Chapter 2: Graphs (More Than One Variable)

Paul Northrop

Source: vignettes/stat0002-ch2c-graphs-vignette.Rmd

The main purpose of this vignette is to provide R code to produce graphs that involve more than one variable. We consider two general situations: (i) plotting the values of a continuous variable for different values of a categorical variable (see The Oxford Birth Times data) and (ii) scatter plots of one variable against another (see The 2000 US Presidential Election data). See also the Chapter 2: Graphs (one variable).

The Oxford Birth Times data

These data are available in the data frame ox_births.

> library(stat0002)
> birth_times <- ox_births[, "time"]
> day <- ox_births[, "day"]

To display these data we manipulate them into a matrix that is of the same format as Table 2.1 in the notes. The number of birth times varies between days so we pad the matrix with R’s missing values code NA in order that each column of the matrix has the same number of rows.

> ox_mat <- matrix(NA, ncol = 7, nrow = 16)
> for (i in 1:7) {
+   day_i_times <- ox_births$time[which(ox_births$day == i)]
+   ox_mat[1:length(day_i_times), i] <- sort(day_i_times)
+   colnames(ox_mat) <- paste("day", 1:7, sep = "")
+ }  
> ox_mat
       day1  day2  day3  day4  day5  day6  day7
 [1,]  2.10  4.00  2.60  1.50  2.50  4.00  2.00
 [2,]  3.40  4.10  3.60  4.70  2.50  4.00  2.70
 [3,]  4.25  5.00  3.60  4.70  3.40  5.25  2.75
 [4,]  5.60  5.50  6.40  7.20  4.20  6.10  3.40
 [5,]  6.40  5.70  6.80  7.25  5.90  6.50  4.20
 [6,]  7.30  6.50  7.50  8.10  6.25  6.90  4.30
 [7,]  8.50  7.25  7.50  8.50  7.30  7.00  4.90
 [8,]  8.75  7.30  8.25  9.20  7.50  8.45  6.25
 [9,]  8.90  7.50  8.50  9.50  7.80  9.25  7.00
[10,]  9.50  8.20 10.40 10.70  8.30 10.10  9.00
[11,]  9.75  8.50 10.75 11.50  8.30 10.20  9.25
[12,] 10.00  9.75 14.25    NA 10.25 12.75 10.70
[13,] 10.40 11.00 14.50    NA 12.90 14.60    NA
[14,] 10.40 11.20    NA    NA 14.30    NA    NA
[15,] 16.00 15.00    NA    NA    NA    NA    NA
[16,] 19.00 16.50    NA    NA    NA    NA    NA

We have a numeric continuous variable, birth_times, and a categorical variable, day. The following code produces separate boxplots of birth_times for each day of the week.

> par(mar = c(4, 4, 0.5, 1))
> xlab <- "time (hours)"
> x_labs <- c(min(birth_times), pretty(birth_times), max(birth_times))
> # top left
> box_plot(birth_times ~ day, col = 8, ylab = xlab, pch = 16, xlab = "day")
> # top right
> box_plot(birth_times ~ day, col = 8, horizontal = TRUE,  axes = FALSE, xlab = xlab, ylab = "day", pch = 16)
> axis(1, at = x_labs, labels = x_labs)
> axis(2, at = 1:7, labels = 1:7, lwd = 0, lty = 0)
> # bottom left
> box_plot(birth_times ~ day, axes = FALSE, ylab = xlab, pch = 16, lty = 1, range = 0, boxcol = "white", staplewex = 0, medlty = "blank", medpch = 16, xlab = "day")
> axis(1, at = 1:7, labels = 1:7, lwd = 0, lty = 0)
> axis(2, at = x_labs, labels = x_labs)
> # bottom right
> box_plot(birth_times ~ day, horizontal = TRUE, axes = FALSE, xlab = xlab, pch = 16, lty = 1, range = 0, boxcol = "white", staplewex = 0, medlty = "blank", medpch = 16)
> axis(1, at = x_labs, labels = x_labs)
> axis(2, at = 1:7, labels = 1:7, lwd = 0, lty = 0, las = 1)

The 2000 US Presidential Election in Florida

These data are available in the data frame USelection. See ?USelection for details.

> # County identifiers and location
> head(USelection[, 1:4])
  co co_names  lat  lon
1  1  Alachua 29.7 82.4
2  2    Baker 30.3 82.3
3  3      Bay 30.2 85.6
4  4 Bradford 29.9 82.2
5  5  Brevard 28.3 80.7
6  6  Broward 26.1 80.5
> # County demographic variables
> head(USelection[, 5:12])
     npop whit blac hisp  o65 hsed coll  inco
1  198326 74.4 21.8  4.7  9.4 82.7 34.6 19412
2   20761 82.4 16.8  1.5  7.7 64.1  5.7 14859
3  146223 84.2 12.4  2.4 11.9 74.7 15.7 17838
4   24646 76.1 22.9  2.6 11.8 65.0  8.1 13681
5  460977 88.3  9.2  4.1 16.5 82.3 20.4 19567
6 1470758 80.3 17.5 10.9 20.3 76.8 18.8 24706
> # Numbers of votes for candidates
> head(USelection[, 13:22])
    bush   gore brow nade harr hage buch mcre phil moor
1  34124  47365  658 3226    6   42  263    4   20   21
2   5610   2392   17   53    0    3   73    0    3    3
3  38637  18850  171  828    5   18  248    3   18   27
4   5414   3075   28   84    0    2   65    0    2    3
5 115185  97318  643 4470   11   39  570   11   72   76
6 177323 386561 1212 7101   50  129  788   34   74  124

For the moment we simply produce some scatter plots. A separate vignette will be devoted to these data.

A plot to show the locations of the counties.

> plot(-USelection[, "lon"], USelection[, "lat"], xlab = "longitude (degrees north)", ylab = "latitude (degrees east)", pch = 16)

  1. Can you see the outline of the state of Florida?

A plot of the percentage of the vote for Buchanan against population size.

> pbuch <- 100 * USelection$buch/USelection$tvot
> is_PB <- USelection[, "co_names"] == "PalmBeach"
> pch <- 1 + 3 * is_PB
> pch
 [1] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
[39] 1 1 1 1 1 1 1 1 1 1 1 4 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
> plot(USelection$npop, pbuch, xlab = "population", ylab = "Buchanan % vote", pch = pch)
> which_PB <- which(is_PB)
> text(USelection[which_PB, "npop"], pbuch[which_PB] + 0.1, "Palm Beach", cex = 0.8)

  1. Can you see how the code used to identify Palm Beach on the plot works?

Pairwise scatter plots of the demographic variables.

> pairs(USelection[, 5:12])

A plot of the square root of the percentage of the vote for Buchanan against population size, in thousands of people. The horizontal axis has been plotted on a log scale.

> x <- USelection$npop / 1000
> y <- sqrt(pbuch)
> ystring <- expression(sqrt("% Buchanan vote"))
> rm_PB <- which(!is_PB)
> scatter(x[rm_PB], y[rm_PB], pch = 16, xlab ="Total Population (1000s)", ylab = ystring, log = "x")
> points(x[which_PB], y[which_PB], pch = "X")
> text(x[which_PB], y[which_PB] + 0.04, "Palm Beach", cex = 0.8)

  1. Can you see how the different method to identify Palm Beach works?

  2. Can you guess what the numbers on the axes are? See scatter to find out.

Similarly, we use scatter_hist to create a scatter plot in which the distribution of each variable is summarized by a histogram.

> scatter_hist(x, y, log = "x", pch = 16, xlab ="Total Population (1000s)", ylab = ystring)

The plot in the lecture slides is produced by specifying particular bins for the histograms.

> logx <- log(x)
> xbreaks <- seq(from = min(logx), to = max(logx), len = 25)
> ybreaks <- seq(from = min(y), to = max(y), len = 25)
> scatter_hist(x, y, log = "x", pch = 16, xlab ="Total Population (1000s)", ylab = ystring, xbreaks = xbreaks, ybreaks = ybreaks)