36-721 Homework 1

This R Markdown file uses the slidify package by Ramnath Vaidyanathan which is not on CRAN yet and has to be manually installed. I make also use of the interactive plotting capabilities provided by the rCharts package. Since these packages are still in rapid development and this feature was added only recently, one will have to install the current development versions from Github if one wants to reproduce the results. Luckily, this is as easy as typing three lines of R code, using the devtools package by Hadley Wickham:

require(devtools)
install_github(c("slidify", "slidifyLibraries"), "ramnathv", ref = "dev")
install_github("rCharts", "ramnathv")

To rebuild this presentation in knitr, the R markdown format can also be accessed under the following address: Click me to open it in Brower. To get the same results, it is also important to replace the slidify.css document in the folder ~/assets/css/slidify.css with the following custom file: Download [Notice: the folder will be created after invoking knit("index.Rmd") for the first time]

require(knitr)
require(slidify)
require(rCharts)
require(xtable)
require(gridExtra)
require(ggplot2)
theme_set(new = theme_gray(base_size = 14))
opts_chunk$set(dev = "svg")
require(lattice)

For the first question, we analyze a survey of 237 students at the University of Adelaide. All subsequently analyzed data sets come with the MASS package which can be loaded as follows:

require(MASS)
data(survey)

The first four observations are displayed in the following table:

df <- head(survey, n = 4)
print(xtable(df), type = "html")

par(mfrow=c(1,2),oma=c(0,0,2,0));
plot(survey$Smoke,ylab="count"); title("Without Reordering");
survey$Smoke <- factor(survey$Smoke,levels=c("Never","Occas","Regul","Heavy"))
plot(survey$Smoke,ylab="count"); title("With Reordering");
title("Barplots of Smoke Status",outer=TRUE)

exer.tab <- xtabs(~survey$Exer)
par(mfrow = c(1, 2), oma = c(0, 0, 2, 0))
barplot(rep(1, length(exer.tab)), exer.tab, space = 0, names.arg = names(exer.tab), 
    col = c("lightblue", "mistyrose", "lavender"), axes = FALSE)
title(main = "Without Reordering", xlab = "Exercise Level", ylab = "")

barplot(rep(1, length(exer.tab)), exer.tab[c(2, 3, 1)], space = 0, names.arg = names(exer.tab[c(2, 
    3, 1)]), col = c("mistyrose", "lavender", "lightblue"), axes = FALSE)
title(main = "With Reordering", xlab = "Exercise Level", ylab = "")

title("Spine Charts of Exercise Level", outer = TRUE)

Concerning the amount of time each student devotes to exercising, the spine charts reveal that there is only a minority of students who do not do any sports at all, with two other almost equally sized groups who practice either sometimes or frequently. However, with only three data points to display, the same information could also be conveyed by the use of a simple table. Of the two plots, it is advisable to go with the ordered one, as the exercise level is an ordinal variable and should be treated as such. If one does not take the inherent ordering into account, this will likely lead to misunderstandings the viewer will not notice unless he carefully looks at the labels.

Similarly, the bar plots on Page 4 show that the overwhelming majority of students does not smoke at all, with less than a quarter of students smoking either occasionally, regularly or heavily. In each of these sub-categories, there are fewer and fewer cases
with increasing smoking level. It is again advisable to use the ordered chart, as the initial ordering is arbitrary, while there is an inherent ordering of the categories which should be reflected.

As can be seen, there does not seem to be any significant relationship between the two categorical variables.

df <- as.data.frame(matrix(c(87, 12, 9, 7, 18, 3, 1, 1, 84, 4, 7, 3), ncol = 4, 
    nrow = 3))
colnames(df) <- c("No Smoking", "Occasional Smoking", "Regular Smoking", "Heavy Smoking")
rownames(df) <- c("Freq", "None", "Some")

a <- rCharts:::Highcharts$new()
a$chart(type = "column")
a$title(text = "Exercise / Smoking")
a$plotOptions(column = list(stacking = "normal"))
a$xAxis(categories = c("No Exercising", "Some Exercising", "Frequent Exercising"))
a$data(df)
a$print("hchart1", include_assets = TRUE, cdn = TRUE)

In this part of the presentation, we study the birthwt data set which also comes with MASS. It comprises 189 observations of 10 different variables, with the goal to discover risk factors associated with low infant birth weight (see the help page of the data set by typing ?birthwt in the console).

We limit our attention to the following three variables:

• race: race of the mother, one of white, black or other
• smoke: smoking status during pregnancy
• ptl: number of previous premature labours

Displayed are bar plots for the univariate distributions of the three considered variables.

par(mfrow=c(1,3)); cortable1 <- table(birthwt[,c("smoke","race")])
mosaicplot (cortable1,cex.axis=1.5,main="Smoke / Race",xlab="Smoking",ylab="Mother's Race",color=TRUE)
cortable2 <- table(birthwt[,c("ptl","race")]); xlab <- "# Premature Labours" 
mosaicplot (cortable2,cex.axis=1.5,main="Premature Labours / Race",xlab=xlab,ylab="Mother's Race",color=TRUE)
cortable3 <- table(birthwt[,c("ptl","smoke")])
mosaicplot (cortable3,cex.axis=1.5,main="Premature Labours / Smoke",xlab=xlab,ylab="Smoking",
color=TRUE)

Finally, we look at the minn38 data set, which contains characteristics about high school graduates of 1938 from Minnesota (type ?help(minn38) in R).

data(minn38); minn38.tab <- xtabs(formula=f~phs+fol+sex,minn38)
minn38.tab.M <-  xtabs(formula=f~phs+fol,minn38[minn38$sex=="M",])
minn38.tab.F <-  xtabs(formula=f~phs+fol,minn38[minn38$sex=="F",])

Code for the plot on the next page:

X <- as.matrix(minn38.tab.F) # female bar chart
mat <- as.data.frame(matrix(X,nrow=4,ncol=7),row.names=c("C","N","E","O"))
colnames(mat) <- paste("F",1:7,sep="")
n1 <- rCharts:::Highcharts$new(); n1$chart(type = "column")
n1$xAxis(title ="Post High School Status", categories = c("College", "Non-Collegiate School",
                                                          "Full-Time Employment", "Other"))
n1$yAxis(title = "count")
n1$data(mat);

Interactive Bar Chart:

Interactive Bar Chart:

One interesting and perhaps surprising result concerning the relationship between gender and post high school status is that women were more than twice as likely employed full-time than their male counterparts. Comparing the two plots from the previous pages, one can see that the bars differ indeed greatly in height: Roughly three times as many females compared to males were employed full-time (keep in mind that the two plots have a different scale on the y-scale).

Second, college enrollment is highest for pupils from a household in which the father's occupational level is "F1". Compared to all other categories of occupational level, this is the only group in which children who go on to enroll in college make up the largest group. To see this, it is advisable to deselect all other groups in the interactive plots and then make one-to-one comparisons between the individual groups.

minn38_prop_tab <- prop.table(minn38.tab,margin=c(2,3)) 
dimnames(minn38_prop_tab)$sex <- c("Female","Male")
dimnames(minn38_prop_tab)$phs <- c("College","Full-Time Employment","Non-Collegiate School","Other")
barchart(Freq~fol|sex,groups=phs,data=as.data.frame(minn38_prop_tab),stack=TRUE,
         xlab="Post High School Status",ylab="Percentage",
         auto.key=list(space="right", columns=1, title="Legend", cex.title=1))

To render visible the distribution in the individual groups, the previous bar chart only displays the proportions inside the respective groups and not the total counts. This allows better insight into the composition of the groups. One last observation is that there seems to be a trend that with increasing occupational level the number of graduates enrolled in college diminishes, which is offset by an increase in graduates of the category "other". The proportion of graduates belonging to the other categories (full-time employment and non-collegiate school) does not vary as much. One blatant exception is given by category "F3", in which less than under this hypothesis expected graduates are college students.