Inspired by this blog post from theBioBucket, I created a script to parse all pdf files in a directory. Due to its reliance on the Terminal, it’s Mac specific, but modifications for other systems shouldn’t be too hard (as a start for Windows, see BioBucket’s script).

First, you have to install the command line tool pdftotext (a binary can be found on Carsten Blüm’s website). Then, run following script within a directory with pdfs:

# helper function: get number of words in a string, separated by tab, space, return, or point.
nwords <- function(x){
	res <- strsplit(as.character(x), "[ \t\n,\\.]+")
	res <- lapply(res, length)
	unlist(res)
}
 
# sanitize file name for terminal usage (i.e., escape spaces)
sanitize <- function(str) {
	gsub('([#$%&~_\\^\\\\{}\\s\\(\\)])', '\\\\\\1', str, perl = TRUE)
}
 
# get a list of all files in the current directory
fi <- list.files()
fi2 <- fi[grepl(".pdf", fi)]
 
 
## Parse files and do something with it ...
res <- data.frame() # keeps records of the calculations
for (f in fi2) {
	print(paste("Parsing", f))
 
	f2 <- sanitize(f)
	system(paste0("pdftotext ", f2), wait = TRUE)
 
	# read content of converted txt file
	filetxt <- sub(".pdf", ".txt", f)
	text <- readLines(filetxt, warn=FALSE)
 
	# adjust encoding of text - you have to know it
	Encoding(text) <- "latin1"
 
	# Do something with the content - here: get word and character count of all pdfs in the current directory
	text2 <- paste(text, collapse="\n")	# collapse lines into one long string
 
	res <- rbind(res, data.frame(filename=f, wc=nwords(text2), cs=nchar(text2), cs.nospace=nchar(gsub("\\s", "", text2)))) 
 
	# remove converted text file
	file.remove(filetxt)
}
 
print(res)

… gives following result (wc = word count, cs = characgter count, cs.nospace = character count without spaces):

> print(res)
                                                    filename    wc     cs cs.nospace
1                              Applied_Linear_Regression.pdf 33697 186280     154404
2                                           Baron-rpsych.pdf 22665 128440     105024
3                              bootstrapping regressions.pdf  6309  34042      27694
4                            Ch_multidimensional_scaling.pdf   718   4632       3908
5                                               corrgram.pdf  6645  40726      33965
6                   eRm - Extended Rach Modeling (Paper).pdf 11354  65273      53578
7                                           eRm (Folien).pdf   371   1407        886
8  Faraway 2002 - Practical Regression and ANOVA using R.pdf 68777 380902     310037
9                             Farnsworth-EconometricsInR.pdf 20482 125207     101157
10                                           ggplot_book.pdf 10681  65388      53551
11                                       ggplot2-lattice.pdf 18067 118591      93737
12                               lavaan_usersguide_0.3-1.pdf 12608  64232      52962
13                                  lme4 - Bootstrapping.pdf  2065  11739       9515
14                                                Mclust.pdf 18191  92180      70848
15                                              multcomp.pdf  5852  38769      32344
16                                       OpenMxUserGuide.pdf 37320 233817     197571

In response to an update to ggplot2 (now verson 0.9.2) I had to make some minor changes to our package TripleR. The CRAN maintainers also asked to …

Please also fix other issues that may be apparent in checks with a current R-devel.

Now, how can this be done? Here’s my workflow on Mac OS (might be slightly different on Win or Linux):

1.   Install R-develparallel to your existing (stable) R version
   1.  Before installation, run sudo pkgutil --forget org.r-project.R.Leopard.fw.pkg in the Terminal, otherwise the installer will overwrite your existing version
   2. Rename your R.app and R64.app or move them temporarily into another folder, as the installer of R-devel probably will replace them by new version that are not compatible with your existing stable R version.
2.   Use RSwitch to change the active R version
3.   Install packages which your own packages depends on; you have to do it from source, as the binaries for the R-devel do not exist: install.packages("lme4", type="source")
4.  Check your own package using following flag: R CMD check pkg --as-cran
5. Check if your package also works on Windows using winbuilder

Furthermore, check whether your package follows the CRAN Repository Policies.

PS: Finally, I managed to get rid of the annoying R CMD check warnings like “no visible binding for global variable ‘x’”. These occured due to the ggplot2 syntax. Here‘s a solution.

Tags: CRAN | package | R-devel

Update Oct-23: Added a new parameter add to the function. Now multiple groups can be plotted in a single plot (see example in my comment)

As a follow-up on my R implementation of Solomon’s watercolor plots, I made some improvements to the function. I fine-tuned the graphical parameters (the median smoother line now diminishes faster with increasing CIs, and the shaded watercolors look more pretty). Furthermore, the function is faster and has more features:

• You can define any standard regression function for the bootstrap procedure.
  • vwReg(y ~ x, df, method=lm)
  • vwReg(y ~ x + I(x^2), df, method=lm)
• Provide parameters for the fitting function.
  • You can make the smoother’s span larger. Then it takes more points into account when doing the local fitting. Per default, the smoother fits a polynomial of degree two – that means as you increase span you will approach the overall quadratic fit: vwReg(y ~ x, df, span=2)
  • You can also make the smoother’s span smaller, then it takes less points for local fitting. If it is too small, it will overfit and approach each single data point. The default span (.75) seemed to be the best choice for me for a variety of data sets: vwReg(y ~ x, df, span=0.5)
  • Use a robust M-estimator for the smoother; see ?loess for details: vwReg(y ~ x, df, family=”symmetric”)
• Provide your own color scheme (or, for example, a black-and-white scheme). Examples see pictures below.
• Quantize the color ramp, so that regions for 1, 2, and 3 SD have the same color (an idea proposed by John Mashey).

At the end of this post is the source code for the R function.

Some picture – please vote!

Here are some variants of the watercolor plots – at the end, you can vote for your favorite (or write something into the comments). I am still fine-tuning the default parameters, and I am interested in your opinions what would be the best default.

Plot 1: The current default

Plot 2: Using an M-estimator for bootstrap smoothers. Usually you get wider confidence intervalls.

Plot 3:Increasing the span of the smoothers

Plot 4: Decreasing the span of the smoothers

Plot 5: Changing the color scheme, using a predefined ColorBrewer palette. You can see all available palettes by using this command: library(RColorBrewer); display.brewer.all()

Plot 6: Using a custom-made palette

Plot 7: Using a custom-made palette; with the parameter bias you can shift the color ramp to the “higher” colors:

Plot 8: A black and white version of the plot

Plot 9: The anti-Tufte-plot: Using as much ink as possible by reversing black and white (a.k.a. “the Milky-Way Plot“)

Plot 10: The Northern Light Plot/ fMRI plot. This plotting technique already has been used by a suspicious company (called IRET – never heard of that). I hurried to publish the R code under a FreeBSD license before they can patent it! Feel free to use, share, or change the code for whatever purpose you need. Isn’t that beautiful?

Plot 11: The 1-2-3-SD plot. You can use your own color schemes as well, e.g.: vwReg(y~x, df, bw=TRUE, quantize=”SD”)

Any comments or ideas? Or just a vote? If you produce some nice plots with your data, you can send it to me, and I will post a gallery of the most impressive “data art”!

Cheers,

Felix

 Loading ...

# Copyright 2012 Felix Schönbrodt
# All rights reserved.
# 
# FreeBSD License
# 
# Redistribution and use in source and binary forms, with or without
# modification, are permitted provided that the following conditions are
# met:
# 
# 1. Redistributions of source code must retain the above copyright
# notice, this list of conditions and the following disclaimer.
#       
# 2. Redistributions in binary form must reproduce the above copyright
# notice, this list of conditions and the following disclaimer in the
# documentation and/or other materials provided with the distribution.
#       
# THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDER `AS IS'' AND ANY
# EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
# IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
# PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR
# CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
# EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
# PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
# PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
# LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
# NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
# SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
# 
# The views and conclusions contained in the software and documentation
# are those of the authors and should not be interpreted as representing
# official policies, either expressed or implied, of the copyright
# holder.
 
# Version history:
# 0.1: original code
# 0.1.1: changed license to FreeBSD; re-established compability to ggplot2 (new version 0.9.2)
 
## Visually weighted regression / Watercolor plots
## Idea: Solomon Hsiang, with additional ideas from many blog commenters
 
 
# B = number bootstrapped smoothers
# shade: plot the shaded confidence region?
# shade.alpha: should the CI shading fade out at the edges? (by reducing alpha; 0 = no alpha decrease, 0.1 = medium alpha decrease, 0.5 = strong alpha decrease)
# spag: plot spaghetti lines?
# spag.color: color of spaghetti lines
# mweight: should the median smoother be visually weighted?
# show.lm: should the linear regresison line be plotted?
# show.CI: should the 95% CI limits be plotted?
# show.median: should the median smoother be plotted?
# median.col: color of the median smoother
# shape: shape of points
# method: the fitting function for the spaghettis; default: loess
# bw = TRUE: define a default b&w-palette
# slices: number of slices in x and y direction for the shaded region. Higher numbers make a smoother plot, but takes longer to draw. I wouldn'T go beyond 500
# palette: provide a custom color palette for the watercolors
# ylim: restrict range of the watercoloring
# quantize: either "continuous", or "SD". In the latter case, we get three color regions for 1, 2, and 3 SD (an idea of John Mashey)
# add: if add == FALSE, a new ggplot is returned. If add == TRUE, only the elements are returned, which can be added to an existing ggplot (with the '+' operator)
# ...: further parameters passed to the fitting function, in the case of loess, for example, "span = .9", or "family = 'symmetric'"
vwReg <- function(formula, data, title="", B=1000, shade=TRUE, shade.alpha=.1, spag=FALSE, spag.color="darkblue", mweight=TRUE, show.lm=FALSE, show.median = TRUE, median.col = "white", shape = 21, show.CI=FALSE, method=loess, bw=FALSE, slices=200, palette=colorRampPalette(c("#FFEDA0", "#DD0000"), bias=2)(20), ylim=NULL, quantize = "continuous",  add=FALSE, ...) {
	IV <- all.vars(formula)[2]
	DV <- all.vars(formula)[1]
	data <- na.omit(data[order(data[, IV]), c(IV, DV)])
 
	if (bw == TRUE) {
		palette <- colorRampPalette(c("#EEEEEE", "#999999", "#333333"), bias=2)(20)
	}
 
	print("Computing boostrapped smoothers ...")
	newx <- data.frame(seq(min(data[, IV]), max(data[, IV]), length=slices))
	colnames(newx) <- IV
	l0.boot <- matrix(NA, nrow=nrow(newx), ncol=B)
 
	l0 <- method(formula, data)
	for (i in 1:B) {
		data2 <- data[sample(nrow(data), replace=TRUE), ]
		data2 <- data2[order(data2[, IV]), ]
		if (class(l0)=="loess") {
			m1 <- method(formula, data2, control = loess.control(surface = "i", statistics="a", trace.hat="a"), ...)
		} else {
			m1 <- method(formula, data2, ...)
		}
		l0.boot[, i] <- predict(m1, newdata=newx)
	}
 
	# compute median and CI limits of bootstrap
	library(plyr)
	library(reshape2)
	CI.boot <- adply(l0.boot, 1, function(x) quantile(x, prob=c(.025, .5, .975, pnorm(c(-3, -2, -1, 0, 1, 2, 3))), na.rm=TRUE))[, -1]
	colnames(CI.boot)[1:10] <- c("LL", "M", "UL", paste0("SD", 1:7))
	CI.boot$x <- newx[, 1]
	CI.boot$width <- CI.boot$UL - CI.boot$LL
 
	# scale the CI width to the range 0 to 1 and flip it (bigger numbers = narrower CI)
	CI.boot$w2 <- (CI.boot$width - min(CI.boot$width))
	CI.boot$w3 <- 1-(CI.boot$w2/max(CI.boot$w2))
 
 
	# convert bootstrapped spaghettis to long format
	b2 <- melt(l0.boot)
	b2$x <- newx[,1]
	colnames(b2) <- c("index", "B", "value", "x")
 
	library(ggplot2)
	library(RColorBrewer)
 
	# Construct ggplot
	# All plot elements are constructed as a list, so they can be added to an existing ggplot
 
	# if add == FALSE: provide the basic ggplot object
	p0 <- ggplot(data, aes_string(x=IV, y=DV)) + theme_bw()
 
	# initialize elements with NULL (if they are defined, they are overwritten with something meaningful)
	gg.tiles <- gg.poly <- gg.spag <- gg.median <- gg.CI1 <- gg.CI2 <- gg.lm <- gg.points <- gg.title <- NULL
 
	if (shade == TRUE) {
		quantize <- match.arg(quantize, c("continuous", "SD"))
		if (quantize == "continuous") {
			print("Computing density estimates for each vertical cut ...")
			flush.console()
 
			if (is.null(ylim)) {
				min_value <- min(min(l0.boot, na.rm=TRUE), min(data[, DV], na.rm=TRUE))
				max_value <- max(max(l0.boot, na.rm=TRUE), max(data[, DV], na.rm=TRUE))
				ylim <- c(min_value, max_value)
			}
 
			# vertical cross-sectional density estimate
			d2 <- ddply(b2[, c("x", "value")], .(x), function(df) {
				res <- data.frame(density(df$value, na.rm=TRUE, n=slices, from=ylim[1], to=ylim[2])[c("x", "y")])
				#res <- data.frame(density(df$value, na.rm=TRUE, n=slices)[c("x", "y")])
				colnames(res) <- c("y", "dens")
				return(res)
			}, .progress="text")
 
			maxdens <- max(d2$dens)
			mindens <- min(d2$dens)
			d2$dens.scaled <- (d2$dens - mindens)/maxdens	
 
			## Tile approach
			d2$alpha.factor <- d2$dens.scaled^shade.alpha
			gg.tiles <-  list(geom_tile(data=d2, aes(x=x, y=y, fill=dens.scaled, alpha=alpha.factor)), scale_fill_gradientn("dens.scaled", colours=palette), scale_alpha_continuous(range=c(0.001, 1)))
		}
		if (quantize == "SD") {
			## Polygon approach
 
			SDs <- melt(CI.boot[, c("x", paste0("SD", 1:7))], id.vars="x")
			count <- 0
			d3 <- data.frame()
			col <- c(1,2,3,3,2,1)
			for (i in 1:6) {
				seg1 <- SDs[SDs$variable == paste0("SD", i), ]
				seg2 <- SDs[SDs$variable == paste0("SD", i+1), ]
				seg <- rbind(seg1, seg2[nrow(seg2):1, ])
				seg$group <- count
				seg$col <- col[i]
				count <- count + 1
				d3 <- rbind(d3, seg)
			}
 
			gg.poly <-  list(geom_polygon(data=d3, aes(x=x, y=value, color=NULL, fill=col, group=group)), scale_fill_gradientn("dens.scaled", colours=palette, values=seq(-1, 3, 1)))
		}
	}
 
	print("Build ggplot figure ...")
	flush.console()
 
 
	if (spag==TRUE) {
		gg.spag <-  geom_path(data=b2, aes(x=x, y=value, group=B), size=0.7, alpha=10/B, color=spag.color)
	}
 
	if (show.median == TRUE) {
		if (mweight == TRUE) {
			gg.median <-  geom_path(data=CI.boot, aes(x=x, y=M, alpha=w3^3), size=.6, linejoin="mitre", color=median.col)
		} else {
			gg.median <-  geom_path(data=CI.boot, aes(x=x, y=M), size = 0.6, linejoin="mitre", color=median.col)
		}
	}
 
	# Confidence limits
	if (show.CI == TRUE) {
		gg.CI1 <- geom_path(data=CI.boot, aes(x=x, y=UL), size=1, color="red")
		gg.CI2 <- geom_path(data=CI.boot, aes(x=x, y=LL), size=1, color="red")
	}
 
	# plain linear regression line
	if (show.lm==TRUE) {gg.lm <- geom_smooth(method="lm", color="darkgreen", se=FALSE)}
 
	gg.points <- geom_point(data=data, aes_string(x=IV, y=DV), size=1, shape=shape, fill="white", color="black")		
 
	if (title != "") {
		gg.title <- theme(title=title)
	}
 
 
	gg.elements <- list(gg.tiles, gg.poly, gg.spag, gg.median, gg.CI1, gg.CI2, gg.lm, gg.points, gg.title, theme(legend.position="none"))
 
	if (add == FALSE) {
		return(p0 + gg.elements)
	} else {
		return(gg.elements)
	}
}

Tags: dataviz | ggplot2 | regression | source code | visualization

Dear valued customer,

it is a well-known scientific truth that research results which are accompanied by a fancy, colorful fMRI scan, are perceived as more believable and more persuasive than simple bar graphs or text results (McCabe & Castel, 2007; Weisberg, Keil, Goodstein, Rawson, & Gray, 2008). Readers even agree more with fictitious and unsubstantiated claims, as long as you provide a colorful brain image, and it works even when the subject is a dead salmon.

The power of brain images for everybody

What are the consequence of these troubling findings? The answer is clear. Everybody should be equipped with these powerful tools of research communication! We at IRET made it to our mission to provide the latest, cutting-edge tools for your research analysis. In this case we adopted a new technology called “visually weighted regression” or “watercolor plots” (see here, here, or here), and simply applied a new color scheme.

But now, let’s get some hands on it!

The example

Imagine you invested a lot of effort in collecting the data of 41 participants. Now you find following pattern in 2 of your 87 variables:

You could show that plain scatterplot. But should you do it? Nay. Of course everybody would spot the outliers on the top right. But which is much more important: it is b-o-r-i-n-g!

What is the alternative? Reporting the correlation as text? “We found a correlation of r = .38 (p = .014)”. Yawn.

Or maybe: “We chose to use a correlation technique that is robust against outliers and violations of normality, the Spearman rank coefficient. It turned out that the correlation broke down and was not significant any more (r = .06, p = .708).”.

Don’t be silly! With that style of scientific reporting, there would be nothing to write home about. But you can be sure: we have the right tools for you. Finally, the power of pictures is not limited to brain research – now you can turn any data into a magical fMRI plot like that:

Isn’t that beautiful? We recommend to accompany the figure with an elaborated description: “For local fitting, we used spline smoothers from 10`000 bootstrap replications. For a robust estimation of vertical confidence densities, a re-descending M-estimator with Tukey’s biweight function was employed. As one can clearly see in the plot, there is  significant confidence in the prediction of the x=0, y=0 region, as well as a minor hot spot in the x=15, y=60 region (also known as the supra-dextral data region).”

Magical Data Enhancer Tool

With the Magical Data Enhancer Tool (MDET) you can …

• … turn boring, marginally significant, or just crappy results into a stunning research experience
• … publish in scientific journal with higher impact factors
• … receive the media coverage that you and your research deserve
• … achieve higher acceptance rates from funding agencies
• … impress young women at the bar (you wouldn’t show a plain scatterplot, dude?!)

FAQ

Q: But – isn’t that approach unethical?
A: No, it’s not at all. In contrast, we at IRES think that it is unethical that only some researchers are allowed to exploit the cognitive biases of their readers. We design our products with a great respect for humanity and we believe that every researcher who can afford our products should have the same powerful tools at hand.

Q: How much does you product cost?
A: The standard version of the Magical Data Enhancer ships for 12’998 $. We are aware that this is a significant investment. But, come on: You deserve it! Furthermore, we will soon publish a free trial version, including the full R code on this blog. So stay tuned!

Best regards,

Lexis “Lex” Brycenet (CEO & CTO Research Communication)
International Research Enhancement Technology (IRET)

Tags: dataviz | fMRI | ggplot2

[Update 1: Sep 5, 2012: Explore the Magical Data Enhancer by IRES, using this visualization technique]

[Update 2: Sep 6, 2012: See new improved plots, and new R code!

Solomon Hsiang proposed an appealing method for visually displaying the uncertainty in regressions (see his blog [1][2], and also the discussions on the Statistical Modeling, Causal Inference, and Social Science Blog [1][2]).

I implemented the method in R (using ggplot2), and used an additional method of determining the shading (especially concerning Andrew Gelman’s comment that traditional statistical summaries (such as 95% intervals) give too much weight to the edges. In the following I will show how to produce plots like that:

I used following procedure:

1. Compute smoothers from 1000 bootstrap samples of the original sample (this results in a spaghetti plot)
2. Calculate a density estimate for each vertical cut through the bootstrapped smoothers. The area under the density curve always is 1, so the ink is constant for each y-slice.
3. Shade the figure according to these density estimates.

Now let’s construct some plots!

The basic scatter plot:

No we show the bootstrapped smoothers (a “spaghetti plot”). Each spaghetti has a low alpha. That means that overlapping spaghettis produce a darker color and already give weight to highly populated regions.

Here is the shading according to the smoother’s density:

Now, we can overplot the median smoother estimate for each x value (the “median smoother”):

Or, a visually weighted smoother:

Finally, we can add the plain linear regression line (which obviously does not refelct the data points very well):

At the end of this post is the function that produces all of these plots. The function returns a ggplot object, so you can modify it afterwards, e.g.:

vwReg(y~x, df, shade=FALSE, spag=TRUE) + xlab("Implicit power motive") + ylab("Corrugator activity during preparation")

Here are two plots with actual data I am working on:

The correlation of both variables is .22 (p = .003).

A) As a heat map (note: the vertical breaks at the left and right end occur due to single data points that get either sampled or not during the bootstrap):

B) As a spaghetti plot:

Finally, here’s the code (sometimes the code box is collapsed – click the arrow on the top right of the box to open it). Comments and additions are welcome.

[Update: I removed the code, as an updated version has been published <a title="Visually weighted/ Watercolor Plots, new variants: Please vote!" href="http://www.nicebread.de/visually-weighted-watercolor-plots-new-variants-please-vote/">here</a> (see at the end of the post)]

Tags: dataviz | ggplot2 | regression | visualization

I currently program an automated report generation in R – participants fill out a questionnaire, and they receive a nicely formatted pdf with their personality profile. I use knitr, LaTex, and the sendmailR package.

Some participants did not provide valid email addresses, which caused the sendmail function to crash. Therefore I wanted some validation of email addresses – here’s the function:

isValidEmail <- function(x) {
	grepl("\\<[A-Z0-9._%+-]+@[A-Z0-9.-]+\\.[A-Z]{2,}\\>", as.character(x), ignore.case=TRUE)
}

Let’s test some valid and invalid adresses:

# Valid adresses
isValidEmail("felix@nicebread.de")
isValidEmail("felix.123.honeyBunny@nicebread.lmu.de")
isValidEmail("felix@nicebread.de  ")
isValidEmail("    felix@nicebread.de")
isValidEmail("felix+batman@nicebread.de")
isValidEmail("felix@nicebread.office")
 
# invalid addresses
isValidEmail("felix@nicebread")  
isValidEmail("felix@nicebread@de")
isValidEmail("felixnicebread.de")

The regexp is taken from www.regular-expressions.info and adapted to the R style of regexp. Please note the many comments (e.g., here or here) about “Is there a single regexp that matches all valid email adresses?” (the answer is no).

Tags: R | source code

For the presentation of norm values, often stanines are used (standard nine). These values mark a person’s relativ position in comparison to the sample or to norm values.
According to Wikipedia:

The underlying basis for obtaining stanines is that a normal distribution is divided into nine intervals, each of which has a width of 0.5 standard deviations excluding the first and last, which are just the remainder (the tails of the distribution). The mean lies at the centre of the fifth interval.

For illustration purposes, I wanted to plot the regions of the stanine values in the standard normal distribution – here’s the result:

First: Calculate the stanine boundaries and draw the normal curve:

# First: Calculate stanine breaks (on a z scale)
stan.z <- c(-3, seq(-1.75, +1.75, length.out=8), 3)
 
# Second: get cumulative probabilities for these z values
stan.PR <- pnorm(stan.z)
 
# define a color ramp from blue to red (... or anything else ...)
c_ramp <- colorRamp(c("darkblue", "red"), space="Lab")
 
# draw the normal curve, without axes; reduce margins on left, top, and right
par(mar=c(2,0,0,0))
curve(dnorm(x,0,1), xlim=c(-3,3), ylim=c(-0.03, .45), xlab="", ylab="", axes=FALSE)

Next: Calculate the shaded regions and plot a polygon for each region:

# Calculate polygons for each stanine region
# S.x = x values of polygon boundary points, S.y = y values
for (i in 1:(length(stan.z)-1)) {
	S.x  <- c(stan.z[i], seq(stan.z[i], stan.z[i+1], 0.01), stan.z[i+1])
	S.y  <- c(0, dnorm(seq(stan.z[i], stan.z[i+1], 0.01)), 0)
	polygon(S.x,S.y, col=rgb(c_ramp(i/9), max=255))
}

And finally: add some legends to the plot:

# print stanine values in white
# font = 2 prints numbers in boldface
text(seq(-2,2, by=.5), 0.015, label=1:9, col="white", font=2)
 
# print cumulative probabilities in black below the curve
text(seq(-1.75,1.75, by=.5), -0.015, label=paste(round(stan.PR[-c(1, 10)], 2)*100, "%", sep=""), col="black", adj=.5, cex=.8)
text(0, -0.035, label="Percentage of sample <= this value", adj=0.5, cex=.8)

And finally, here’s a short script for shading only one region (e.g., the lower 2.5%):

# draw the normal curve
curve(dnorm(x,0,1), xlim=c(-3,3), main="Normal density")
 
# define shaded region
from.z <- -3
to.z <- qnorm(.025)
 
S.x  <- c(from.z, seq(from.z, to.z, 0.01), to.z)
S.y  <- c(0, dnorm(seq(from.z, to.z, 0.01)), 0)
polygon(S.x,S.y, col="red")

Tags: didactic example | R

Summary: A new function in the WRS package compares many quantiles of two distributions simultaneously while controlling the overall alpha error.

When comparing data from two groups, approximately 99.6% of all psychological research compares the central tendency (that is a subjective estimate).

In some cases, however, it would be sensible to compare different parts of the distributions. For example, in reaction time (RT) experiments two groups may only differ in the fast RTs, but not in the long. Measures of central tendency might obscure or miss this pattern, as following example demonstrates.

Imagine RT distributions for two experimental conditions (“black” and “red”). Participants in the red condition have some very fast RTs:

set.seed(1234)
RT1 <- rnorm(100, 350, 52)
RT2 <- c(rnorm(85, 375, 55), rnorm(15, 220, 25))
plot(density(RT1), xlim=c(100, 600))
lines(density(RT2), col=2)

A naïve (but common) approach would be to compare both distributions with a t test:

t.test(RT1, RT2)
######################
data:  RT1 and RT2
t = -0.3778, df = 168.715, p-value = 0.706
alternative hypothesis: true difference in means is not equal to 0
95 percent confidence interval:
 -22.74478  15.43712
sample estimates:
mean of x mean of y
 341.8484  345.5022

Now let’s do the same with a new method!

The function qcomhd from the WRS package compares user-defined quantiles of both distributions using a Harrell–Davis estimator in conjunction with a percentile bootstrap. The method seems to improve over other methods: “Currently, when there are tied values, no other method has been found that performs reasonably well. Even with no tied values, method HD can provide a substantial gain in power when q ≤ .25 or q ≥ .75 compared to other techniques that have been proposed”. The method is described in the paper “Comparing two independent groups via the upper and lower quantiles” by Wilcox, Erceg-Hurn, Clark and Carlson (2013).
You can use the function as soon as you install the latest version (17) of the WRS package:
install.packages("WRS", repos="http://R-Forge.R-project.org")

Let’s compare all percentiles from the 10th to the 90th:

qcomhd(RT1, RT2, q = seq(.1, .9, by=.1))

The graphical output shows how groups differ in the requested quantiles, and the confidence intervals for each quantile:

The text output (see below) also shows that groups differ significantly in the 10th, the 50th, and the 60th percentile. The column labeled ‘’.value’’shows the p value for a single quantile bootstrapping test. As we do multiple tests (one for each quantile), the overall Type 1 error (defaulting to .05) is controlled by the Hochberg method. Therefore, for each p value a critical p value is calculated that must be undercut (see column ‘_crit’. The column ‘signify’ marks all tests which fulfill this condition:

    q  n1  n2    est.1    est.2 est.1.est.2    ci.low       ci.up      p_crit p.value signif
1 0.1 100 100 285.8276 218.4852   67.342399  41.04707 84.67980495 0.005555556   0.001      *
2 0.2 100 100 297.5061 264.7904   32.715724 -16.52601 68.80486452 0.025000000   0.217
3 0.3 100 100 310.8760 320.0196   -9.143593 -33.63576 32.95577465 0.050000000   0.589
4 0.4 100 100 322.5014 344.0439  -21.542475 -40.43463  0.03938696 0.010000000   0.054
5 0.5 100 100 331.4413 360.3548  -28.913498 -44.78068 -9.11259108 0.007142857   0.006      *
6 0.6 100 100 344.8502 374.7056  -29.855369 -46.88886 -9.69559705 0.006250000   0.005      *
7 0.7 100 100 363.6210 388.0228  -24.401872 -47.41493 -4.13498039 0.008333333   0.016
8 0.8 100 100 385.8985 406.3956  -20.497097 -47.09522  2.23935390 0.012500000   0.080
9 0.9 100 100 419.4520 444.7892  -25.337206 -55.84177 11.49107833 0.016666667   0.174

Recommendations for comparing groups:

1. Always plot the densities of both distributions.
2. Make a visual scan: Where do the groups differ? Is the central tendency a reasonable summary of the distributions and of the difference between both distributions?
3. If you are interested in the central tendency, think about the test for trimmed means, as in most cases this describes the central tendency better than the arithmetic mean.
4. If you are interested in comparing quantiles in the tails of the distribution, use the qcomhd function.

References

Wilcox, R. R., Erceg-Hurn, D. M, Clark, F., & Carlson, M. (in press). Comparing two independent groups via the lower and upper quantiles. Journal of Statistical Computation and Simulation. doi:10.1080/00949655.2012.754026.

Tags: source code

This is the evolution of a bivariate correlation between two questionnaire scales, “hope of power” and “fear of losing control”. Both scales were administered in an open online study. The video shows how the correlation evolves from r = .69*** (n=20) to r = .26*** (n=271). It does not stabilize until n = 150.

Data has not been rearranged – it is the random order how participants dropped into the study. This had been a rather extreme case of an unstable correlation – other scales in this study were stable right from the beginning. Maybe this video could help as an anecdotal caveat for a careful interpretation of correlations with small n’s (and with ‘small’ I mean n < 100) …

The evolution of correlations from Felix Schönbrodt on Vimeo.

Tags: correlation | didactic example

A little follow up to my testosterone comment (written in German):
When three variables are correlated to each other, and two of the three correlations are known, the range for the third correlation is restricted according to this formula (Olkin, 1981):

Now comes the new part: here’s the graphical representation of that range restriction:

As one can see, one, or both of the two given correlations have to be fairly high to imply a positive third correlation.