Description

Presented to the
Washington State Deptment of Ecology
Dr. Robin Matthews, Institute for Watershed Studies
Graphical Presentation of Environmental Data
How NOT to Lie with Statistics
• One of the most important goals of research is to provide clear and unbiased summaries of the data
• Unfortunately, it is all too easy to obscure important elements from research, intentionally or unintentionally
• This portion of the R-minicourse will focus on creating effective graphical output while avoiding some of the more common problems
For more on data visualization:
How to Lie with Charts by Gerald Everett Jones (ISBN 978-1-419-65143-4)
Now You See It: Simple Visualization Techniques for Quantitative Analysis by Stephen Few (ISBN 978-0-970-60198-8)
Information Dashboard Design: Displaying Data for At-a-Glance Monitoring by Stephen Few
(ISBN 978-1-938-37700-6)
Memory Used for Processing Visual Information
We use three basic types of memory to process scientific information:
• Iconic memory (pre-attentive processing) for detecting visual information
• Short-term memory (attentive or perceptual processing) for temporary (limited) storage and is limited to ∼3–9 items
• Long-term memory for retaining information
• Long-term memory can be created consciously or unconsciously
• Information is stored more permanently, with cross-links that allow access back intoshort-term memory
• Required for recognizing images, interpreting words and numbers, understandingcontext

Pre-Attentive Processing of Visual Information
• Iconic memory provides quick, subconscious processing of graphical information and is influenced by variations in:
• form
• color
• spatial position
• motion
• Graphics that make use of these features tend to make a strong impression on us, even when we don’t know why
Examples of Pre-Attentive Processing in Graphics

Figures modified from Show Me The Numbers by Stephen Few, Analytics Press, 2004
Example of Pre-Attentive Processing in Tables
How many zeros are there?
6 4 4 2 1 5 7 2 2 2 2 8
9 8 9 3 6 5 5 5 7 8 7 6
1 3 5 9 5 6 0 6 7 6 6 6
7 4 2 5 7 7 1 5 5 5 4 2
5 2 1 1 4 2 6 6 4 9 6 3
5 7 2 0 6 1 6 8 0 6 0 2
9 8 7 4 4 5 4 4 9 1 5 1
2 1 3 7 8 6 2 0 2 9 4 9
3 4 9 6 2 1 7 9 4 8 2 8
2 5 5 2 2 4 5 5 8 7 1 5
How many zeros are there?
6 4 4 2 1 5 7 2 2 2 2 8
9 8 9 3 6 5 5 5 7 8 7 6
1 3 5 9 5 6 0 6 7 6 6 6
7 4 2 5 7 7 1 5 5 5 4 2
5 2 1 1 4 2 6 6 4 9 6 3 5 7 2 0 6 1 6 8 0 6 0 2
9 8 7 4 4 5 4 4 9 1 5 1
2 1 3 7 8 6 2 0 2 9 4 9
3 4 9 6 2 1 7 9 4 8 2 8
2 5 5 2 2 4 5 5 8 7 1 5
Perceptual Processing of Visual Information
• Short-term and long-term memory require conscious interpretation of visual information
• As a result, it is easy to fool our visual perception of data, especially if you use pre-attentive processing
• In creating scientific graphics, careful use of color, shape, and position can emphasize or de-emphasize information
• Two major objectives in designing good tables or figures:
• Highlight the data by enhancing “data ink” (reduce non-data ink)
• Organize the data by grouping, prioritizing, and sequencing
Perceptual Processing of Visual Information
• Short-term and long-term memory involves conscious interpretation of visual information
• As a result, it is easy to fool our visual perception of data, especially if you use pre-attentive processing
• In creating scientific graphics, careful use of color, shape, and position can emphasize or de-emphasize information
• Two major objectives in designing good tables or figures:
• Highlight the data by enhancing “data ink” (reduce non-data ink)
• Organize the data by grouping, prioritizing, and sequencing

Building Simple Scatterplots Using plot()
One of the most versatile plotting tools in R is the plot() function. In its simplest form, it can be used with very little modification to explore the data
If necessary, re-enter read.table(“lakes.csv”, T, sep=”,”); attach(lakes)

Index

Index
Plotting One Variable Using Points, Lines, or Both

0 100 200 300 0 100 200 300
Index Index

0 100 200 300 0 100 200 300
Index Index
Changing Colors, Characters, Lines

0 100 200 300 0 100 200 300
Index Index

0 100 200 300 0 100 200 300
Index Index

Saving and Copying R Figures
• R figures are directed to the graphics window
• Individual figures can be saved or copied from this window – select “emf” to minimize pixelation
• Each new figure overwrites the previous one unless you direct R to pause between figures:
par(ask=T) ### graphics window freezes between plots
### hit any key to see next figure
par(ask=F) ### unfreezes graphics window
• A better approach is to save the output using a source file
⇒This would be a good time to use source files (R-minicourse, Part 1) • The syntax for saving graphical output varies slightly for different operating systems; use savePlot for Windows:
plot(tp, chl) savePlot(filename = “simpleplot”, type=”emf”) ### type=”pdf” also produces nice figures
Plotting One Variable vs. Time
We usually want an informative x-axis rather than the row number (Index). It is very simple to add month (column 2) and year (column 4)

month Month

year
Plotting Time Using the chron Library
• One of the most powerful features of R is that it is open-source and programmable, so individuals can contribute libraries or packages containing specialized programs
• The chron library is designed to recognize time in a variety of formats, and is easily integrated with other functions like plot()
• Before you can use the library you need to tell R to read the library:
library(chron) ### this will load chron during your work session library() ### this lists all active libraries
Using the chron Library, continued
mdy.chron <- function(month, day, year) {
chron(dates.=paste(month, day, year, sep=”/”)) }
• Now we can use mdy.chron(month, day, year) as a variable for the x-axis (see top figure on page 17)
plot(tp ~ mdy.chron(month, day, year))
Using the chron Library, continued
Here is a more advanced example (see bottom figure on page 17)
### plot the data, with x/y axis labels and annotations
plot(tp ~ mdy.chron(month, day, year), xlim=xdates, xlab=” “, ylim=c(0, 1000), ylab=”TP (ug-P/L)”, pch=21, bg=”skyblue”, cex=1.5)
### add a text line to identify the outlier

mdy.chron(month, day, year)

Plotting Two Variables Using plot()

tp

log10(tp)
Advanced Scatterplot Features
Legends, Text, Expressions, Polygons
### Step #1: create an empty plot (type=”n”);
### this will let us place the polygon layer beneath the data
plot(log10(chl), log10(tp), type=”n”, xlab=expression(paste(“Chl”[log10] ~ (mu * “g/L”))), ylab=expression(paste(“TP”[log10] ~ (mu * “g-P/L”))))
### Step #2: draw a shaded, borderless rectangle showing tp detection limit rect(xleft=-1.1, ybottom=-0.5, xright=2.9, ytop=log10(2), col=”pink”, border=NA)
### Step #3: add the chlorophyll and total phosphorus data using points points(log10(chl), log10(tp), pch=21, bg=”skyblue”, cex=1.5)
### Step #4: add a horizontal line at the tp “action” level (20 ug/L) abline(h=log10(20), lty=2, lwd=2, col=”red”)
### Step #5: use text and legend to annotate the figure;
### paste and expression are used to add math symbols and subscripts text(x=2.5, y=0.25, “TP detection limit”, cex=0.7, col=”red”) legend(x=”topleft”, expression(“20” * ~ mu * “g-P/L”), lty=2, lwd=2, col=”red”, bty=”n”)

Chllog10 (µg/L)
Summary of Scatterplot Syntax

Basic plotting syntax
plot(x,y) or plot(y∼x) Plot x (horizontal) and y (vertical) type=points (p), lines (l), both (b), overplot (o)
points(x,y), lines(x, y) Can be used for scatterplots; adds points/lines to existing plot xlim, ylim set x- or y-limits (e.g., xlim=c(0, 100)) lty, lwd Sets line type and line width
Syntax for annotating scatterplots
cex character expansion; subgroups can be specified (e.g., cex.axis)
col, bg Sets color; subgroups can be specified (e.g., col.axis);
bg used for pch 21-25
col=NA is transparent
pch Plotting characters (1-16 regular; 21-25 dual color) xlab, ylab, main Adds main, x- or y-axis labels; can include spaces, etc
Misc
abline Add lines to existing plot; modify with lty, lwd
h or v = numerical value (horizontal/vertical lines) a, b = intercept and slope (0,1 for 1:1 diagonal) lm object (regression line)
rect, polygon, segments Add rectangles, polygons, line segments to existing plot legend, text Add legends or text to existing plot

?par, ?plot, legend, etc. will bring up help screen
Plotting Examples Using Iris Data

Iris setosa Iris versicolor Iris virginica
• Boxplots are an excellent exploratory tool for summarizing categorical groups of data
• We will use Fisher’s Iris data to illustrate scatterplot techniques
• The iris data consist of sepal and petal width and length measurements collected from 150 iris flowers representing three species of iris (n=50 for each species; species=Iris setosa, Iris versicolor, and Iris virginica)
• These data were first published by R.A. Fisher in “The use of multiple measurements in taxonomic problems” (Annals of Eugenics 7:179-188, 1936)
• The iris data are included with the R base library and can be loaded and attached using data(iris); attach(iris)
Photographs by C. Hensler and D. Kramb; used with permission
boxplot (Petal.Width ~ Species)

Annotated Boxplots of the Iris Data
• Many of the commands you learned for scatterplots will also work with boxplots
• This code produces notched, annotated boxplots (page 25) that shows intervals of significance:
IQR
median
If the notches overlap, the medians are not significantly different
boxplot(Sepal.Width ~ Species, ylab=”Sepal Width (cm)”, main=”Boxplot of Iris Sepal Width”,
notch = T, boxwex = 0.5,
col = c(“mistyrose”, “skyblue”, “orchid”), border=c(“hotpink4”, “skyblue4”, “mediumorchid4”), names = c(“Iris setosa”, “Iris versicolor”, “Iris virginica”))
### want a list of all colors? type colors()
Boxplot of Iris Sepal Width

Requesting Boxplots Summary Statistics
You can request the plotting statistics, including notch intervals, by adding plot=F in the boxplot syntax
boxplot(Sepal.Width ~ Species, notch=T, plot=F)
lower whisker
$stats Species (1=setosa, etc.)
[,1] [,2] [,3] lower box edge (IQR)
[1,] 2.9 2.0 2.2
[2,] 3.2 2.5 2.8
[3,] 3.4 2.8 3.0median
[4,] 3.7 3.0 3.2
[5,] 4.4 3.4 3.8upper box edge (IQR)
$nupper whisker
[1] 50 50 50
$conf
[,1] [,2] [,3]lower notch
[1,] 3.288277 2.688277 2.910622
[2,] 3.511723 2.911723 3.089378 upper notch
$out
[1] 2.3Value(s) for outliers
$group
[1] 1Group(s) containing outliers
$names
[1] “setosa” “versicolor” “virginica”
Adding Legends to Simple Boxplots
Here is how to use legend to identify categorical groups:
legend(x=”topleft”, c(“Iris setosa”, “Iris versicolor”, “Iris virginica”), fill=c(“pink”, “violet”, “purple”), bty=”n”)

Paired Boxplots Using Guinea Pig Data
• You can used paired boxplots to plot more than one type of categorical data on the x-axis
• This example uses guinea pig tooth growth data receiving three doses of Vitamin C (0.5, 1, and 2 mg) from either orange juice or ascorbic acid
data(ToothGrowth) #data included with R base library attach(ToothGrowth) summary(ToothGrowth)
len supp dose
Min. : 4.20 OJ:30 Min. :0.500
1st Qu.:13.07 VC:30 1st Qu.:0.500
Median :19.25 Median :1.000
Mean :18.81 Mean :1.167
3rd Qu.:25.27 3rd Qu.:2.000
Max. :33.90 Max. :2.000
Paired Boxplots – Annotated R Syntax
boxplot(len ~ dose, boxwex = 0.25, at = 1:3 – 0.2, subset = supp == “VC”, col = “lightyellow”, xlab = “Vitamin C dose (mg)”,
ylab = “Tooth Length (mm?)”, ylim = c(0, 35), yaxs = “i”)
### the first plot sets up the template, including axis and main lagels
### yaxs = “i” helps create better axis intervals
### “at” lists the number of primary categories (1:3) for vitamin C doses
### and adds location (-0.2) to offset each box slightly left of center
### “subset” selects the ascorbic acid group (VC)
boxplot(len ~ dose, add = TRUE, boxwex = 0.25, at = 1:3 + 0.2, subset = supp == “OJ”, col = “darkorange”)
### “add=TRUE” will add the second plot to the same figure ### “at” matchs previous but offsets boxes in opposite direction
legend(x=”bottomright”, c(“Ascorbic acid”, “Orange juice”), fill = c(“lightyellow”, “darkorange”))
### note that default legend outline was NOT removed

Vitamin C dose (mg)

Vitamin C dose (mg)
Advanced Boxplot Features
Adding Raw Data to Boxplots using points() and jitter()
with(ToothGrowth,
{ boxplot(len~supp, border=c(“darkorange3”, “gold4”), col=c(“darkorange”, “gold”), boxwex=0.5, ylab=”Tooth Growth”,
names=c(“Orange Juice”, “Vitamin C”))
### “with” defines the data set; the rest is basic boxplot syntax
points(jitter(rep(1:2, each=30), 0.5), unlist(split(len, supp)), cex=1.25, pch=16,
col=c(“gold4”, “darkorange3”)[unclass(ToothGrowth$supp)]) })
### “points” is similar to previous scatterplot examples
### “jitter” prevents points from plotting on top of each other
### with 30 points in each group centered on boxes 1-2)
### “unlist(split) puts the tooth length data into “supp” groups
### “unclass” is used to assign correct colors based on “supp” groups
Boxplot With Jittered Data Points

Summary of Boxplot Syntax
Syntax Description

Syntax for changing widths
boxwex Set scale for all boxes; values <1 make boxes narrower staplewex Set scale width of staple line; proportional to box width outwex Set scale width of outlier line; proportional to box width
Syntax for changing colors
border Use to add colors to the box borders (see iris examples) col Use to add colors to the boxes (see iris examples)
Syntax for adding features
names Use to add group labels (see iris examples) notch notch=T will add notches
range Defines range for boxplot whiskers; default=1.5 ×box width; range=0 will extend whiskers to max/min values
Misc
add add=TRUE will add boxplot to current plot at Box locations; when add=TRUE, at = 1:n (n=number of boxes) plot plot=F suppresses plotting, but lists statistics

Also see scatterplot syntax (page 21)
Supplemental References
• Lander, Jared P. 2014. R for Everyone, Advanced Analytics and Graphics. Addison Wesley Data & Analytics Series, ISBN 978-0-321-88803-7. • Murrell, Paul. 2011. R Graphics, CRC Press. ISBN 978-1-4398-3176-2. • Teetor, Paul. 2011. The R Cookbook. O’Reilly Publishers. ISBN 978-0-596-880915-7.
• Wickham, Hadley. 2009. ggplot2: Elegant Graphics for Data Analysis (UseR!). Springer. ISBN 978-0-387-98140-6.