Course Outline

segmentGetting Started (Don't Skip This Part)

segmentIntroduction to Statistics: A Modeling Approach

segmentPART I: EXPLORING VARIATION

segmentChapter 1  Welcome to Statistics: A Modeling Approach

segmentChapter 2  Understanding Data

segmentChapter 3  Examining Distributions

segmentChapter 4  Explaining Variation

4.4 Even More Ways: Putting these Plots Together

segmentPART II: MODELING VARIATION

segmentChapter 5  A Simple Model

segmentChapter 6  Quantifying Error

segmentChapter 7  Adding an Explanatory Variable to the Model

segmentChapter 8  Models with a Quantitative Explanatory Variable

segmentPART III: EVALUATING MODELS

segmentChapter 9  Distributions of Estimates

segmentChapter 10  Confidence Intervals and Their Uses

segmentChapter 11  Model Comparison with the F Ratio

segmentChapter 12  What You Have Learned

segmentResources
list Introduction to Statistics: A Modeling Approach
Even More Ways: Putting These Plots Together
gf_point()
and gf_jitter()
are useful. They emphasize that data are made up of individual numbers, and yet they help us to notice clusters of those individual points. There are times, however, when we want to transcend the individual data points and focus only on where the clusters are.
Boxplots, which we have seen before, are helpful in this regard, and are especially useful for comparing the distribution of an outcome variable across different levels of a categorical explanatory variable.
Here’s how we would create a boxplot of thumb length broken down by sex.
gf_boxplot(Thumb ~ Sex, data = Fingers)
In making boxplots we can play with the arguments color
and fill
much like we did before.
gf_boxplot(Thumb ~ Sex, data = Fingers, color = "orange")
Recall that the rectangle at the center of the boxplot shows us where, on the scale of the outcome variable, the middle .50 of data fall. The thick line inside the box is the median.
Think back to the fivenumber summary. We can get the fivenumber summary for Thumb broken down by Sex by modifying how we previously used favstats()
.
favstats(Thumb ~ Sex, data = Fingers)
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The big box with the thick line would contain half of the data points, the half that are closest to the middle of the distribution.
In ggformula, when we chain on multiple functions, the later functions assume the same variables and data frames so we don’t need to type those in again. Handy!
gf_boxplot(Thumb ~ Sex, data = Fingers, color = "orange") %>%
gf_jitter()
We can also add in any arguments to modify gf_jitter
.
gf_boxplot(Thumb ~ Sex, data = Fingers, color = "orange") %>%
gf_jitter(height = 0, color = "gray", alpha = .5, size = 3)
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In this situation where we are looking at the variation in Thumb length by Sex, the boxes are in different vertical positions. The male box is higher than the female box.
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Instead of an explanatory variable like Sex, let’s try one that is unlikely to help us explain the variation in thumb length.
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Modify this code to depict a boxplot for Thumb length by Job (instead of by Sex).
require(mosaic)
require(ggformula)
require(tidyverse)
Fingers < read.csv(file="https://raw.githubusercontent.com/UCLATALL/introstatsmodeling/master/datasets/fingers.csv", header=TRUE, sep=",")
Fingers < data.frame(Fingers)
# clean up str
Fingers$RaceEthnic < as.factor(Fingers$RaceEthnic)
Fingers$SSLast < as.numeric(Fingers$SSLast)
Fingers$Year < as.factor(Fingers$Year)
Fingers$MathAnxious < as.numeric(Fingers$MathAnxious)
Fingers$Interest < as.numeric(Fingers$Interest)
Fingers$GradePredict < as.numeric(Fingers$GradePredict)
Fingers$Thumb < as.numeric(Fingers$Thumb)
Fingers$Index < as.numeric(Fingers$Index)
Fingers$Middle < as.numeric(Fingers$Middle)
Fingers$Ring < as.numeric(Fingers$Ring)
Fingers$Pinkie < as.numeric(Fingers$Pinkie)
Fingers$Height < as.numeric(Fingers$Height)
Fingers$Weight < as.numeric(Fingers$Weight)
# label a few factors
Fingers$RaceEthnic < factor(Fingers$RaceEthnic, levels = c(1,2,3,4,5), labels = c("White","African American","Asian","Latino","Other"))
Fingers$Year < factor(Fingers$Year, levels = c(1,2,3,4), labels = c("freshman", "sophomore", "junior", "senior"))
# prerun
Fingers$Job < as.factor(Fingers$Job)
Fingers$Job < factor(Fingers$Job, levels=c(0,1,2), labels=c("no job", "parttime", "fulltime"))
# Modify this boxplot to look at Thumb length by Job
gf_boxplot(Thumb ~ Sex, data = Fingers, color = ~Sex) %>%
gf_jitter(height = 0, color = "gray", alpha = .5, size = 3)
gf_boxplot(Thumb ~ Job, data = Fingers) %>%
gf_jitter(height=0, color="gray", alpha=.5, size=3)
test_function("gf_boxplot")
Notice that in this boxplot, the boxes are at approximately the same vertical position and are about the same size. The one exception is the box for the fulltime level of Job.
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The fulltime box only includes one student, so, we wouldn’t want to draw any conclusions about the relationship between working full time and thumb length. Most of the students in the Fingers data frame either work parttime or not at all. The thumbs of students with no job are not much longer or shorter than thumbs of students with parttime jobs. But within each group, their thumb lengths vary a lot. There are longthumbed and shortthumbed students with parttime jobs and with no jobs.
Now let’s return our attention to the whisker part (the lines) that go out from the box. The whiskers are drawn in relation to IQR, the interquartile range.
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In gf_boxplot()
, outliers, defined as observations more than 1.5 IQRs above or below the box, are represented with dots. The ends of the whiskers (the lines that extend above and below the box) represent the maximum and minimum observations that are not defined as outliers.
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Any data that is greater or less than the whiskers are depicted in a boxplot as individual points. By convention, these can be considered outliers.