have an opportunity to interact with each of you to make sure that you are comfortable with all of the content and skills. If this were an in-person course with regular class meetings, we would use a flipped classroom model in which you would read this textbook and watch videos before coming to class and then we would do lab-style activities during the class meeting in which you would apply skills in R and interpret results, together as a group. The three Oral Exams in this course are used to replace these in-person interactions and make sure that each student has at least 3–6 hours of interaction with an instructor while doing quantitative analysis during the semester.

How and when do I schedule my oral exams?

Please e-mail ALL course instructors with times that work for your schedule, a week or two before you want to do each exam.
The recommended timings of the oral exams are given in the course calendar.

0.5 Final project details and requirements

This section contains specific expectations and requirements for the final project in this class.

These requirements have not yet been updated and might change slightly for spring 2025.

0.5.1 Description

The final project is not meant to be even close to a full quantitative research study. Another way to think about the project is that you will be writing an extended methods section and a condensed results section of an empirical research article, without writing a literature review or anything else.

Note that you can ask for help from instructors as you do the project. It is not like an exam in which you have to do each skill alone. You can send us drafts of your project at intermediate stages and we can give you feedback. We can also meet individually to discuss and advise about your project.

The requirements for the project can be changed for individual students on a case-by-case basis and only with permission from Anshul. If you think that a modification to the goals and/or requirements below may be more productive for your own professional goals and/or your goals in the PhD program, please discuss this with Anshul.

The due date for the final project can be found in the course calendar.

0.5.2 Project goals

The goals of this final project are to…

Present and interpret the results of one regression model that answers a clear and specific research question.
Run, interpret, and appropriately respond to all required diagnostic tests for this regression model and present the results of all tests.

0.5.3 Project requirements

Here are the items you must present and tasks you must complete:

Write a clear research question (RQ) that can be solved using regression analysis techniques. This research question should be a single sentence with a question mark at the end.⁵
To answer your RQ, relevant concepts will have to be first measured, recorded in a dataset as variables, and then related to each other quantitatively. Present a DAG (directed acyclic graph) that shows the relationship between all of the variables that will be involved in answering your RQ.⁶ The DAG you present does not need to be aesthetically pleasing.⁷
Identify a dataset that you will use to answer your research question. Clearly describe the dataset, including: a) population from which the data sample was drawn, b) unit of observation, c) all variables that you will use in your analysis and the unit of measurement of each variable, d) background information about the data.
Given the structure of the data and the RQ of interest, explain which type of regression model is most appropriate to answer your RQ and why. Also identify at least one other type of regression model that could also be used and explain why you instead chose the type of model that you did.
Present basic descriptive statistics that are relevant to your RQ. You should include at least one table and at least one figure/chart. All variables from your DAG must be included in these descriptive statistics.
Show the R code and results of one regression model that answers your RQ.⁸
Run and present the results of all diagnostic tests that pertain to the type of regression model you ran. Your regression model must pass all of the tests. If your diagnostics show that your model specification violates any of the assumptions of your regression model, you should fix the problem and try again until your model no longer violates the assumptions.⁹
Interpret the results of your regression model that are relevant to your RQ.
Briefly explain any limitations in your analysis.
Include all R code and results in your final submission.
Present all writing in well-written English.
Present everything in an aesthetically pleasing manner (with the exception of your DAG). It is recommended that you use an RMarkdown document, but this is not required.

0.5.4 Grading rubric

The final project will be graded according to the rubric below. Each criterion is worth a maximum score of two points unless otherwise noted.

Criterion	Score = 0	Score = 1	Score = 2
Clear RQ	Unclear, more than one sentence, not a question.	Confusingly presented but understandable.	Clear, simply written, single sentence ending with a question mark.
DAG	Not all relevant variables are shown, items that are not variables in the data are shown, arrows do not make sense, unblocked backdoor paths are present, graph is cyclical.	Minor errors.	DAG clearly shows hypothesized relationship among all variables, including any confounding, mediating, separately-acting, or unmeasurable variables.
Population and sample	Relationship between sample and population is unclear, details about population is omitted.	Minor omissions, but overall description of the population is understandable.	It is very clear what the population is and how many observations from this population were sampled and then included in the dataset used in the project.
Unit of observation	The meaning of each row in the data is not understandable from what is written.	Reader can figure out based on context, but a clear explanation is missing.	It is very clear what each row of the data means/represents. This is explicitly stated with no ambiguity or confusion.
Variables used	The variables used in the analysis are not addressed.	Some variables are mentioned but not all. How each variable is measured is not clear.	Dependent variable and all independent variables are described in one sentence each. Unit of measure (and any relevant explanation of how a variable is coded in the data) is given for each variable.
Background on data	It is not understandable where the data came from and from what context.	Few details are given about the data.	Clear explanation of where the data came from, when it was collected, who collected it, etc.
Choose model	No explanation of why the presented regression model was chosen. No comparison to another regression model. Incorrect selection of model type.	An explanation may be there but it might be incorrect, or a comparison to another model is missing.	Logical explanation of the way the data is structured and how the selected regression model is best suited to that data structure. Clear explanation of why at least one alternative regression model was not used.
Descriptive statistics	No or very few statistics presented. Statistics for irrelevant variables or information are presented.	Descriptive statistics do not cover all variables and observations relevant to the RQ. Only one of two required charts is included.	Descriptive statistics are presented for all variables listed in the DAG and used in the regression model. One well-made figure is presented. One well-made table is presented.
Regression model	Code and/or summary is not shown for regression. Code does not accomplish the type of regression that was supposed to be used.	Only partial work or result is shown. Type of regression model is unclear.	Correct regression model result is shown along with appropriate R code to execute it.
Multicollinearity test	Test not presented.	Results do not satisfy assumption. Results presented but interpreted incorrectly.	Regression model passes the VIF test of multicollinearity. A correlation matrix should be presented if necessary, but this is not required.
Independence assumption	Assumption not considered.	Assumption is mentioned but incorrectly interpreted.	The issue of independence of sampled observations is carefully discussed. Non-independent data should be accounted for appropriately in the regression model.
Other assumption 1	Assumption not considered.	Assumption is mentioned but incorrectly interpreted.	Assumption is tested correctly and interpreted correctly.
Other assumption 2	Assumption not considered.	Assumption is mentioned but incorrectly interpreted.	Assumption is tested correctly and interpreted correctly.
Other assumption 3	Assumption not considered.	Assumption is mentioned but incorrectly interpreted.	Assumption is tested correctly and interpreted correctly.
Interpret results	Many irrelevant details are given. Research question is not clearly answered.	Research question is answered but interpretation of results is not exactly correct.	Succinct interpretation of the portion of the regression output that pertains to the RQ.
Limitations	Limitations are not addressed or are completely incorrect given the regression model used.	Limitations are partially addressed.	Multiple plausible limitations to the analysis and the conclusions we can draw from it are addressed.
R code included	No R code is included	Only partial R code for the results presented is given.	R code is included (displayed in final document) for all results that were generated using R.
Writing quality (+)	Sentences and paragraphs are not formatted according to convention. Full sentences are not used much or well.	Minor grammar and/or spelling errors occur throughout, but the main points are understandable.	Writing is clear and succinct. It is easy to read quickly and understand the analysis and the results. No grammar or spelling errors.
Aesthetics	Project is presented in a confusing manner. Order and flow of requested items is not logical. Unnecessary fonts, symbols, and formatting layout appears.	Minor blemishes and errors are visible in the submitted project.	Order of all content is clear and logical. Sections and sub-sections are logically and clearly marked. The write-up is easy to read.

Items marked with a (+) in the table above will carry more weight than just two points. All other items have a maximum score of two points.

Your grade on the project will be the number of points achieved divided by the total number of points possible.

If you are not satisfied with your grade on this project, you do have the option of taking an INCOMPLETE grade for the course. Then, you will improve and re-submit your project in the weeks that follow the end of the course. We will re-grade the project and then put your improved final grade for the course into the grading system. Please be sure to communicate with course instructors about this option right away, if you think you might choose it.

0.6 Materials, software, and accounts

No purchases are necessary (as long as you already have a computer that can run the necessary software). All necessary materials are either a) free and available online or b) provided to you by the Institute for free.

Texts/Readings: There is no requirement for students to purchase any texts or readings for this class. All materials are available freely online.
Statistical software: All students are required to install R and RStudio on their own computer. R is a free and open-source statistical computing platform and RStudio is a free software that makes R easier to use. Instructions for installing R and RStudio will be provided by the instructor. R and RStudio should run well on computers running Mac, Windows, and Linux operating systems.
Flashcard account: All students are required to make an account in the Adaptive Learner App (or make an alternate arrangement with the instructors) to answer questions presented on at least 15 flashcards per week.
Videoconferencing software: All students will have access Zoom Pro based on enrollment in the PhD-HPEd program at MGHIHP; it should be installed on the student’s computer for group and/or individual meetings with instructors and classmates.
Generative AI account: When used responsibly, generative AI tools such as Chat GPT are very useful for conducting statistical analysis. Throughout this course, we will be recommending that students use Chat GPT for selected portions of the quantitative analysis process. We strongly recommend that all students make an account to use the free version¹⁰ of Chat GPT.
Spreadsheet software: Some exercises or data manipulation in this course may need to be done in Excel or a similar spreadsheet software. Students can complete this work in any spreadsheet software such as Microsoft Excel, Google Sheets within Google Drive (free), or Open Office (free).

0.7 Always remember

Below is a list of items that it is critical to always remember, once you have finished learning many of the topics in this textbook.

Every p-value is the result of a hypothesis test. Every time you see a p-value, figure out the null and alternate hypotheses. \$1-p\$ is the level of support for the alternate hypothesis. Click here to read more about it.
Magic words to interpret linear regression results: For every one unit increase in \$x\$ (an independent variable), \$y\$ (dependent variable) is predicted to change on average by \$b_x\$ (slope) units, controlling for all other independent variables. DO NOT reverse the positions of X and Y in these words. Read more.
Magic words to interpret odds ratios: For every one unit increase in \$x\$ (an independent variable), the odds of \$y\$ (event or outcome) are predicted to change on average by \$OR\$ (odds ratio) times, controlling for all other independent variables. DO NOT reverse the positions of X and Y in these words. Read more.
All quantitative results are only telling us associations between variables, NOT causal relationships. Read more.
No regression model conclusions can be trusted for inference until the model passes ALL required diagnostic tests of model assumptions.
Use estimated effect sizes and confidence intervals—NOT p-values—to determine if quantitative results are meaningful and relevant. Read about effect size, read about confidence intervals.
Unmeasured confounding,¹¹ selection bias, measurement error,¹² and model misspecification are four possible problems that can make quantitative results un-trustworthy. Read more.
You must know the structure and data generating mechanism of your data very well. Otherwise, clustering, non-independence, Simpson’s paradox, and other problems could cause you to draw false conclusions. Read more.
All quantitative analyses have limitations. Be sure to report what you did transparently and responsibly.

0.8 Acknowledgments

The building blocks for this textbook are taken from A Minimal Book Example by Yihui Xie. This work would not be possible without this excellent guide.
Much of the content for this book is influenced by the teaching and research conducted by my colleagues and students.
The various efforts of Roger Edwards, Nicole Danaher-Garcia, Grace Ming, Valay Maskey, Tony Sindelar, Rupali Khadye-Hadshi and all students who have taken the course HE902 at MGHIHP in the past have been particularly instrumental in the development of this course and online textbook.

This is a footnote. You can go back to where you were reading by clicking on the little squiggle arrow right here: ↩︎
This paragraph includes input from experts at the JEDI office and instructional design team at MGHIHP.↩︎
If you prefer not to use the Adaptive Learner App, ask the instructors for an alternative way to complete this course requirement.↩︎
But it could take less than an hour and it could take more than two hours. Both have happened before and are perfectly fine. The goal is not to be fast. The goal is to do everything at a high quality level.↩︎
There are no exceptions to this requirement.↩︎
You SHOULD include variables that you theoretically believe are related to your RQ, even if you don’t have those variables in your dataset.↩︎
You can even submit a photo of a hand-drawn DAG if you would like. All that matters is the content of your DAG, not the presentation.↩︎
In reality, you will likely run many regression models on your own to arrive at the one that fits your data the best. But you do not need to show all of this work in your final submission. If you do wish to show all of this additional work, you can include it in an appendix to your assignment, but this is not required.↩︎
It is common to take advice from an instructor during this process. Feel free to contact us during this or any other part of your final project work.↩︎
It is also fine to use the paid version, but we do not believe this will give you any advantages over the free version, for the purposes of this class.↩︎
Unmeasured confounding can cause omitted variable bias in quantitative results.↩︎
Measurement error is also called information bias.↩︎

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Handling Data in R, Linear Relationships Review

This chapter contains the only content that you need to look at for the first week of the course. You can ignore all subsequent chapters in this textbook, for now.

Please read this entire chapter and then complete the assignment at the end. As you read, I recommend that you copy and paste all of the code into RStudio on your own computer, both to practice and to make it easier to do the assignment.

Since this is an advanced, PhD-level course, the first few weeks will include a review of basic statistical and math concepts at a fast pace.

I recommend that you quickly skim through the assignment at the end of the chapter before going through this chapter's content, so that you know in advance the tasks that you will be expected to do.

This week, our goals are to...

Become familiar with this textbook and the structure of the course.
Import, explore, and manipulate data in R and RStudio.

Please continue to the next section to begin your work in this course!

Welcome video

If you have not done so already, please watch the following welcome video for our course, HE-902:

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This video can be viewed externally at https://youtu.be/XUMwNmyGhh0{target=\"_blank\"}.

Course basics

rm(list=ls())

Since this is the first week of the course in which you will submit an assignment, we will go over a few administrative and workflow items now.

Below is some information about how to use this textbook and how the course will work on a weekly basis.

Like most other courses in the PhD program in Health Professions Education at MGHIHP, this is an online asynchronous course. This means that there are no regularly scheduled class meetings. Instead, you and your fellow students will consume each week's learning materials and complete all assignments according to your own preferred schedule within each week. We will also hold optional (not required) \"office hour\" meetings on Zoom each week which you can attend if you have questions and/or would like to work together with your classmates.
Chapter 0{target=\"_blank\"} of this textbook contains information about the course. Please read it if you have not done so already. The course calendar{target=\"_blank\"}, final project{target=\"_blank\"}, and oral exams{target=\"_blank\"} sections might be particularly useful.
Throughout this textbook, you will find many links that you can click on. These are marked in blue underlined text like this{target=\"_blank\"}. Any time you see blue text like that, keep in mind that you can click on it! You can practice by clicking here{target=\"_blank\"}.
Each week of the course, a chapter of this textbook will be assigned for you to use. This week---the first of the course---the assigned chapter is Chapter 1, the one you are reading right now. You can look up which chapter is assigned for each week in the course calendar{target=\"_blank\"} in the introductory chapter. This week, you should read through all of the text in this chapter, watch any videos, and then complete the assignment at the end of the chapter. Everything you need to do this week is exclusively in this chapter. And you will do the same for chapters assigned in future weeks.
The due date of each assignment is usually Sunday night at the end of each week. Assignment due dates are given in the course calendar{target=\"_blank\"} in the introductory chapter. Assignments should be submitted in D2L. Any other submission instructions will be included in each individual assignment.
For the majority of this course, as you go through each chapter, you will encounter R code. As you read, I highly recommend that you copy and paste all provided R code into an R file on your own computer and run it on your own computer. This will not only help you practice you data analysis skills but also make it easier and faster for you to do each assignment. Remember that you should paste/write all of your code into an R script file and then save your work in that file as you go. DO NOT type your code directly into the console, because then it will not be saved.
Sometimes in this online textbook, the code provided is for illustrative purposes only and may not run for you when you copy and paste it into RStudio on your own computer. Nevertheless, I recommend that you still paste all code into RStudio into your own computer as you read, so that you have it available for future use, including when you do the assignment at the end of the chapter.
In RStudio, note that you can customize the layout. For example, you can click on View -> Panes -> Console on Right to move RStudio's console to the right side of the screen. I personally prefer the console to be on the right side. In some of the instructional videos you watch in this course, the layout of RStudio might be a little bit different from how you have it on your own computer.
If you find that the work for a given week is taking you too long, I recommend that you stop and send an e-mail to all course instructors. For example, if you get stuck on the first few lines of code and realize that you have spent a long time trying to debug them but you still can't get them to run properly, I recommend that you stop at that point (or even sooner) and contact us. We can meet on Zoom and work through a section of the code and/or content with you so that you finish at a pace that is reasonable for your schedule. Please overcommunicate with us rather than undercommunicate. Do not hesitate to contact us!
In this textbook, we will often learn multiple ways of achieving the same result. For example, we will see multiple ways to recode a variable or display results. You are not required to learn all of the ways to do each task. It is fine if you choose a strategy that works for you and use that. You also do not need to memorize all of the code and details in this textbook. It is fine to refer back to these materials, your own notes, and other resources on a regular basis to look up how to do certain tasks in R.

Now you are ready to start the course, by reading the rest of this chapter and then doing the assignment at the end!

Set up and test software {#orientation}

Before we start learning about data analysis, we need you to set up some tools on your computer. You can complete this process synchronously during a meeting with an instructor or on your own. If you do this procedure on your own, the videos embedded below might be helpful (although you are not required to watch them). You do not need to submit any proof or documentation that you did this process.

Make sure you do the following procedure on the same computer that you plan to use during the course.

o1 <- 0

Basic use

We'll start with some basics to get everyone set up and navigate within RStudio, the software you'll be using for most of your work in this class.

This video summarizes how you can install R and RStudio on your computer:

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The video above can be viewed externally at https://youtu.be/6Xc2wuUVDWA{target=\"_blank\"}.

Task r o1<-o1+1; o1: Download and install the appropriate version^[This is usually just the latest version.] of R from https://cran.rstudio.com/{target=\"_blank\"}.

You do NOT need to open R, which you just installed above, on your computer. R just needs to be there. We won't actually use it directly. I know this might be confusing or frustrating. We will use RStudio instead, which you will install next.

Task r o1<-o1+1; o1: Download and install the appropriate version of RStudio from https://posit.co/download/rstudio-desktop/{target=\"_blank\"}.

Now that you have RStudio downloaded and installed on your computer, you can open RStudio (not R, which you installed previously) on your computer and proceed to the next task. We will use RStudio (not R) for all of our work in this course. Please Open RStudio on your computer and proceed to the next task.

The following video will walk you through the first steps of using RStudio (once you have already installed it).

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The video above can be viewed externally at https://youtu.be/_FVq-Vyyyfs{target=\"_blank\"}.

Task r o1<-o1+1; o1: Create a new R file.

To create a new R file, click on File -> New File -> R Script.

You can think of an R file as a Microsoft Word file but for data analysis.

Task r o1<-o1+1; o1: Save the new R file you just created. You could also create a new folder for all your work in our class, if you want, and save your R file in there.

Task r o1<-o1+1; o1: Find your new file within the Files tab within RStudio.

Task r o1<-o1+1; o1: Type 2+3 into a line of your new R file and then click the Run button. Locate the console and see what happened there. It should look approximately like this:

2+3

Task r o1<-o1+1; o1: In a new line of your R file, type 2*3 and click on Run. You should see something like this in the console:

2*3

As you can see, R can help us do basic arithmetic. You could also type 2-3 or 2/3 for subtraction and division. And you can of course change the numbers 2 and 3 to other numbers.

Data loading and viewing

Now it's time to load some data and look at it together!

This video demonstrates the process of loading and viewing data in R and RStudio:

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The video above can be viewed externally at https://youtu.be/A9mQSqbx2hE{target=\"_blank\"}.

Task r o1<-o1+1; o1: Let's make a new dataset called d, using the code below.

Type this code into a new line of your R file and run it:

d<-mtcars

Now look in your Environment tab in RStudio. You should see a new data item called d.

What we did using the command above is that we created a new data object called d and we assigned d to contain the data within mtcars. mtcars is a dataset that comes along with R. It is built-in for us to practice with, like we are doing now!

Task r o1<-o1+1; o1: You can run the command ?mtcars to pull up some information about this data, if you would like.

Task r o1<-o1+1; o1: Type View(d) (with a capital V) into your R code file (in a new line, of course!) and run it.

A data viewer should pop up in a new tab, showing you your dataset in spreadsheet view.

Close the data viewer.

Task r o1<-o1+1; o1: Double click on d in the Environment tab. This should also bring up the data viewer.

Task r o1<-o1+1; o1: Now let's inspect our data in the data viewer. What are some of your observations?

Task r o1<-o1+1; o1: What does each row in the data represent?

Task r o1<-o1+1; o1: What does each column in the data represent?

Descriptive statistics

Let's go back to the R code file tab and do some simple analysis on our data.

In the video below, you can see how to calculate some basic descriptive statistics in R and RStudio.

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The video above can be viewed externally at https://youtu.be/SNF01zoJ42I{target=\"_blank\"}.

Task r o1<-o1+1; o1: Type d$ into your code file (in a new line, of course). A list of columns (variables) should pop up. Select mpg.

Now your line of code should say d$mpg.

Go ahead and run that line. You should get a result like this:

d$mpg

Above, the computer gave you all of the data just from the column labeled mpg from our data.

Task r o1<-o1+1; o1: Now let's calculate the mean of the column (variable) mpg.

mean(d$mpg)

Remember, put the command above into a new line of your code file and then run it. And you should see the result above in your console.

Task r o1<-o1+1; o1: How about the standard deviation of mpg? See below.

sd(d$mpg)

We have now calculated the mean and standard deviation of the mpg variable.

Task r o1<-o1+1; o1: We can also get a summary of the mpg variable as follows. Please add it to your code file and try it out!

summary(d$mpg)

The output above gives us a number of metrics, although it does not include standard deviation.

Task r o1<-o1+1; o1: Try running the mean, sd, and summary commands for a different variable that you choose.

Simple visualizations

We will continue with our brief exploration of our data by making some visualizations.

The video below demonstrates how to make a few simple visualizations---histograms and scatterplots---in R and RStudio. It also shows one possible way to close RStudio on your computer.

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The video above can be viewed externally at https://youtu.be/qS3Fh2S7Kd4{target=\"_blank\"}.

Task r o1<-o1+1; o1: Run the command hist(d$mpg) (again, make sure you're adding the command in a new line of your code file). You should then see a histogram in RStudio.

hist(d$mpg)

Task r o1<-o1+1; o1: And now let's make a scatterplot using plot(d$wt,d$mpg).

plot(d$wt,d$mpg)

Above, we see that the more a car weighs (wt), the worse its fuel efficiency (mpg).

Task r o1<-o1+1; o1: Try making some other histograms and scatterplots!

Installing and loading packages

Finally, we will practice installing and loading packages to make sure this functionality is working correctly on your computer.

As always, make sure that you put all new lines of code into your R code file.

The following video shows how to install a package and then load that package in R and RStudio:

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The video above can be viewed externally at https://youtu.be/66HUNn4-92k{target=\"_blank\"}.

Task r o1<-o1+1; o1: Run the command install.packages(\"car\"). You should then see a bunch of output in the console. The process might take a while.

Once the process is over, the car package should be installed on your computer. You can see a list of installed packages in the Packages tab, if you want. There will be many packages there.

Task r o1<-o1+1; o1: Finally, run the command library(car) to load the car package into your current R session.

You have reached the end of the R and RStudio setup process! Please continue below to set up other tools.

Set up Adaptive Learner App

As part of this course, you are required to answer questions on at least 15 flashcards each week (you do not need to get all of the questions correct). The best way to do this is in the Adaptive Learner App,^[Discuss with the instructors if you prefer to do your weekly flashcards without using the app.] which you can see how to set up below.

This video shows the setup process and basic use for the Adaptive Learner App:

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This video can also be viewed externally at https://youtu.be/hADmBJ0aD-g{target=\"_blank\"}

Task r o1<-o1+1; o1: Go to https://educ-app-2.vercel.app/{target=\"_blank\"} and click on sign up.

Task r o1<-o1+1; o1: Enter your registration information (any email address is fine), review the terms of service and privacy policy, and click sign up.

Task r o1<-o1+1; o1: You should receive an email asking you to verify your email address. The email should come from noreply@educ-app-2.firebaseapp.com. You might need to search in your junk folder for it. Click the link within the email to verify your account.

Task r o1<-o1+1; o1: Click on the tile that says Spring 2025 HE902: Advanced Regression Analysis.

Note that each week when you do your flashcards, you do not need to submit a record of completion. The system will remember how many flashcards you did and we (the instructors) will be able to see it on our end.

Now you are ready to use the Adaptive Learner App! Continue the set-up process below.

Set up Chat GPT (optional)

Generative AI tools such as Chat GPT can be useful when doing data analysis, especially to debug R code. During this course, we encourage you to experiment with using Chat GPT or a similar tool to debug R code. We recommend that you set up a free Chat GPT account at this time if you don't already have one. It is not necessary to have a paid Chat GPT account or other paid generative AI account.

The following video demonstrates how to sign up for the free version of Chat GPT as well as some other example uses. If you already have an account have have used Chat GPT for a few hours, this video will not be useful.

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The video above can be viewed externally at https://youtu.be/0NUkAoO_yi4{target=\"_blank\"}.

Task r o1<-o1+1; o1: Go to http://chat.openai.com{target=\"_blank\"}

Task r o1<-o1+1; o1: Sign into your existing account or make a new free account.

Task r o1<-o1+1; o1: Put the text from the following box into a new Chat GPT prompt (copy all of the lines at once).

In R, I want to get the mean of the variable mpg within the dataset R. Here's my code:\n\nmean(d%mpg)\n\nBut it's not working. I get this error message: \n\nError: unexpected input in \"mean(d%mpg)\"

Chat GPT should reply to you with an explanation that your code should be mean(d$mpg) instead of mean(d%mpg). This is helpful. But it might also provide other information that is confusing to a beginner.

IMPORTANT RECOMMENDATION: Note that Chat GPT might sometimes give you incorrect or confusing code. I recommend that you use it only for fixing errors, instead of for generating new code to do your assignments and analysis. This means that you should use the code given to you in this textbook, not code given to you from Chat GPT. If the code in this textbook doesn't run correctly, then giving the code and the error message to Chat GPT might be helpful. If the textbook uses one line of code to accomplish an analysis task and Chat GPT recommends four lines of code instead (or Chat GPT recommends code that uses different symbols and operators), that is probably not the best approach. But if Chat GPT can slightly modify the single line of text from the textbook so that it works correctly, then it might be useful to you.

You have now completed the process of setting up the tools that you will use in this class.

Selected R functionality and operations

During the set-up procedure, we downloaded R and RStudio, ran some basic operations, loaded the built-in dataset mtcars, and created a few descriptive tables and visualizations. In this section, we will learn about a few additional basic functionalities in R that we will be using on a regular basis.

You might be wondering about what R and RStudio are exactly. Here are some key distinctions:

R is the programming language that we will use to do all of our work. All of the code that you will write and run will be in the R programming language. You can think of R just like a language like English, which we write using numbers, letters, and symbols. When someone asks you which software you used to do your analysis, you should say, \"I used R.\"
RStudio is a software that we use to help us use the programming language R. RStudio makes it easier to write R code and also provides us with a number of additional tools to do our work. While R is a language like English, RStudio is a tool---analogous to Microsoft Word---that we use to write that language. When someone asks you which software you used to do your analysis, you should NOT say: \"I used RStudio.\" You should say: \"I used R.\"^[There may be exceptions to this guideline depending on what exactly you use RStudio for, but in general this is likely the right thing to say.]

When you are doing work for this course, ALWAYS open the program called \"RStudio\" on your computer. DO NOT open the program called \"R\" or anything else.

Functions

Many of the actions that you will do in R will use functions. A function will have its own unique name, such as table or lm or SomeOtherName. When you use a function, you will type the name of the function and then parentheses. Within those parentheses, you will often---but not always---write some more instructions. These instructions within the parentheses are called arguments. Arguments should be separated by commas. Two examples are below.

Example with table(...) function:

table(mtcars$vs, mtcars$am)

Above, we told the computer to run the table function and it contained two arguments: mtcars$vs and mtcars$am.

Example with a hypothetical function called SomeOtherName, for illustrative purposes only:

SomeOtherName(data = df, title = \"cats have one life each\",'AuntArtIca', mustard, worms)

The code above is completely fake and made up. Nevertheless, it follows the logic of R code and functions in R. Above, we are telling the computer to run the hypothetical function SomeOtherName and we are giving five arguments to the function, within parentheses and separated by commas. These five arguments are all very different from each other, which is common in R commands that you might write.

Note that in situations where quotation marks are used, both single (') and double (\") quotation marks can be used interchangeably. In the function above, the words cats have one life each are surrounded by double quotation marks but they could be surrounded by single quotation marks (like AuntArtIca is) and that would also be fine.

You will encounter a huge variety of functions and arguments within those functions as you continue to use R.

Installing and loading packages

When you download R to your computer, it comes along with many possible commands and analysis options that you can use. Quite often, you will find the need to run additional commands that did not come with R when you downloaded it. To add functionality to R on your computer, we have to install what are called packages.

To install a package to your computer, you will run a command like this:

if (!require(packagename)) install.packages('packagename')

In the code above, you would replace the word packagename with the actual name of the package you want to install. The code above checks whether a package is already on your computer or not. If it is not, the package will get installed to your computer. If it is already on your computer, nothing will happen.

If you want to force the computer to install a package no matter what, you can run this code:

install.packages('packagename')

Once a package is on your computer, you can load it using the library(...) function:

library(packagename)

When you are using the code above on your own, you would replace the word packagename with the name of the package you want to load.

My favorite way to use a package is with the following two lines of code:

if (!require(packagename)) install.packages('packagename')\nlibrary(packagename)

The code above should take care of everything. Just replace packagename---in all three places where it appears above---with the name of the package you want to load.

What is the difference between installing and loading a package?

Installing: Installing a package---if (!require(packagename)) install.packages('packagename')--- is like going to a hardware store, buying a new toolbox full of tools, bringing it home and putting it in the closet. You can also think of it as analogous to downloading an app from the app store onto your smartphone. A new package only needs to be installed once.
Loading: Loading a package---library(packagename)---is like going to your closet, getting a toolbox, and opening the toolbox so that you are ready to use the tools inside. You can also think of this as analogous to going to the home screen and opening an app that has already been downloaded to your smartphone, but had not been open recently. Every time you want to use a package, you have to load it again using the library(...) function.

It is fine if installing, loading, and any other details about packages still do not make sense to you at this time. You will get a better sense for it as you use R and some of its packages more.

Example of installing and loading a package

One package we will use later in this textbook is the NHANES package. This is how we first install and then load the NHANES package:

if (!require(NHANES)) install.packages('NHANES')\nlibrary(NHANES)

Additionally, information about many packages is often available online. For the NHANES package, information is available here: https://cran.r-project.org/web/packages/NHANES/NHANES.pdf{target=\"_blank\"}.

Quick-reference resources

The following quick-reference guides might be useful to you as you use R. Opening these guides is optional (not required).

Base R Cheat Sheet -- https://iqss.github.io/dss-workshops/R/Rintro/base-r-cheat-sheet.pdf{target=\"_blank\"}
Getting Started with R Cheat Sheet -- https://www.datacamp.com/cheat-sheet/getting-started-r{target=\"_blank\"}

Loading and exploring data in R

In this section of the chapter, we will learn how to set R's working directory, load data from an Excel file into R, make descriptive tables, subset our data, transform variables (columns in our data), recode variables, and remove duplicate observations (rows in our data). You will also practice skills such as installing and loading any required R packages, writing code into an R script file, and saving your work.

As you go through this section of this chapter, I recommend that you follow along by copying and pasting all of the provided code below into your own R file on your own computer.

Set the working directory in R and RStudio

As you practiced during the set-up procedure, R can interact with files on your computer. You practiced saving an R script file on your computer. To save the file, you had to tell your computer a folder in which you wanted to save the file. Note that directory is another name for folder (on your computer).

When you are loading files from and saving files to your computer, you need to tell R where on your computer to look for those files. The place where R will look is called the working directory. Any time you start using R, you should set the working directory. This will be done using a line of code which you can keep towards the top of the code file you are using.

Here is the function that you can use to set the working directory on your computer:

setwd(\"C:/path/on/your/computer/to/a/folder\")

Above, you will replace C:/path/on/your/computer/to/a/folder with an actual file path on your computer. There are a number of ways to do this in RStudio.

To figure out what the current working directory on your computer is---both before and after you run the setwd() command---you can run the following function:

getwd()

Please watch the video below which shows multiple methods of how to set your working directory in R and RStudio.

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The video above can also be viewed externally at https://youtu.be/_YK6Gwvr1Fw{target=\"_blank\"} or https://tinyurl.com/RStudioSetWD{target=\"_blank\"}.

Remember that you only need to know one way to set your working directory in R and RStudio. You can choose whichever way is best for you. You do not need to use all of the methods demonstrated in the video, just one.

In the video, the command used to set the working directory is:

setwd(\"C:/My Data Folder/Project1\")

Above, I had a folder on my computer that was called Project1 which was located in another folder called My Data Folder which was on my C: drive. Perhaps you have created a folder for all the work you do in this course, in which case you can set that folder as your working directory using the setwd() command like I did above, but with a different file path within the quotation marks.

It is also possible to see a list of all of the files within your working directory by running the following code:

list.files()

The result of the code above is not shown. If you run the list.files() function (with no arguments included) on your own computer, you should get a list of files in your working directory (which is where R will look for files if you ask it to).

Remember that a folder is different from a file. A folder is a container on your computer that holds files. Work you do in Microsoft Word, Excel, and R are saved in individual files. Those files are then saved in folders on your computer. A directory is the same thing as a folder. setwd stands for \"set working directory,\" which means \"set the folder where R should look for stuff.\" When you set the working directory, you have to put a folder---not a file---inside the quotation marks in the setwd() function.

Load Excel data into R

Loading data into R from an Excel file is a very useful skill that you are likely to need both in our course and in your own quantitative analysis work in the future. As with most processes in R, there are multiple ways to do this. Two methods are shown below, but you only need to know one. In most cases, either of these methods will accomplish what you need to do. I have included a video that shows how to do this for one of the methods.

Of course, before you load data from Excel into R, you first need to have an Excel data file to load. Please follow the procedure below:

Click here{target=\"_blank\"} to download an Excel file.^[Data source: Excel Sample Data. Contextures. https://www.contextures.com/xlsampledata01.html{target=\"_blank\"}.]
Save the downloaded file in your working directory, the same working directory you designated in the earlier section. The file is a ZIP file called sampledatafoodsales.zip.
Open the file sampledatafoodsales.zip and you should find an Excel file within it called sampledatafoodsales.xlsx.
Copy sampledatafoodsales.xlsx into your working directory.
Open the file sampledatafoodsales.xlsx in Excel (not R or RStudio) to see what it is like.
Notice that the data file (in Excel) contains three sheets. The data we want is in the second sheet, called FoodSales.

Now you are ready to load the Excel data in sampledatafoodsales.xlsx into R using one of the two methods below. If one of the methods doesn't work, try the other! It is fine if only one method works for you.

Method 1 -- readxl package

This method uses the readxl package to load data from an Excel file into R. This is my favorite way to load Excel data into R.

The video below goes through the procedure, in case you wish to watch rather than read about it:

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The video above can also be viewed externally at https://youtu.be/AxDcbmxQnxE{target=\"_blank\"} or https://tinyurl.com/LoadExcelRStudio{target=\"_blank\"}.

Below is a written explanation of the procedure to load Excel data into R using the readxl package.

You can begin the procedure by loading the readxl package with the following code:

if (!require(readxl)) install.packages('readxl')\nlibrary(readxl)

Remember, any time I give you some code, you should copy and paste it into your own code file in RStudio on your own computer! Be sure to copy the lines of code above---and all subsequent lines of code---into your own code file.

Let's review the two lines of code above:

if (!require(readxl)) install.packages('readxl') -- This line checks if the package readxl is already installed on your computer. If it is not, then it installs the package for you. Keep in mind that installing a new package can often take many minutes.
library(readxl) -- This line loads the readxl package into your current session of R. By the time we get to this line, the readxl package should be installed already, because either it was already on your computer or it was installed by the previous line of code.

Now that the package is installed and loaded, you can load the Excel file from the working directory, using the code below:

dat<- read_excel(\"sampledatafoodsales.xlsx\", sheet = \"FoodSales\")

Above, we created a new dataset in R (technically called a data frame) which is called dat. We could have called it anything else we wanted, different than dat. Our new dataset dat contains the data in the sheet called FoodSales in the Excel file called sampledatafoodsales.xlsx.

Here are some more detailed notes about what we did:

You can change dat to whatever you want your dataset to be called in R. This name should show up in RStudio's Environment tab once you run the command.
The read_excel() function has two arguments in the code above. Let's go through them:
- file=\"sampledatafoodsales.xlsx\" -- This tells the computer which Excel file you want it to look at, within the working directory.
- sheet = \"FoodSales\" -- This tells the computer to look at the sheet called FoodSales within the Excel file.

Method 2 -- xlsx package

DO NOT use this method if Method 1 above worked for you. This (Method 2) is just a backup option. You can skip to the next section if Method 1 worked.

This method uses the xlsx package, which you can load by running the following code:

if (!require(xlsx)) install.packages('xlsx')\nlibrary(xlsx)

Let's review the two lines of code above:

if (!require(xlsx)) install.packages('xlsx') -- This line checks if the package xlsx is already installed on your computer. If it is not, then it installs the package for you. Keep in mind that installing a new package can often take many minutes.
library(xlsx) -- This line loads the xlsx package into your current session of R. By the time we get to this line, the xlsx package should be installed already, because either it was already on your computer or it was installed by the previous line of code.

Now that the package is installed and loaded, you can load the Excel file from the working directory, using the code below:

d <- read.xlsx(file=\"sampledatafoodsales.xlsx\", sheetIndex = 2, header=TRUE)

Above, we created a new dataset in R (technically called a data frame) which is called d. We could have called it anything else we wanted, different than d. Our new dataset d contains the data in the second sheet of the Excel file called sampledatafoodsales.xlsx.

Here are some more detailed notes about what we did:

You can change d to whatever you want your dataset to be called in R. This name should show up in RStudio's Environment tab once you run the command.
The read.xlsx() function has three arguments in the code above. Let's go through them:
- file=\"sampledatafoodsales.xlsx\" -- This tells the computer which Excel file you want it to look at, within the working directory.
- sheetIndex = 2 -- This tells the computer to look at the second sheet within the Excel file. If you want it to look at sheet #3, change the 2 to 3 in this code.
- header=TRUE -- This tells the computer that the very first row of your Excel file contains variable names, and not raw data.

Double-check your data

Once your data is loaded into R from the Excel file, you should double-check to make sure that it was loaded correctly. Let's say that you named your data file dat, as in one of the examples above. You should be able to see a new Data item within the Environment tab in RStudio. You can double-click on dat within the Environment tab and a data viewer should pop up, showing you your Excel data within RStudio itself.

Another way to view the data is to run the following command:

View(dat)

Running the command above should also open up a data viewer in RStudio for you to view your data. If you named your data something other than dat, then replace dat with your data's name in the command above. For example: View(someothername).

Compare your data in the RStudio viewer with the data in Excel. It should be identical. Always be sure to double-check everything before you proceed!

If you want to just look at the first few rows of your dataset, you can use the head(...) function:

head(dat, n=10)

In the code above, we put dat and n=10 as two separate arguments^[These two arguments are separated by a comma.] into the head(...) function. This tells the computer to take the dataset dat and display the first 10 rows of it for us. If we had changed the number 10 to a different number, like 15, then it would show us the first 15 rows of the data.

If you want your entire dataset to be outputted by R, you can simply type the name of the dataset into a line of code and run it, like this:

dat

The result of the code above is not shown, because it would be too long and not useful for us. All 244 rows of the dataset would have been displayed. You can try this on your own computer as you follow along.

Now that you have loaded data into R, the next sections will show you how to explore and manipulate this data.

Explore our data

Below, you will learn how to explore selected aspects of any data that you have loaded into R, such as the looking up the number of rows and columns and the names of all variables (columns). In the examples below, the name of the data that we are using in R is dat. But you can replace dat with any other name such as d, mydata, mtcars, AnyNameYouDecide.

Since we have already loaded a dataset called dat above, we will continue to use dat as our example dataset in this chapter. When you do analysis of your own, the name of your dataset might be something other than dat, so you can replace the word dat with the name of your own dataset when you use the R commands shown below. Your data will also contain variables (columns) with different names than the variables in the examples below. You can write your own dataset's variable's names in place of the ones in the examples.

Size of dataset

Let's start by looking up the number of rows in the data:

nrow(dat)

Above, using the nrow() function, we asked the computer to tell us how many rows are in the dataset dat. It told us that there are 244 rows. A row of data is also called an observation.

Next, let's look up the number of columns in the data:

ncol(dat)

Above, using the ncol() function, we asked the computer to tell us how many columns are in the dataset dat. It told us that there are 8 columns. A column of data is also called a variable.

There is also a way to look up the rows and columns simultaneously:

dim(dat)

Above, the computer told us that dat contained 244 rows (observations) and 8 columns (variables).

Variable names and characteristics

As mentioned above, each column represents a variable. A variable is a characteristic that we have recorded about each observation. Each variable has a name, which is listed in the very first row of the spreadsheet in which the data is kept.

You can quickly view the names of all of the variables in your data using the following command:

names(dat)

As you can see above, when we ran the names() function on our dataset dat, the computer printed out all of the names of the 8 variables.

We can also use the str(...) function to learn more about our dataset dat:

str(dat)

str stands for structure. The str(...) function can be used to examine a variety of stored objects in R, not only datasets like dat. In the output above, we see a list of all variables as well as some details about each variable. We see that variables like Region and City are variables of type chr, which stands for character. Character variables contain words and letters. Qualitative categorical variables like Region and City are often coded as chr or factor variables. Variables like Quantity and UnitPrice are numeric variables, which is why they are labled as num.

It is also possible to look up some specific details of a single variable.
We can determine a variable's type by using the class(...) function:

class(dat$Region)

Above, the computer tells us that the variable Region within the dataset dat is a character variable. This tells us that Region is not a numeric variable and is instead a qualitative categorical variable.

Looking up the number of rows, number of columns, names of columns (variables), and variable types in your data are important processes to keep in mind and use on a regular basis as you do your data analysis.

One-way tables

Another very important tool is a table. A table will tell you how your observations fall into categories of a particular variable. It is easiest to start with an example.

You can run the following code to make a one-way table:

table(dat$City)

Here is what we did with the code above:

We used the table() function to tell the computer to make a table.
We had to tell the computer what to make a table of, by putting something into the parentheses within the table() function. We told the computer that we wanted it to make a table based on the City variable within the dataset dat.

The computer then broke down the 244 observations in the dataset dat into the four possible values of City that an observation can have. For example, we know that 62 observations have New York as their City.

If we wanted to, we could change City in the code above to a different variable, like this:

table(dat$Region)

Above, the computer now broke down all 244 observations according to the variable Region.

What if we make a table of the variable Quantity? Let's try it.

table(dat$Quantity)

Above, we received an enormous table from the computer which isn't that helpful to us. City and Region are categorical variables that allow us to easily group our observations. Quantity is a continuous numeric variable and most observations have a unique value for Quantity, so making a table isn't as useful.

What if you want to slice your data according to more than just one variable? That's where two-way tables come in. Keep reading!

Two-way tables {#TwoWayTable}

A two-way table is very similar to a one-way table, except it allows you to use two variables to divide up your observations. Let's see an example.

You can run the following code to make a two-way table:

table(dat$City, dat$Region)

Here is what we did with the code above:

We used the table() function to tell the computer to make a table.
We had to tell the computer what to make a table of, by putting something into the parentheses within the table() function. We told the computer that we wanted it to make a table with a) the City variable within the dataset dat in the rows and b) the Region variable within the dataset dat in the columns.

The computer then broke down the 244 observations in the dataset dat into the four possible values of City that an observation can have and the two possible values of Region that an observation can have. For example, we know that 55 observations have Los Angeles as their City and West as their Region. 0 cities have Los Angeles as their City and East as their Region.

You may have noticed that the two-way table above does not label which variable is shown in the rows and columns. Sometimes, this can make it confusing to figure out which variable is in which place. If we use the with(...) function and put the table function within it, we can add variable labels.

Here we put the table(...) function within the with(...) function to make a two-way table with labels:

with(dat, table(City, Region))

While the table(...) function is a convenient way to make tables that is built into R, there are also other ways to make tables. One way is the cro(...) function from the expss package.

This code recreates the two-way table above using cro(...):

if (!require(expss)) install.packages('expss')\nlibrary(expss)\n\ncro(dat$City, dat$Region)

Percentage tables {#proptables}

It is also possible to make one-way and two-way tables that show percentages instead of counts. Please see below for examples and code.

Let's start with a one-way table of the variable Category from the dataset dat, using the code below:

table(dat$Category)

To convert the table above to a table with proportions, we will take the code above---table(dat$Category)---and put it all inside of the prop.table(...) function, as shown here:

prop.table(table(dat$Category))

Above, the one-way table now shows proportions of observations in each category, as fractions of 1.

Finally, we can multiply the entire table by 100, such that it shows percentages:

prop.table(table(dat$Category))*100

Above, we see that for the variable Category, 38.9% of all observations have the level Cookies. This means that 38.9% of orders were for cookies. Optionally (not required), see this sentence's footnote regarding reducing the number of displayed decimal places.^[You may have noticed that the numbers in these tables contain an unnecessary number of decimal places, making the table a bit unpleasant to look at. If you want to fix this, one change you can make is to put all of the code we used---prop.table(table(dat$Category))*100---into the round(...) function, like this: round(prop.table(table(dat$Category))*100,1). In this code, the number 1 is telling the computer how many decimal places we want to include. More precisely: we are inserting two arguments into the round(...) function, separated by commas: 1) prop.table(table(dat$Category))*100 -- this is the object (a table in this case) that we want to round; 2) 1 -- this is the number of decimal places to which we want to round the object given in the first argument (try changing this to 0 or any other number and see what happens).]

We will now turn to two-way tables, starting with this two-way table of City and Category:

table(dat$City, dat$Category)

Again, we will use the prop.table(...) function to convert the table above into a proportion table:

prop.table(table(dat$City, dat$Category))

And like before we can multiply this entire table by 100 to get percentages:

prop.table(table(dat$City, dat$Category))*100

The table above tells us that 13.1% of all observations have a City value of Boston and a Category value of Cookies. More plainly: 13.1% of all orders are cookies sent to Boston. Note that the table above has 4 rows and 4 columns, meaning it has 16 cells in total. The total sum of the numbers in all 16 cells adds up to 100%.

Alternatively, you can calculate the percentages by row or column. Let's do row percentages first, using this code:

prop.table(table(dat$City, dat$Category), margin = 1)*100

Here are key characteristics about the code and resulting table above:

We added an argument to the prop.table(...) function. The first argument is table(dat$City, dat$Category), as you have seen above already. Then we add a comma. And then we put the new argument: margin = 1. This new argument tells the computer that we want proportions calculated separately for each row.
Now the totals in each row add up to 100%. This table tells us the percentage breakdown of our observations in Category for each level of City.
Within orders to New York alone, 41.9% were bars, 35.5% were cookies, 8.1% were crackers, and 14.5% were snacks. These four percentages add up to 100%.

By slightly modifying the code above---by changing margin = 1 to margin = 2, we can get column percentages:

prop.table(table(dat$City, dat$Category), margin = 2)*100

Here is some information about this new table:

Now the totals in each column add up to 100%. This table tells us the percentage breakdown of our observations in City for each level of Category.
Just within orders for bars, 30.9% went to Boston, 25.5% went to Los Angeles, 27.7% went to New York, and 16.0% went to San Diego. These four percentages add up to 100%.

As a final edit for readability, we can reduce the number of digits after the decimal point that are displayed in the table. We use the round(...) function to do this:

round(prop.table(table(dat$City, dat$Category), margin = 2)*100, digits = 1)

Above, we told the computer to round each reported percentage to one decimal point, by setting digits = 1. If you change it to digits = 2, you will see that you are given two digits after the decimal point instead!

Now that you know how to explore your dataset in a few different was, we will turn to how to make a few basic changes and manipulations to datasets in R.

Sum totals in tables {#sumtables}

Another additional output that you may want to add to a table is sum totals. This can be done using the addmargins(...) function, as demonstrated in this section.

Let's again start with the one-way table of the variable Category from the dataset dat, using the code below:

table(dat$Category)

To convert the table above to a table with a sum calculation, we will take the code above---table(dat$Category)---and put it all inside of the addmargins(...) function, as shown here:

addmargins(table(dat$Category))

Above, the one-way table now includes a sum of all observations at the end.

We will now turn to two-way tables, starting with this two-way table of City and Category:

table(dat$City, dat$Category)

Again, we will use the addmargins(...) function to add totals to each row and column:

addmargins(table(dat$City, dat$Category))

The table above shows sum totals for each row and column in our two-way table!

Manipulating data in R

Once you have your data loaded into R correctly, as demonstrated in the previous section, you will often find that you cannot immediately do your data analysis. First, you might still have to make changes to your data. This section covers a few common changes that you will need to know how to make to your data.

Note that in many of the examples below, I will no longer use dat as our example dataset, even though you could, if you wanted to, do all of the operations below using the dataset dat.

Subsetting data -- selecting observations (Rows)

Imagine you had a dataset called mydata loaded into R. Now let's say that you wanted to remove some observations in mydata and keep some others. This means that you want to create a subset of your data. Typically, you will want this subset to be created based on some criteria. For example, let's say that your dataset mydata had a variable called gender and all observations were marked as either M (for male) or F (for female). And let's say that you wanted to remove all males from your data and keep all females.

The following code^[Source: Subsetting Data. https://www.statmethods.net/management/subset.html{target=\"_blank\"}.] creates a subset of the data that only retains female observations:

newdata <- mydata[ which(mydata$gender=='F'), ]

Note that the code above is based on a hypothetical dataset called mydata that doesn't already exist. The code above will not run unless it is modified, as explained below.

Here's what the code above did:

newdata <- -- Create a new dataset called newdata into which the computer will copy over only some of the observations (rows) that are in the already-existing dataset called mydata.^[Remember, in other examples that you may have encountered so far, the name of the dataset mydata may have been d, dat, or even something else!] Since you're creating newdata here for the first time in your code, you could call it something different. It's not a rule that you call it newdata; you could call it apple or esophagus if you wanted.
mydata[...] -- Look within the dataset mydata.
which(mydata$gender=='F') -- Select only the rows in which the variable gender is equal to F.
, -- You'll see that in the line of code, there is a comma and then nothing. If we wanted to, we could have put criteria after this comma to make selections based on columns. In this situation, we did not want to do that, so we are leaving it blank. Since we left it blank, all variables (columns) will be copied into newdata that were there in mydata, for the selected observations.

Any time you see square brackets after a dataset or dataframe, as you do in the code above where it says mydata[some stuff], it means that we're getting some specific data out of the dataframe, as we did above, where we just extracted the observations for which gender is equal to F.

Note that we now have a new dataset called newdata which contains only females. We still have the initial version of the dataset---mydata---as well. It didn't go anywhere! So now we can easily work with the original data by referring to it as mydata in our code, or with the newly created subset by referring to it as newdata in our code. You can also look in the Environment tab of RStudio and see that both mydata and newdata are listed there separately.

Keep the following guidelines in mind when you are adapting the code above to do data analysis of your own:

Replace mydata with the name of your dataset (such as dat in the example earlier in this chapter).
Replace gender with the name of the variable within your dataset that you want to use for subsetting (such as City in the example earlier in this chapter).
Replace F with the specific value of your subsetting variable that you want to use to select observations (such as Boston in the example earlier in this chapter).
If you want, you can replace newdata with a different name--- perhaps one that is more meaningful or descriptive---to call your new data (such as dat2 or datBoston in the example earlier in this chapter).

If you want to use a numeric variable (like age) to select a subset of observations instead of a categorical variable (like gender), you can do so like this:

newdata <- mydata[ which(mydata$age==8), ]

The code above creates a new dataset called newdata which contains only the people from the original dataset mydata who are 8 years old. Note that the number 8 is not in quotation marks, while the F to indicate female was in quotation marks earlier. Numbers should not go in quotation marks. Words or letters should go in quotation marks.

It is also possible to specify multiple criteria for subset selection, simultaneously:

newdata <- mydata[ which(mydata$gender=='F' & mydata$age > 65), ]

Above, newdata will contain all observations from mydata which meet both of the following criteria:

Variable gender equal to F
Variable age greater than 65.

You may notice the characters == in the code above. Two equal signs next to each other are used for comparison of two values. We sometimes refer to this as \"equals equals\".

Also in the code above, the & operator is used. This corresponds to the English word \"and\" and helps us specify two criteria at once, telling the computer that we want both of the criteria to be satisfied. If we wanted to, we could also change the & to |, like this:

newdata <- mydata[ which(mydata$gender=='F' | mydata$age > 65), ]

Above, newdata will contain all observations from mydata which meet at least one of the following criteria:

Variable gender equal to F
Variable age greater than 65.

In the code above, the | operator is used. This corresponds to the English word \"or\" and helps us specify two criteria at once, telling the computer that we want at least one of the criteria to be satisfied.

Below is a list of operators that you might find useful to refer to.^[Adapted from: Operators. Quick-R by datacamp. https://www.statmethods.net/management/operators.html{target=\"_blank\"}.] You can replace the operators in the example code above---such as == and &---with the other options in the table below, as needed.

Operator	What it checks
x < y	if x is less than y
x <= y	if x is less than or equal to y
x > y	if x is greater than y
x >= y	if x is greater than or equal to y
x == y	if x is exactly equal to y
x != y	if x is not equal to y
x \| y	if x OR y is true
x & y	if x AND y are true

In this section, we learned about how to take an existing dataset in R and make a copy of it, such that the copy (a subset) contained only selected observations (rows of data) from the original dataset.

Keep reading to learn about more ways to manipulate your data in R!

Subsetting data -- selecting variables (columns) {#subsetvariables}

You may sometimes want to create a subset of your data that contains only selected variables (columns) from your original data. In other words, you may want to take an original already-existing dataset and then create a copy of that dataset, such that the copy only has a few variables from the original.

For example, let's use the mtcars dataset in R as our original data. We'll make a copy of this dataset using the code below:

dOriginal <- mtcars

Above, we created a copy of mtcars called dOriginal, which is our original already-existing dataset that we are starting with.

We can use the names(...) function to look at the variables that are in our original already-existing dataset called dOriginal:

names(dOriginal)

Above, we asked the computers to tell us the names of all variables within the dataset called dOriginal.

We can also use the ncol(...) function in R to determine how how many variables we have in our dataset dOriginal:

ncol(dOriginal)

Above, we see that our dataset dOriginal contains 11 variables.

Now let's say we want to make a new dataset called dSelectedVariables, which will contain all of the observations (rows) as dOriginal but only three variables: mpg, cyl, and hp.

We will use the following code to accomplish this:

dSelectedVariables <- dOriginal[c(\"mpg\",\"cyl\",\"hp\")]

In the code above, here's what we asked the computer to do:

dSelectedVariables <- -- Create a new dataset called dSelectedVariables which will contain whatever it is that the code to the right creates. You can change the name dSelectedVariables to anything else of your choosing for the name of the newly created dataset.
dOriginal[...] -- From the dataset dOriginal, select a subset of data.
c(\"mpg\",\"cyl\",\"hp\") -- Select the columns labeled mpg, cyl, and hp. This list can be as long or short as you would like. You can add or remove the names of variables in quotation marks, separated by commas.

Let's see if we were able to successfully create dSelectedVariables such that it contains only our selected variables from our original dataset dOriginal.

We will now run the familiar names(...) function on our new dataset, dSelectedVariables:

names(dSelectedVariables)

You can see above that the dataset dSelectedVariables only has three variables, which is what we want!

We can also run the ncol(...) function on dSelectedVariables to double-check:

ncol(dSelectedVariables)

And we see above that dSelectedVariables does indeed only have three columns.

Note that you can also separately run the following lines of code to visually inspect the original and subsetted datasets on your own computer:

View(dOriginal)\nView(dSelectedVariables)

If you run the two lines of code above, you will see both the initial and new datasets in spreadsheet view.

Selecting variables using dplyr {#subsetvariablesdplyr}

Above, you saw how to create a subset of your data based on selecting variables using the simple built-in way in R. This process of selecting variables from an existing dataset to make a new dataset can also be conducted using the dplyr package. Both processes should accomplish the same outcome, so you can choose whichever one you prefer!

To select variables using the dplyr package, use the following code:

if (!require(dplyr)) install.packages('dplyr')\nlibrary(dplyr)\n\nNewData <- OldData %>% dplyr::select(var1, var2, var3)

Here is what we are asking the computer to do with the code above:

if (!require(dplyr)) install.packages('dplyr') -- Check if the dplyr package is on the computer and install it if not.
library(dplyr) -- Load the dplyr package.
NewData <- -- Create a new dataset called NewData which will contain whatever is generated by the code to the right.
OldData %>% -- Do the following using the dataset OldData.^[This is a simplified version of what the %>% operator---called the pipe operator---technically does for us. ]
dplyr::select(var1, var2, var3) -- Using the select(...) function from the dplyr package, select variables var1, var2, and var3. The variables are listed, separated by commas. The number of variables given can change depending on your preferences.

And below we can see this procedure in action with our mtcars example from earlier. Remember that we created a dataset called dOriginal which was a copy of mtcars. Then, we want to create a subset of dOriginal which contains only the variables mpg, cyl, and hp.

Here is the code to make a subset of dOriginal:

if (!require(dplyr)) install.packages('dplyr')\nlibrary(dplyr)\n\ndSelectedVariables2 <- dOriginal %>% dplyr::select(mpg, cyl, hp)

Above, we created a new subset of dOriginal called dSelectedVariables2.

Let's use the names(...) and ncol(...) functions to see if this worked:

names(dSelectedVariables2)\nncol(dSelectedVariables2)

As you can see above, the new dataset dSelectedVariables2 only contains the three variables we want.

Now you know two ways to subset your data based on variables!

Recoding variables {#recode}

Sometimes we might want to modify the data within a variable (column) that already exists in our data. This is referred to as recoding a variable. It is often useful to recode our data to make it more meaningful or readable to help us answer a question.

In the following few sections, we will learn a few common ways to recode categorical and numeric variables. We will take examples from the infert dataset, which is built into R for our convenience. You can run the command ?infert in the console to get information about this dataset. And the command View(infert) will allow you to look at the data, as you have done before with other data.

Categorical variable recoding

The infert dataset contains a variable called education. There are three possible values (or levels) that an observation can have for the variable education.

We can see this with the following command:

levels(as.factor(infert$education))

In the command above, we used the levels() and as.factor() functions and we asked them to tell us the levels of the variable education which is within the dataset infert. We learned that there are three possible values of education that an observation can have. You can run the command View(infert) on your computer, look at the education column in the spreadsheet that appears, and confirm that there are only three possible values for education.

Let's say we want to change this variable so that its levels are either Less than high school education or More than high school education. We want to recode the variable education such that what used to be 0-5yrs and 6-11yrs is now LessThanHS. And we want what was 12+ yrs to now be HSorMore.

To accomplish this, first load the plyr package:

if (!require(plyr)) install.packages('plyr')\nlibrary(plyr)

Now we'll create a new variable in the data called EducBinary^[We could call it whatever we want. I'm calling it this because it's now a binary variable with just two possible values.] which is a recode of the already-existing variable education:

infert$EducBinary <- revalue(infert$education, c(\"0-5yrs\"=\"LessThanHS\", \"6-11yrs\"=\"LessThanHS\",\"12+ yrs\"=\"HSorMore\"))

Here's what we asked the computer to do with the command above:

infert$EducBinary <- -- Within the already-existing dataset called infert, create a new variable called EducBinary. Assign EducBinary whatever is returned from the revalue() function.
The revalue() function has two parts within it, separated by a comma. These are called two arguments. We'll look at them individually:
1. infert$education -- This is the already-existing variable that we are recoding.
2. c(\"0-5yrs\"=\"LessThanHS\", \"6-11yrs\"=\"LessThanHS\",\"12+ yrs\"=\"HSorMore\") -- This is a vector^[A vector is denoted by the c(...) notation.] (list) of changes we want to make to the already-existing variable that we specified earlier. \"0-5yrs\"=\"LessThanHS\" means that we are asking the computer to change all values that are 0-5yrs to LessThanHS.

When you run the code above in RStudio on your own computer and then once again view the dataset with View(infert), you will see that the new variable (column) has been added. You can confirm if the recoding happened correctly.

Another way to make sure the recoding worked is to look at a two-way table with the old and new variables:

table(infert$education, infert$EducBinary)

As you can see, every single observation (row of data) that was in the 0-5 or 6-11 range for the old variable education are now in the LessThanHS category in the new variable EducBinary. And all observations that were in the 12+ range in the old education variable are now in the HSorMore category in the new EducBinary variable. Therefore, we know our recoding was successful.

We could have also accomplished this recoding using basic R functions, without using the revalue() function:

infert$EducBinary2[infert$education==\"0-5yrs\"] <- \"LessThanHS\"\ninfert$EducBinary2[infert$education==\"6-11yrs\"] <- \"LessThanHS\"\ninfert$EducBinary2[infert$education==\"12+ yrs\"] <- \"HSorMore\"

The lines above follow the following form:

DataSetName$NewVariable[DataSetName$OldVariable==\"SomeValue\"] <- \"NewValue\"

Again, we can test to see if our new variable, EducBinary2 was created successfully:

table(infert$education, infert$EducBinary2)

Once again, we see that this second method also successfully allowed us to recode an existing categorical variable in our data---education---into a new variable with different groupings.

Now we will learn how to recode a numeric variable.

Numeric variable recoding {#RecodeNumeric}

Sometimes you may want to recode a continuous numeric variable, such as infert$age. If you again run the command View(infert$age), you can inspect the age variable (column) and see that age is a continuous numeric variable within the dataset infert. You may have noticed that the youngest person in the dataset is 21 years old and the oldest is 44.

We can confirm the range of ages of the observations in the dataset like this:

range(infert$age)

Above, we used the range() function to tell us the minimum and maximum values of the variable age within the dataset infert. It confirmed to us that the minimum age is 21 and maximum age is 44.

Now imagine that we want to take the continuous numeric variable age and create a new variable with 10-year-interval age groups.

Here is one way to do this:

infert$AgeGroup <- cut(infert$age, breaks=c(-Inf,19,29,39, Inf), labels=c(\"Age 19-\",\"Age 20-29\",\"Age 30-39\",\"Age 40+\"))

Here's what the code above is telling the computer to do:

infert$AgeGroup -- In the existing dataset called infert, make a new variable called AgeGroup.
<- cut(...) -- Assign values to AgeGroup according to the result of the function cut(...). Inside the cut function, there are three arguments, which are described below:
1. infert$age -- Use this already-existing variable to modify into a new variable.
2. breaks=c(-Inf,19,29,39, Inf) -- Split up the selected already-existing variable such that there are four groups according to these intervals: negative infinity through 19, 20 to 29, 30 to 39, and 40 to positive infinity.^[The number of groups is also the same as the number of commas that you can count inside the c(...) portion of the breaks. There are four commas.]
3. labels=c(\"Age 19-\",\"Age 20-29\",\"Age 30-39\",\"Age 40+\") -- For each of the four groups made by the previously specified intervals, label the values of the new variable with these four labels, respectively: \"Age 19-\", \"Age 20-29\", \"Age 30-39\", \"Age 40+\".

Like before, we can use a two-way table to check to make sure that we recoded correctly:

table(infert$age, infert$AgeGroup)

For example, in the table above, we see that there are 8 observations who are 38 years old (according to the previously-existing age variable which is displayed in rows). These 8 people were correctly grouped into the \"Age 30-39\" age group in the newly created AgeGroup variable (displayed in columns).

One reason why we might recode the age variable into the AgeGroup variable is that we want to see a summary of how many observations (people) in our data fall into ten-year age ranges. To obtain these numbers, we can use a one-way table:

table(infert$AgeGroup)

In the simple one-way table above, we can very easily see how many people fall into each age group. For example, we see that 18 people in the data are 40 years old or older.

Basic R functions can also be used to create age group categories:

infert$AgeGroup2[infert$age< 20] <- \"Age 19-\"\ninfert$AgeGroup2[infert$age>=20 & infert$age<30] <- \"Age 20-29\"\ninfert$AgeGroup2[infert$age>=30 & infert$age<40] <- \"Age 30-39\"\ninfert$AgeGroup2[infert$age>=40] <- \"Age 40+\"

The code above will accomplish the same recoding as the cut() command, but requires multiple separate lines of code, whereas the cut() command accomplishes our goal in just a single line.

In the example above, we recoded a numeric variable into a categorical (group) variable. But you may also find in the future that you want to recode a numeric variable into another numeric variable. One way to do that is shown below.

To recode from an already-existing numeric variable to a new numeric variable, you can use this approach:

infert$NewVariable[infert$OldVariable==1] <- 0\ninfert$NewVariable[infert$OldVariable==2] <- 1

In the code above, this is what the first line is telling the computer to do:

infert$NewVariable -- In the dataset called infert, make a new variable called NewVariable.
[infert$OldVariable==1] -- Select all observations in infert that meet the criteria that the value of OldVariable is equal to 1.
<- 0 -- Assign the selected observations the value of 0.

All observations that have OldVariable equal to 1 will be recoded as 0 for NewVariable.

The same process can be done for recoding from categorical to numeric:

d$female <- NA\nd$female[d$gender==\"female\"] <- 1\nd$female[d$gender==\"male\"] <- 0

The code above creates a new variable called female, based on the old variable called gender. First, it sets the new variable female equal to NA (which means missing or empty) for all observations. For observations (rows of data) in which gender is equal to female, the new variable female will be equal to 1. For observations in which gender is equal to male, the new variable female will be equal to 0.

It is important to note that in the code above, the new variable female is coded as 1 or 0 and the numbers 1 and 0 are NOT in quotation marks. It is good that the numbers are NOT in quotation marks, because that's how the computer knows that you want to code the female variable as a numeric variable. If you were to instead put 1 and 0 into quotation marks, the computer would read these as letters and not numbers---such as a label that you want to give to your observations, like Age 20-29 above---and it would not work for any numerical analysis.

Transforming variables {#VariableTransformationsR}

Transforming is similar to recoding, or could be considered a type of recoding that we conduct on numeric data. If we wanted to add 2 to everyone's age in the infert data, we would transform the variable infert$age.

Here's how we do it:

infert$age2 <- infert$age + 2

In the code above, we tell the computer to create a new variable called age2 in the dataset infert. For each observation (row of data), make each observation's age2 equal to 2 plus its age.

After you run the code above, you can once again run View(infert). You will see that there is a new age2 column as well as the pre-existing age column. You can confirm that all values of age2 are 2 higher than all values of age in every column.

Here are other transformations we could do, if we wanted:

infert$age2 <- infert$age^2 -- New variable is square of old variable
infert$age2 <- sqrt(infert$age) -- New variable is square root of old variable
infert$age2 <- log(infert$age) -- New variable is log of old variable
infert$age2 <- infert$age * 2 -- New variable is the old variable multiplied by 2.
infert$age2 <- infert$age + infert$parity -- New variable is sum of old variable age and old variable parity
infert$age2 <- infert$age * infert$parity -- New variable is multiplication of old variable age and old variable parity
d$NewVariable <- d$OneVariable + d$AnotherVariable + d$AThirdVariable -- Within the dataset called d, create a new variable called NewVariable which is the sum of the already-existing variables OneVariable, AnotherVariable, and AThirdVariable. This example shows that we can add and put together a number of transformations all at once, including more than just two variables.

Remember that you can run the command View(YourDataSetName), which in this case is View(infert), to confirm that your transformations were made correctly!

In the examples above, we

Next, we will turn to a different type of manipulation you may need to make to your data in R before you do any analysis.

Removing duplicate observations

You may occasionally find yourself with a dataset in which some rows are duplicates of each other. Before you do your analysis, you might want to remove any duplicates so that just one of each observation remains in your data. You can accomplish this easily in R.

Here is the code to remove duplicates:

WithoutDuplicatesDataset<-OldDataset[!duplicated(OldDataset), ]

Above, we create a new dataset called WithoutDuplicatesDataset (you can call it something shorter when you actually do this yourself). This new dataset is a version of our initial dataset---called OldDataset above---that has all but one of each duplicated observation removed.

Below is an example of how this works.^[Adapted from the answer by Rahul at https://stats.stackexchange.com/questions/6759/removing-duplicated-rows-data-frame-in-r{target=\"_blank\"}. Accessed on April 28 2020.] Let's start by creating a fake dataset called df which contains some duplicates:

a <- c(rep(\"A\", 3), rep(\"B\", 3), rep(\"C\",2))\nb <- c(1,1,2,4,1,1,2,2)\ndf <-data.frame(a,b)

This is what the code above accomplished (it is optional for you to know these details):

a <- c(rep(\"A\", 3), rep(\"B\", 3), rep(\"C\",2)) -- Create a column of data---technically called a vector in R, which is created using the c(...) notation---called a that is not part of a dataset and contains the following eight items: A three times, B three times, and C two times.
b <- c(1,1,2,4,1,1,2,2) -- Create another vector/column of data called b containing eight items (numbers rather than letters this time). b is also a vector of data that is not par of any data set.
df <-data.frame(a,b) -- Create a new data set---technically called a data frame in R---called df, in which one of the columns is the already-existing column a and another is the already-existing column b.

Now we will inspect our dataset:

df

As you can see, there are some rows that are duplicates of each other. Next, we will run the code to remove duplicates:

new.df <- df[!duplicated(df), ]

Above, we created a new dataset called new.df which is a version of df that does not contain the second, third, fourth, etc. occurrence of a duplicated observation. Let's inspect our new dataset to double-check this:

new.df

You can compare df and new.df to verify that the duplicate observations were removed!

Closing RStudio

In this brief section, I will share with you the way I close RStudio when I am done working. This is not the only possible way, but this should work for you while you are a student in this course.

How I close RStudio:

Save all of my work, especially all open code files.
Click on the X to close RStudio.
A window pops up asking if I want to save the workspace image. I click \"Don't save\". RStudio closes.

When you follow the procedure above, your code will be saved. Modifications or manipulations that you made to datasets may not be saved, but you can recreate those modifications by running your code again. Therefore, the most important things to save are your initial raw data (which should already be saved unless you created it in R, which is unlikely) and your code files.

We have now completed this week's introduction to R and RStudio. We will now turn to a review of linear relationships, which will introduce some basic statistical theory.

Terminology -- selected ambiguities {#terminology}

As you continue your study of quantitative analysis, you will notice that we sometimes use terms interchangeably. For example, the words dataset, spreadsheet, and data frame all mean the same thing. In case this is confusing, the list below might help. It is not necessary for you to read or understand all of these terms this week. Rather, you can refer back to this list as needed.

List of terms that mean the same thing as each other:

dataset, data set, spreadsheet, dataframe, data frame -- A collection of data, formatted like a spreadsheet. You can run View(mtcars) in R on your computer to see an example of this. Also, note that a data.frame is a type of object in R that stores datasets for us. In this textbook, we will use data.frame objects in R to store and interact with our data.
observation, subject, row, data point -- A collection of measurements related to a single unit or item that is being studied. These measurements are typically all stored within a single horizontal row of a data spreadsheet.
variable, column, characteristic, quantitatively measured construct -- Attributes that are measured on each observation, typically stored in vertical columns of a data spreadsheet. The names of the variables are typically stored in the topmost row of the data spreadsheet.
coefficient, estimate, slope -- When we run a regression model, we get numeric results for each independent variable included in that regression model. One such number tells us the relationship between the dependent variable and a single independent variable. This particular number can be referred to as a coefficient, estimate, or slope.
intercept, constant -- Where a regression line or equation intercepts the y-axis. More precisely, the predicted value of the dependent variable when all independent variables are equal to 0.
regression, regression model, regression result, regression equation, regression analysis -- These terms all describe the average relationships between a dependent variable and one or more independent variables, as calculated by a regression analysis procedure (such as OLS linear regression, logistic regression, or others).
p-value, p, significance level -- The probability that rejecting the null hypothesis in a hypothesis test is a mistake. The probability that the alternate hypothesis was observed due to random chance (rather than because it is the truth).
independent variables, IVs, X variables, the X's, predictors, covariates, explanatory variables, regressors -- The measured quantities that we want to use to predict an outcome of interest.
dependent variable, DV, Y variable, outcome of interest, response variable, regressand -- The measured quantity that we want to predict or model based on the independent variables.
predicted value, fitted value -- These terms both mean the same thing, meaning the guess that a statistical model makes about the value of the dependent variable for a particular observation.
number of observations, sample size, n -- These terms all refer to the number of rows that are in a dataset.
controlling for a variable, holding a variable constant, compare similar observations -- These terms all refer to how a regression analysis or matching procedure help us see the relationship between our dependent variable and each independent variable (meaning how the dependent variable is predicted to change for every one unit increase in the independent variable) while all of the other independent variables do not change. This concept is used throughout our study of regression analysis and is also specifically discussed mid-way through the book{target=\"_blank\"}.
one-way or two-way table, crosstab, cross table, frequency table, pivot table -- These terms all refer to a table that counts and displays the number of observations in each level of a variable (or combinations of levels of a variable, in the case of a two-way table).
dummy variable, binary variable, dichotomous variable, yes-no variable, 0-1 variable -- All of these terms refer to a variable with only two levels. Dummy variables are often used to including qualitative categorical data into quantitative analyses.
OLS linear regression, OLS, least squares, least squares regression, ordinary least squares linear regression -- All of these terms mean regression analysis that was conducted using the ordinary least squares linear regression procedure. You might hear someone say phrases like \"I ran OLS on my data\" or \"Do least squares and see what happens.\" They are talking about OLS linear regression. OLS is also the most common type of \"linear regression,\" although there are other types of linear regression too (like linear mixed effects regression).
residuals, residual errors -- These terms both refer to the difference between the actual and predicted value for each observation in a regression model.

Once again, it is not necessary for you to understand all of the terms above at this early stage in your study of quantitative methods.

You have now reached the end of this week's content. Please proceed to the assignment below.

Assignment

This and all future assignments are broken up into multiple sections. Please complete all tasks in all sections and submit them to the instructors. You will turn in all R code that you write in an R script file. You will turn in any other work you do in whatever format you prefer. It is fine for you to submit multiple files in D2L (meaning that you do not need to put all assignment responses into a single file).

Before you begin this assignment, make sure you have completed all set-up tasks from earlier in this chapter.

In this and all future assignments, you will be given a dataset to use to complete a series of tasks. With instructor permission, you are allowed and encouraged to use a dataset of your own instead of the one supplied in each assignment. If you have some data that is organized in spreadsheet format that you would like to analyze, the assignments in this course are a great way to do that. Talk to an instructor about this as soon as possible!

In this assignment, you will practice handling and manipulating data in R.

The deadline for submitting this and future assignments can be found in the course calendar{target=\"_blank\"}.

Handling and manipulating data in R

To complete this part of the assignment, you should copy lines of code from earlier in this chapter and paste them in a brand new, empty R script file. You will then modify these copied and pasted lines of code to accomplish the tasks below. You will then submit a copy of your R script file (which will of course contain the modifications you made to the code in this chapter after you copied and pasted).

This portion of the assignment will use a single dataset that you will download to your computer. Click here to download the data in an Excel file{target=\"_blank\"}.^[Data source: Excel Sample Data. Contextures. https://www.contextures.com/xlsampledata01.html{target=\"_blank\"}.] The data will be in a zipped folder. Move the Excel file to your working directory on your computer. In Excel or another spreadsheet software, open the Excel file and browse through it for a minute or two. It is a dataset about workplace incidents. The dataset is in the SafetyData sheet within the Excel file. In the SafetyData sheet within Excel, remove all spaces from the variable names (in row 1) and then save your work.^[For example, one of the variables is called Report Type. Please change this to ReportType, with no space in between the words \"Report\" and \"Type.\"]

library(readxl)\nw <- read_excel(\"sampledatasafety.xlsx\", sheet= \"SafetyData\")

Now that you have downloaded and prepared the Excel file, you are ready to begin!

c2 <- 0

Task r c2<-c2+1; c2: Set the working directory. Put a line of code in your R script file that accomplishes this. Then run that line of code to make sure it works. Once this task is complete, make a new line in your code file and move to the next task!

Task r c2<-c2+1; c2: Check to see what the working directory is. Again, you will put the code that accomplishes this task into its own line in your R script file. Please put the code for each task in its own line and run it, even though I won't remind you to do that anymore!

Task r c2<-c2+1; c2: Load the workplace safety data into R. Name the dataset w.

Important note: You should ALWAYS use the code earlier in this chapter (or similar code) to load Excel files. Do NOT use the File -> Import Dataset tool in RStudio and do NOT use any other point-and-click options you might see to import your data into R, because this will give you trouble later on when you are trying to replicate your work or re-run your entire analysis at once.

Task r c2<-c2+1; c2: View your dataset w as a spreadsheet in RStudio to make sure it was loaded correctly.

Task r c2<-c2+1; c2: How many observations are in the data?

Task r c2<-c2+1; c2: How many variables are in the data?

Task r c2<-c2+1; c2: Write a line of code to display the names of all variables in the data.

Task r c2<-c2+1; c2: How many qualitative/categorical variables are in the data? What are the names of these variables?

Task r c2<-c2+1; c2: How many numeric variables are in the data? What are the names of these variables?

Task r c2<-c2+1; c2: Make a one-way table to figure out how many women and how many men are in the dataset.

Task r c2<-c2+1; c2: Make a two-way table to look at the distribution of incidents involving men and women across different report types.

Task r c2<-c2+1; c2: Create a subset of w, called wburns, which contains only incidents that involved burns. Remember that it may be useful to look at your data as a spreadsheet---either in Excel or RStudio---as you figure this out!

Task r c2<-c2+1; c2: In wburns, create a new version of the Shift variable, called ShiftBinary. The table below will tell you what exactly to recode. Make a two-way table to check if your recode was successful.

Old Shift variable	New ShiftBinary variable
Day	Light
Afternoon	Light
Night	Dark

Task r c2<-c2+1; c2: In w, Recode the IncidentCost variable into a new variable called CostBinary such that incidents costing less than or equal to 2500 are labeled as Low and costs over 2500 are labeled as High. Make a one-way table of CostBinary to see how many low and high cost incidents there are.

Task r c2<-c2+1; c2: Create a new variable in w called DaysLostSq which is the square of the variable DaysLost.

Task r c2<-c2+1; c2: As far as you can tell, what is the unit of observation in the workplace incidents data (w)?

Additional items

You have now reached the end of this week's assignment. The tasks below will guide you through submission of the assignment, remind you of any other items you need to complete this week, and allow us to gather questions and/or feedback from you.

Task r c2<-c2+1; c2: You are required to complete 15 quiz question flashcards in the Adaptive Learner App{target=\"_blank\"} by the end of this week. Note that each week when you do your flashcards, you do not need to submit a record of completion. The system will remember how many flashcards you did and we (the instructors) will be able to see it on our end. Also note that it is normal to see the same quiz question multiple times.

Task r c2<-c2+1; c2: Please write any questions you have for the course instructors and include them in your submitted assignment (optional).

Task r c2<-c2+1; c2: Please write any feedback you have about the instructional materials and include them in your submitted assignment (optional).

Task r c2<-c2+1; c2: Please submit your assignment to the D2L assignment drop-box corresponding to this chapter and week of the course (multiple files are fine). To get to the drop-box, go to the D2L page for this course, click on Assessments -> Assignments. Please e-mail all instructors if you experience any difficulty with this process.

library(plyr)\nd<-infert\ninfert$EducBinary <- revalue(infert$education, c(\"0-5yrs\"=\"LessThanHS\", \"6-11yrs\"=\"LessThanHS\",\"12+ yrs\"=\"HSorMore\"))\n\ninfert$EducBi <- NA\ninfert$EducBi[infert$EducBinary==\"LessThanHS\"] <- 1\n\ninfert$EducBi[infert$EducBinary==\"HSorMore\"] <- 0\n\n\nd$EducBinary <- revalue(d$education, c(\"0-5yrs\"=\"LessThanHS\", \"6-11yrs\"=\"LessThanHS\",\"12+ yrs\"=\"HSorMore\"))\n\nd$EducBi <- NA\nd$EducBi[d$EducBinary==\"LessThanHS\"] <- 1\n\nd$EducBi[d$EducBinary==\"HSorMore\"] <- 0

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Quantitative Research in Genetic Counseling

By Unknown Author

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