When analyzing a questionnaire, one often wants to view the correlation between two or more Likert questionnaire item’s (for example: two ordered categorical vectors ranging from 1 to 5).

When dealing with several such Likert variable’s, a clear presentation of all the pairwise relation’s between our variable can be achieved by inspecting the (Spearman) correlation matrix (easily achieved in R by using the “cor.test” command on a matrix of variables).
Yet, a challenge appears once we wish to plot this correlation matrix. The challenge stems from the fact that the classic presentation for a correlation matrix is a scatter plot matrix – but scatter plots don’t (usually) work well for ordered categorical vectors since the dots on the scatter plot often overlap each other.

There are four solution for the point-overlap problem that I know of:

Jitter the data a bit to give a sense of the “density” of the points

Use a color spectrum to represent when a point actually represent “many points”

Use different points sizes to represent when there are “many points” in the location of that point

Add a LOWESS (or LOESS) line to the scatter plot – to show the trend of the data

In this post I will offer the code for the a solution that uses solution 3-4 (and possibly 2, please read this post comments). Here is the output (click to see a larger image):

In this post I showcase a nice bar-plot and a balloon-plot listing recommended Nutritional supplements , according to how much evidence exists for thier benefits, scroll down to see it(and click here for the data behind it)
* * * *
The gorgeous blog “Information Is Beautiful” recently publish an eye candy post showing a “balloon race” image (see a static version of the image here) illustrating how much evidence exists for the benefits of various Nutritional supplements (such as: green tea, vitamins, herbs, pills and so on) . The higher the bubble in the Y axis score (e.g: the bubble size) for the supplement the greater the evidence there is for its effectiveness (But only for the conditions listed along side the supplement).

There are two reasons this should be of interest to us:

This shows a fun plot, that R currently doesn’t know how to do (at least I wasn’t able to find an implementation for it). So if anyone thinks of an easy way for making one – please let me know.

The data for the graph is openly (and freely) provided to all of us on this Google Doc.

The advantage of having the data on a google doc means that we can see when the data will be updated. But more then that, it means we can easily extract the data into R and have our way with it (Thanks to David Smith’s post on the subject)

For example, I was wondering what are ALL of the top recommended Nutritional supplements, an answer that is not trivial to get from the plot that was in the original post.

In this post I will supply two plots that present the data: A barplot (that in retrospect didn’t prove to be good enough) and a balloon-plot for a table (that seems to me to be much better).

Barplot
(You can click the image to enlarge it)

The R code to produce the barplot of Nutritional supplements efficacy score (by evidence for its effectiveness on the listed condition).

# loading the data
supplements.data.0 <-read.csv("http://spreadsheets.google.com/pub?key=0Aqe2P9sYhZ2ndFRKaU1FaWVvOEJiV2NwZ0JHck12X1E&output=csv")
supplements.data<- supplements.data.0[supplements.data.0[,2]>2,]# let's only look at "good" supplements
supplements.data<- supplements.data[!is.na(supplements.data[,2]),]# and we don't want any missing data
supplement.score<- supplements.data[, 2]
ss <-order(supplement.score, decreasing =F)# sort our data
supplement.score<- supplement.score[ss]
supplement.name<- supplements.data[ss, 1]
supplement.benefits<- supplements.data[ss, 4]
supplement.score.col<-factor(as.character(supplement.score))levels(supplement.score.col)<-c("red", "orange", "blue", "dark green")
supplement.score.col<-as.character(supplement.score.col)# mar: c(bottom, left, top, right) The default is c(5, 4, 4, 2) + 0.1.par(mar =c(5,9,4,13))# taking care of the plot margins
bar.y<-barplot(supplement.score, names.arg= supplement.name, las =1, horiz =T, col= supplement.score.col, xlim =c(0,6.2),
main =c("Nutritional supplements efficacy score","(by evidence for its effectiveness on the listed condition)", "(2010)"))axis(4, labels= supplement.benefits, at = bar.y, las =1)# Add right axisabline(h = bar.y, col= supplement.score.col , lty =2)# add some lines so to easily follow each bar

Also, the nice things is that if the guys at Information Is Beautiful will update there data, we could easily run the code and see the updated list of recommended supplements.

Balloon plot
So after some web surfing I came around an implementation of a balloon plot in R (Thanks to R graph gallery)
There where two problems with using the command out of the box. The first one was that the colors where non informative (easily fixed), the second one was that the X labels where overlapping one another. Since there is no “las” parameter in the function, I just opened the function up, found where this was plotted and changed it manually (a bit messy, but that’s what you have to do sometimes…)

Here are the result (you can click the image for a larger image):

And here is The R code to produce the Balloon plot of Nutritional supplements efficacy score (by evidence for its effectiveness on the listed condition).
(it’s just the copy of the function with a tiny bit of editing in line 146, and then using it)

Daniel Malter just shared on the R mailing list (link to the thread) his code for performing the Siegel-Tukey (Nonparametric) test for equality in variability.
Excited about the find, I contacted Daniel asking if I could republish his code here, and he kindly replied “yes”.
From here on I copy his note at full.

As a statistics (and WordPress) lover myself, I was inspired to extend the list of wordpress statistics plugins for the hope of benefiting the community: Blog Metrics
This plugin is based on ideas in an excellent post by Avinash Kaushik (Whom I consider a Web analytics guru and a brilliant blogger!).

it calculates:

Raw Author Contribution:

average number of posts per month

average number of words per post

Conversation Rate:

average number of comments per postwithout your own comments

average number of words used in comments to posts

Both for all the time you’ve been blogging, and for the last month, it then adds these values in a page on your WordPress dashboard.

If you have a Search box on your blog, Search Meter automatically records what people are searching for — and whether they are finding what they are looking for. Search Meter’s admin interface shows you what people have been searching for in the last couple of days, and in the last week or month. It also shows you which searches have been unsuccessful. If people search your blog and get no results, they’ll probably go elsewhere. With Search Meter, you’ll be able to find out what people are searching for, and give them what they want by creating new posts on those topics. […]

Google Analytics Dashboard gives you the ability to view your Google Analytics data in your WordPress dashboard. You can also alow other users to see the same dashboard information when they are logged in or embed parts of the data into posts or as part of your theme.

The biggest advantage of this plugin in my view is that it adds sparklines in the “posts -> edit” page in the admin area.

Analytics360
I don’t use this one much. But one feature it has that I find interesting is that is adds information of when you posted something with the trend line of the google analytics traffic data. It also mixes data from MailChimp’s, which I don’t use.

MailChimp’s Analytics360 plugin allows you to pull Google Analytics and MailChimp data directly into your dashboard, so you can access robust analytics tools without leaving WordPress.

This plugin adds a Piwik stats site to your WordPress dashboard. It’s also able to add the Piwik tracking code to your blog. Piwik is an open source (GPL licensed) web analytics software program. It provides you with detailed real time reports on your website visitors: the search engines and keywords they used, the language they speak, your popular pages and so on…

You can install Piwik more or less like you install WordPress, and then you are left to integrate it into your blog. The only real down side of it for me (compared to google analytics) is the advanced segmentation and pivoting. But in general it is a free, great (and growing!) Web analytics solution.

Woopra Analytics Plugin
I have been using Woopra since their release thanks to lorelle. I enjoy the ability to follow the live actions that are happening inside the blog. Although since woopra went from BETA to GOLD, I lost most interest because the total blogs I track have more traffic volume then woopra allow tracking in their free account. But small bloggers could find the service gratifying.

Woopra is the world’s most comprehensive, information rich, easy to use, real-time Web tracking and analysis application.

Features include:

Live Tracking and Web Statistics

A rich user interface and client monitoring application

Real-time Analytics

Manage Multiple Blogs and Websites

Deep analytic and search capabilities

Click-to-chat

Visitor and member tagging

Real-time notifications

Easy Installation and Update Notification

Final notes

If you are into web analytics, I also encourage you to give the following a try: Nuconomy,ClickTale, Crazy Egg. And of course, Google analytics. Each of them (and also Woopra) strips you and your visitors a bit more from their privacy. But that is the ultimate price we pay for the strong Web analytics solutions that exists out there.
If you got any more statistics plugins I missed, feel encouraged to share them with me in the comments

This post will eventually grow to hold a wide list of books on statistics (e-books, pdf books and so on) that are available for free download. But for now we’ll start off with just one several books:

The Elements of Statistical Learning written by Trevor Hastie, Robert Tibshirani and Jerome Friedman. you can legally download a copy of the book in pdf format from the authors website! Direct download (First discovered on the “one R tip a day” blog)

Introduction to Statistical Thought by Michael Lavine. The book is organized into seven chapters: “Probability,” “Modes of Inference,” “Regression,” “More Probability,” “Special Distributions,” “More Models,” and “Mathematical Statistics.” and makes extensive use of R. Here is a favoring review the book received in JASA. 328 pages. Download link (approx. 40 mbyte)

Collaborative Statistics by Barbara Illowsky and Susan Dean. This textbook is intended for introductory statistics courses. 627 pages. R is not used in this book. Download link

Using R for Introductory Statistics by John Verzani Publisher: Chapman & Hall/CRC 2004 ISBN/ASIN: 1584884509 ISBN-13: 9781584884507 Number of pages: 114 Description: The author presents a self-contained treatment of statistical topics and the intricacies of the R software. The book treats exploratory data analysis with more attention than is typical, includes a chapter on simulation, and provides a unified approach to linear models. This text lays the foundation for further study and development in statistics using R. Download link

R Graphics (Three chapters only) by Paul Murrell ISBN: 9781584884866 ISBN 10: 158488486X Publication Date: July 29, 2005 Number of Pages: 328 Description: Chapter 1: An Introduction to R Graphics Chapter 4: Trellis Graphics: The Lattice Package Chapter 5: The Grid Graphics Model Download link (see scripts and images here)

Psychometric Theory with Applications in R by William Revelle (a work in progress) Download link

A great long list of R related texts, for free download, can be found here.

Using Graphs Instead of Tableswebsite link (This web page accompanies the article “Using Graphs Instead of Tables in Political Science”, by Jonathan Kastellec and Eduardo Leoni, which appears in the December 2007 issue of Perspectives on Politics. It contains complete replication code for all the graphs that appear in the text)

R is a free software environment for statistical computing and graphics. It compiles and runs on a wide variety of UNIX platforms, Windows and MacOS. If you wish to download R, please choose your preferred CRAN mirror.

The R language has become a de facto standard among statisticians for the development of statistical software,and is widely used for statistical software development and data analysis.

Basic questions about R like how to download and install the software, or what the license terms are, are answered in the answers to frequently asked questions section.

Introduction to R

R is a language and environment for statistical computing and graphics. R provides a wide variety of statistical (linear and nonlinear modelling, classical statistical tests, time-series analysis, classification, clustering, …) and graphical techniques, and is highly extensible.

One of R’s strengths is the ease with which well-designed publication-quality plots can be produced, including mathematical symbols and formulae where needed. Great care has been taken over the defaults for the minor design choices in graphics, but the user retains full control.

R is available as Free Software under the terms of the Free Software Foundation‘s GNU General Public License in source code form. It compiles and runs on a wide variety of UNIX platforms and similar systems (including FreeBSD and Linux), Windows and MacOS.

R and S

R is a GNU project which is similar to the S language and environment which was developed at Bell Laboratories (formerly AT&T, now Lucent Technologies) by John Chambers and colleagues. R can be considered as a different implementation of S. There are some important differences, but much code written for S runs unaltered under R. The S language is often the vehicle of choice for research in statistical methodology, and R provides an Open Source route to participation in that activity.

The R environment

R is an integrated suite of software facilities for data manipulation, calculation and graphical display. It includes

an effective data handling and storage facility,

a suite of operators for calculations on arrays, in particular matrices,

a large, coherent, integrated collection of intermediate tools for data analysis,

graphical facilities for data analysis and display either on-screen or on hardcopy, and

a well-developed, simple and effective programming language which includes conditionals, loops, user-defined recursive functions and input and output facilities.

The term “environment” is intended to characterize it as a fully planned and coherent system, rather than an incremental accretion of very specific and inflexible tools, as is frequently the case with other data analysis software.

R, like S, is designed around a true computer language, and it allows users to add additional functionality by defining new functions. Much of the system is itself written in the R dialect of S, which makes it easy for users to follow the algorithmic choices made. For computationally-intensive tasks, C, C++ and Fortran code can be linked and called at run time. Advanced users can write C code to manipulate R objects directly.

Many users think of R as a statistics system. We prefer to think of it of an environment within which statistical techniques are implemented. R can be extended (easily) via packages. There are about eight packages supplied with the R distribution and many more are available through the CRAN family of Internet sites covering a very wide range of modern statistics.

R has its own LaTeX-like documentation format, which is used to supply comprehensive documentation, both on-line in a number of formats and in hardcopy.