--- title: "SDM4 in R: Displaying and Describing Quantitative Data (Chapter 3)" author: "Nicholas Horton (nhorton@amherst.edu)" date: "June 13, 2018" output: pdf_document: fig_height: 4 fig_width: 6 html_document: fig_height: 3 fig_width: 5 word_document: fig_height: 4 fig_width: 6 --- ```{r, include = FALSE} # Don't delete this chunk if you are using the mosaic package # This loads the mosaic and dplyr packages require(mosaic) ``` ```{r, include = FALSE} # knitr settings to control how R chunks work. require(knitr) opts_chunk$set( tidy = FALSE, # display code as typed size = "small" # slightly smaller font for code ) ``` ## Introduction and background This document is intended to help describe how to undertake analyses introduced as examples in the Fourth Edition of *Stats: Data and Models* (2014) by De Veaux, Velleman, and Bock. More information about the book can be found at http://wps.aw.com/aw_deveaux_stats_series. This file as well as the associated R Markdown reproducible analysis source file used to create it can be found at http://nhorton.people.amherst.edu/sdm4. This work leverages initiatives undertaken by Project MOSAIC (http://www.mosaic-web.org), an NSF-funded effort to improve the teaching of statistics, calculus, science and computing in the undergraduate curriculum. In particular, we utilize the `mosaic` package, which was written to simplify the use of R for introductory statistics courses. A short summary of the R needed to teach introductory statistics can be found in the mosaic package vignettes (http://cran.r-project.org/web/packages/mosaic). A paper describing the mosaic approach was published in the *R Journal*: https://journal.r-project.org/archive/2017/RJ-2017-024. ## Chapter 3: Displaying and describing quantitative data ### Section 3.1: Displaying quantitative variables See Figure 3.1 on page 46. ```{r message = FALSE} library(mosaic) library(readr) options(digits = 3) Tsunami <- read_delim("http://nhorton.people.amherst.edu/sdm4/data/Tsunami_Earthquakes.txt", delim = "\t") nrow(Tsunami) gf_histogram(~ Magnitude, binwidth = 0.5, center = 0.5/2+0.001, data = Tsunami) gf_histogram(..density.. ~ Magnitude, binwidth = 0.5, center = 0.5/2+0.001, data = Tsunami) ``` Note that Figure 3.3 on page 47 displays a histogram with the y-axis measured by percent in each bar. The first histogram displays the count and the last the density (where the total area of the bars adds up to 1). ```{r message = FALSE} Pulse_rates <- read_delim("http://nhorton.people.amherst.edu/sdm4/data/Pulse_rates.txt", delim = "\t") with(Pulse_rates, stem(Pulse)) gf_dotplot(~ Pulse, data = Pulse_rates) ``` Or on page 49 ```{r} with(Pulse_rates, stem(Pulse, scale = 2)) ``` ### Section 3.2: Shape ### Section 3.3: Center See calculation and Figure 3.11 on page 53. ```{r} recent <- filter(Tsunami, Year >= 1989, Year <= 2013) nrow(recent) median(~ Magnitude, data = recent) gf_histogram(~ Magnitude, binwidth = 0.2, data = recent) ``` ### Section 3.4: Spread See statistics reported on pages 54-55. ```{r} favstats(~ Magnitude, data = recent) range(~ Magnitude, data = recent) diff(range(~ Magnitude, data = recent)) IQR(~ Magnitude, data = recent) ``` ### Section 3.5: Boxplots and 5-Number Summaries See display on page 57. ```{r} gf_boxplot(Magnitude ~ 1, data = recent) ``` Note that boxplots of a single distribution aren't usually very interesting (more useful displays will be seen in Chapter 4 when we start comparing groups). ### Section 3.6: The Center of Symmetric Distributions: The Mean See calculation on page 59. ```{r} mean(~ Magnitude, data = recent) median(~ Magnitude, data = recent) ``` ### Section 3.7: The Spread of Symmetric Distributions: The Standard Deviation ```{r} sd(~ Magnitude, data = recent) var(~ Magnitude, data = recent) sqrt(var(~ Magnitude, data = recent)) 0.702^2 ``` The standard deviation squared equals the variance.