Introduction

These Notes provide a series of examples using R to work through issues that are likely to come up in PQHS/CRSP/MPHP 431.

While these Notes share some of the features of a textbook, they are neither comprehensive nor completely original. The main purpose is to give 431 students a set of common materials on which to draw during the course. In class, we will sometimes:

reiterate points made in this document,
amplify what is here,
simplify the presentation of things done here,
use new examples to show some of the same techniques,
refer to issues not mentioned in this document,

but what we don’t do is follow these notes very precisely. We assume instead that you will read the materials and try to learn from them, just as you will attend classes and try to learn from them. We welcome feedback of all kinds on this document or anything else. Just email us at 431-help at case dot edu, or submit a pull request.

What you will mostly find are brief explanations of a key idea or summary, accompanied (most of the time) by R code and a demonstration of the results of applying that code.

Everything you see here is available to you as HTML or PDF. You will also have access to the R Markdown files, which contain the code which generates everything in the document, including all of the R results. We will demonstrate the use of R Markdown (this document is generated with the additional help of an R package called bookdown) and RStudio (the “program” which we use to interface with the R language) in class.

All data and R code related to these notes are available through the course website.

Structure

The Notes, like the 431 course, fall in three main parts.

Part A is about visualizing data and exploratory data analyses. These Notes focus on using R to work through issues that arise in the process of exploring data, managing (cleaning and manipulating) data into a tidy format to facilitate useful work downstream, and describing those data effectively with visualizations, numerical summaries, and some simple models.

Part B is about making comparisons with data. The Notes discuss the use of R to address comparisons of means and of rates/proportions, primarily. The main ideas include confidence intervals, using the bootstrap and making decisions about power and sample size. We’ll also discuss the value (or lack thereof) of p values for assessing hypotheses. Key ideas from Part A that have an impact here include visualizations to check the assumptions behind our inferences, and cleaning/manipulating data to facilitate our comparisons.

Part C is about building models with data. The Notes are primarily concerned (in 431) with linear regression models for continuous quantitative outcomes, using one or more predictors. We’ll see how to use models to accomplish many of the comparisons discussed in Part B, and make heavy use of visualization and data management tools developed in Part A to assess our models.

Course Philosophy

In developing this course, we adopt a modern approach that places data at the center of our work. Our goal is to teach you how to do truly reproducible research with modern tools. We want you to be able to answer real questions using data and equip you with the tools you need in order to answer those questions well (Çetinkaya-Rundel (2017) has more on a related teaching philosophy.)

The curriculum includes more on several topics than you might expect from a standard graduate introduction to statistics.

data gathering
data wrangling
exploratory data analysis and visualization
multivariate modeling
communication

It also nearly completely avoids formalism and is extremely applied - this is most definitely not a course in theoretical or mathematical statistics.

There’s very little of this:

\[ f(x) = \frac{e^{-(x - \mu)^{2}/(2\sigma^{2})}}{\sigma{\sqrt{2 \pi }}} \]

Instead, there’s a lot of this:

nyfs1 %>%
    group_by(bmi.cat) %>%
    summarise(mean = mean(waist.circ), 
              median = median(waist.circ),
              sd = sd(waist.circ))

The 431 course is about getting things done. It’s not a statistics course alone, nor is it a course in computer programming alone. I think of it as a course in data science.

Working with this Document

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The document is updated occasionally through the semester. Check the Version information above to verify the last update time.

References

Çetinkaya-Rundel, Mine. 2017. “Teaching Data Science to New useRs.” bit.ly/user2017.

Data Science for Biological, Medical and Health Research: Notes for PQHS 431