Dataviz
18 March 09.
This is a continuation of last episode
That said, let's start with a little exercise.
The first figure is a TrellisTM or lattice plot, giving a 2-D dot plot of each of three variables against each other variable. I didn't try too hard in producing the plot, and just pulled out three variables at random from a random data set. With three variables, you can get three plots (Var1 x Var2, Var1 x Var3, Var2 x Var3), and the mirror image of those graphs (i.e., the same plots with the axes reversed).
Figure One: A lattice plot, relating three variables to each other
But we can already see some patterns: GDP/capita and height have the positive correlation you'd expect, as per the blow up in the next figure. In this figure, I fit a linear regression to the data, and it looks pretty good, but for an outlier or two at the left. Pretty good for an initial eyeballing, upon which we can perhaps improve with closer inspection.
Figure Two: A close-up of the upper left plot in the lattice, with the line of best fit
So that's DataViz at work. We took a lot of data, displayed many
relations at once, and zeroed in on one that works.
Except, uh, for all that I said about this being a random data set. I just made up some pleasant-sounding variable names, ran the random number generator for a bit, and plotted the results. And yet we were able to find a plausible pattern in there.
Thus, another way of casting the descriptive versus inferential war, i.e., the problem of too many hypothesis tests. The descriptivists are working to produce methods like the lattice plot that let you see more relationships at once; the inferentialists are asking: if you fed complete noise to this method, what are the odds that we'd still see some sort of pattern? As our methods get better at putting more data on the screen at once, they get worse at testing whether the patterns we see are real or just beautiful noise.
Tools for cloudgazing
Thanks to a number of technological advances, dataViz is trendy right now. There are a few icons of the field purveying what is often called infoporn, such as Edward Tufte, whose books show how graphs can be cleaned up, chartjunk eliminated, and grainy black and white fliers from the 1970s cleaned up through the use of finely detailed illustrations in full color. John Tukey's Exploratory Data Analysis was an aggressively quirky book from the `70s that offered a number of methods for seeing your data even if all you have is a pencil and paper, and encouraged disdain for inferential rules when they get in the way of the limited descriptive tools available. Our descriptive tools aren't nearly as limited, but the attitude seems to persist.
These guys, and their followers, are right that we could do a whole lot better with our data visualizations, and that the stuff based on facilitating fitting the line with a straightedge should have been purged at least twenty years ago. Strunk and White gave us standards for writing clearly in 1959; it's about time we developed guidelines for exposition via graphics.
But we're talking not just about presenting a known relationship, but exploratory data analysis via graphics. In this context, the underlying philosophy is humanist to a fault. The claim is that the human brain is the best data-processor out there, and our computers still can't see a relationship among a blob of dots as quickly as our eye/brain combo can. This is true, and a fine justification for better graphical data presentation. And hey, we humans would all rather look at plots than at tables of numbers.
Figure Three: If you don't see faces, you're crazy. Oh, and there's a penis and vagina in every inkblot too.
But apophenia is a powerful force. We look at clouds and see bunnies, or read the horoscope and think that it's talking directly to us, or listen to a Beatles song about playground equipment and think it's telling us to kill people. Given a handful of scatterplots like the lattice plot above, you will find a pattern--in fact, if a psychologist were to show you a series of ten seemingly random inkblots and you didn't see a reasonable number of patterns in them, the psychologist might consider you to be mentally unhealthy in any of a number of ways.
The moral here is that our data visualization technology is getting really good really fast--I'll have even slicker examples next time. Though you'd be silly to ignore these recommendations and novel display methods, we need to bear in mind that all that power can work as well on noise as on signal.
Next time: even more dataviz tools, which touch on an even bigger problem.
Please note: full references are given in the PDF version
[link] [No comments]
[Previous entry: "Too many tests"]
[Next entry: "Crowdsourcing data mining"]