Head First Data Analysis

Chapter 4. Data Visualization: Pictures make you smarter

You need more than a table of numbers.

Your data is brilliantly complex, with more variables than you can shake a stick at. Mulling over mounds and mounds of spreadsheets isn’t just boring; it can actually be a waste of your time. A clear, highly multivariate visualization can in a small space show you the forest that you’d miss for the trees if you were just looking at spreadsheets all the time.

New Army needs to optimize their website

New Army is an online clothing retailer that just ran an experiment to test web layouts. For one month, everyone who came to the website was randomly served one of these three home page designs.

They had their experiment designers put together a series of tests that promise to answer a lot of their questions about their website design.

What they want to do is find the best stylesheets to maximize sales and get people returning to their website.

The results are in, but the information designer is out

Now that they have a store of fantastic data from a controlled, randomized experiment, they need a way to visualize it all together.

So they hired a fancy information designer and asked him to pull together something that helped them understand the implications of their research. Unfortunately, all did not work out as planned.

You’ll need to redesign the visualizations for the analysis. It could be hard work, because the experiment designers at New Army are an exacting bunch and generated a lot of solid data.

But before we start, let’s take a look at the rejected designs. We’ll likely learn something by knowing what sort of visualizations won’t work.

Let’s take a look at the rejected designs...

The last information designer submitted these three infographics

The information designer submitted these three designs to New Army. Take a look at these designs. What are your impressions? Can you see why the client might not have been pleased?

What data is behind the visualizations?

“What is the data behind the visualizations?” is the very first question you should ask when looking at a new visualization. You care about the quality of the data and its interpretation, and you’d hate for a flashy design to get in the way of your own judgments about the analysis.

Brain Power

What sort of data do you think is behind these visualizations?

Show the data!

You can’t tell from these visualizations what data is behind them. If you’re the client, how could you ever expect to be able to make useful judgments with the visualizations if they don’t even say clearly what data they describe?

Show the data. Your first job in creating good data visualizations is to facilitate rigorous thinking and good decision making on the part of your clients, and good data analysis begins and ends with thinking with data.

New Army’s actual data, however, is really rich and has all sorts of great material for your visualizations.

Here’s some unsolicited advice from the last designer

You didn’t ask for it, but it appears that you’re getting it anyway: the outgoing information designer wants to put in his two cents about the project. Maybe his perspective help...

Sharpen your pencil

Dan seems to think that an excess of data is a real problem for someone trying to design good data visualizations. Do you think that what he is saying is plausible? Why or why not?

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Sharpen your pencil Solution

Is Dan being reasonable when he says it’s too hard to do good visualizations when there is too much data?

This isn’t very plausible. The whole point of data analysis is to summarize data, and summarizing tools, like taking the average of a number, will work regardless of whether you have just a few data points or millions. And if you have a bunch of different data sets to compare to each other, really great. visualizations facilitate this sort of data analysis just like all the other tools.

Too much data is never your problem

It’s easy to get scared by looking at a lot of data.

But knowing how to deal with what seems like a lot of data is easy, too.

If you’ve got a lot of data and aren’t sure what to do with it, just remember your analytical objectives. With these in mind, stay focused on the data that speaks to your objectives and ignore the rest.

Oh, really? Do you think it’s your job as a data analyst to create an aesthetic experience for your clients?

Making the data pretty isn’t your problem either

If the data visualization solves a client’s problem, it’s always attractive, whether it’s something really elaborate and visually stimulating or whether it’s just a plain ol’ table of numbers.

Making good data visualizations is just like making any sort of good data analysis. You just need to know where to start.

Brain Power

So how do you use a big pile of data with a bunch of different variables to evaluate your objectives? Where exactly do you begin?

Data visualization is all about making the right comparisons

To build good visualizations, first identify what are the fundamental comparisons that will address your client’s objectives. Take a look at their most important spreadsheets:

While New Army has more data than these three sheets, these sheets have the comparisons that will speak directly to what they want to know. Let’s try out a comparison now...

Sharpen your pencil

Take look at the statistics that describe the results for Home Page #1. Plot dots to represent each of the users on the axes below.

Use your spreadsheet’s average formula (AVG) to calculate the average Revenue and TimeOnSite figures for Home Page #1, and draw those numbers as horizontal and vertical lines on the chart.

Load this!

www.headfirstlabs.com/books/hfda/hfda_ch04_home_page1.csv

How do the results you see compare to their goals for revenue and time on site?

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Sharpen your pencil Solution

How did you visualize the Revenue and TimeOnSite variables for Home Page #1?

How do the results you see compare to their goals for revenue and time on site?

On average, the time people spend looking at the website under Home Page #1 is greater than New Army’s goal for that statistic. On the other hand, the average amount of revenue for each user is less than their goal.

Your visualization is already more useful than the rejected ones

Now that’s a nice chart, and it’ll definitely be useful to your client. It’s an example of a good data visualization because it...

• Shows the data

• Makes a smart comparison

• Shows multiple variables

Note

Here’s another feature of great visualizations.

Use scatterplots to explore causes

Scatterplots are great tools for exploratory data analysis, which is the term statisticians use to describe looking around in a set of data for hypotheses to test.

Analysts like to use scatterplots when searching for causal relationships, where one variable is affecting the other. As a general rule, the horizontal x-axis of the scatterplot represents the independent variable (the variable we imagine to be a cause), and the vertical y-axis of a scatterplot represents the dependent variable (which we imagine to be the effect).

You don’t have to prove that the value of the independent variable causes the value of the dependent variable, because after all we’re exploring the data. But causes are what you’re looking for.

The best visualizations are highly multivariate

A visualization is multivariate if it compares three or more variables. And because making good comparisons is fundamental to data analysis, making your visualizations as multivariate as possible makes it most likely that you’ll make the best comparisons.

And in this case you’ve got a bunch of variables.

Brain Power

How would you make the scatterplot visualization you’ve created more multivariate?

Show more variables by looking at charts together

One way of making your visualization more multivariate is just to show a bunch of similar scatterplots right next to each other, and here’s an example of such a visualization.

All of your variables are plotted together in this format, which enables you to compare a huge array of information right in one place. Because New Army is really interested in revenue comparisons, we can just stick with the charts that compare TimeOnSite, Pageviews, and ReturnVisits to revenue.

Sharpen your pencil

You’ve just created a pretty complex visualization. Look at it and think about what it tells you about the stylesheets that New Army decided to test.

Do you think that this visualization does a good job of showing the data? Why or why not?

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Just looking at the dots, you can see that Home Page #2 has a very different sort of spread from the other two stylesheets. What do you think is happening with Home Page #2?

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Which of the three stylesheets do you think does the best job of maximizing the variables that New Army cares about? Why?

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Sharpen your pencil Solution

Does the new visualization help you understand the comparative performance of the stylesheets?

Do you think that this visualization does a good job of showing the data? Why or why not?

Definitely. Each dot on each of the nine panels represents the experience of a single user, so even though the data points are summarized into averages, you can still see absolutely all of them. Seeing all the points makes it easy to evaluate the spread, and the average lines make it easy to see how each stylesheet performs relative to each other and relative to New Army’s goals.

Just looking at the dots, you can see that Home Page #2 has a very different sort of spread from the other two stylesheets. What do you think is happening with Home Page #2?

It looks like Home Page #2 is performing terribly. Compared to the other two stylesheets, Home Page #2 isn’t bringing in much revenue and also performs poorly on the Time on Site, Pageviews, and Return Visits figures. Every single user statistic is below New Army’s goals. Home Page #2 is terrible and should be taken offline immediately!

Which of the three stylesheets do you think does the best job of maximizing the variables that New Army cares about? Why?

Home Page #3 is the best. While #1 performs above average when it comes to the metrics besides Revenue, #3 is way ahead in terms of revenue. When it comes to Return Visits, #1 is ahead, and they’re neck-and-neck on Pageviews, but people spend more time on the site with #3. It’s great that #1 gets a lot of return visits, but you can’t argue with #3’s superior revenue.

There are no Dumb Questions

Q:	Q: What software tool should I use to create this sort of graphic?
A:	A: Those specific graphs are created in a statistical data analysis program called R, which you’re going to learn all about later in the book. But there are a number of charting tools you can use in statistical programs, and you don’t even have to stop there. You can use illustration programs like Adobe Illustrator and just draw visualizations, if you have visual ideas that other software tools don’t implement.
Q:	Q: What about Excel and OpenOffice? They have charting tools, too.
A:	A: Yes, well, that’s true. They have a limited range of charting tools you can use, and you can probably figure out a way to create a chart like this one in your spreadsheet program, but it’s going to be an uphill battle.
Q:	Q: You don’t sound too hot on spreadsheet data visualizations.
A:	A: Many serious data analysts who use spreadsheets all the time for basic calculations and lists nevertheless wouldn’t dream of using spreadsheet charting tools. They can be a real pain: not only is there a small range of charts you can create in spreadsheet programs, but often, the programs force you into formatting decisions that you might not otherwise make. It’s not that you can’t make good data graphics in spreadsheet programs; it’s just that there’s more trouble in it than you’d have if you learned how to use a program like R.
Q:	Q: So if I’m looking for inspiration on chart types, the spreadsheet menus aren’t the place to look?
A:	A: No, no, no! If you want inspiration on designs, you should probably pick up some books by Edward Tufte, who’s the authority on data visualization by a long shot. His body of work is like a museum of excellent data visualizations, which he sometimes calls “cognitive art.”
Q:	Q: What about magazine, newspapers, and journal articles?
A:	A: It’s a good idea to become sensitive to data visualization quality in publications. Some are better than others when it comes to designing illuminating visualizations, and when you pay attention to the publications, over time, you’ll get a sense of which ones do a better job. A good way to start would be to count the variables in a graphic. If there are three or more variables in a chart, the publication is more likely to be making intelligent comparisons than if there’s one variable to a chart.
Q:	Q: What should I make of data visualizations that are complex and artistic but not analytically useful?
A:	A: There’s a lot of enthusiasm and creativity nowadays for creating new computer-generated visualizations. Some of them facilitate good analytical thinking about the data, and some of them are just interesting to look at. There’s absolutely nothing wrong with what some call data art. Just don’t call it data analysis unless you can directly use it to achieve a greater understanding of the underlying data.
Q:	Q: So something can be visually interesting without being analytically illuminating. What about vice versa?
A:	A: That’s your judgement call. But if you have something at stake in an analysis, and your visualization is illuminating, then it’s hard to imagine that the graphic wouldn’t be visually interesting!

Let’s see what the client thinks...

The visualization is great, but the web guru’s not satisfied yet

You just got an email from your client, the web guru at New Army, assessing what you created for him. Let’s see what he has to say...

He wants to know about causality.

Knowing what designs work only takes him so far. In order to make his website as powerful as possible, he needs some idea of why people interact with the different home pages the way they do.

And, since he’s the client, we definitely need to address the theories he put forward.

Good visual designs help you think about causes

Your and your client’s preferred model will usually fit the data.

But there are always other possibilities, especially when you are willing to get imaginative about the explanations. What about other models?

You need to address alternative causal models or explanations as you describe your data visualization. Doing so is a real mark of integrity: it shows your client that you’re not just showing the version of the story that you like best: you’re thinking through possible failure points in your theories.

The experiment designers weigh in

The experiment designers saw the web guru’s theories and sent you some of their thoughts. Perhaps their input will enable you to evaluate the web guru’s hypotheses about why some home pages performed better than others.

To:	Head First
From:	New Army experiment designers
Re:	The boss’s ideas
He thinks that page loads count? That could be. We haven’t taken a look at the data yet to see for sure. But in our testing, #2 was the fastest, followed by #3, and then #1. So, sure, he could be right. Note Here’s what the experiment designers think about the first hypothesis.
As for the cooler color palette, we kind of doubt it. The color palette of Home Page #3 is coolest, followed by #2, then #1, by the way. There’s research to show that people react differently, but none of it has really persuaded us. Note Here’s their response to the second hypothesis.

Sharpen your pencil

Let’s take a look at the data to see whether the bosses hypotheses fit. Does the data fit either of the hypotheses?

Hypothesis 1: The snappy performance of snappy web pages accounts for why Home Page #3 performed best.

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Hypothesis 2: The relaxing, cool color palette of Home Page #3 accounts for why it performed best.

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Sharpen your pencil Solution

How well did you find the web guru’s hypotheses to fit the data?

Hypothesis 1: The snappy performance of snappy web pages accounts for why Home Page #3 performed best.

This can’t be true, since #3 isn’t the fastest, according to the experiment designers. It might be that as general rule people prefer faster pages, but page load speed can’t explain #3’s success in the context of this experiment.

Hypothesis 2: The relaxing, cool color palette of Home Page #3 accounts for why it performed best.

This hypothesis fits the data. Home Page #3 is the highest-performing page, and it has the coolest color palette. The data don’t prove that the color palette is the reason that #3 performed so well, but it fits the hypothesis.

The experiment designers have some hypotheses of their own

They’ve had an opportunity to take a look at your scatterplots and sent you some of their own thinking about what’s going on. These people are data junkies, and their hypotheses definitely fit.

To:	Head First
From:	New Army experiment designers
Re:	We don’t know why Home Page #3 is stronger
We’re delighted to hear that #3 is the best, but we really don’t know why. Who knows what people are thinking? But that is actually OK: as long as we’re showing improvement on the business fundamentals, we don’t need to understand people in a deep way. Still, it’s interesting to learn as much as we can. The stylesheets are really different from each other in many ways. So when it comes to isolating individual features that might account for the performance differential, it’s hard. In the future, we’d like to take Home Page #3 and test a bunch of subtle permutations. That way, we might learn things like how button shape or font choice affect user behavior. Note Here’s what the experiment designers want to do next. But we conjecture that there are two factors. First, Home Page #3 is really readable. We use fonts and a layout that are easy on the eyes. Second, the page hierarchy is flatter. You can find pretty much everything in three clicks, when for Home Page #1 it takes you more like seven clicks to find what you want. Both could be affecting our revenue, but we need more testing to say for sure. Note Maybe it’s fonts and layout. Note Maybe it’s hierarchy of the pages.

Sharpen your pencil

On the basis of what you’ve learned, what would you recommend to your client that he do regarding his web strategy?

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Sharpen your pencil Solution

What would you tell your client to do with his website on the bases of the data you visualized and the explanatory theories you evaluated?

Stick with Home Page #3 and test for finer-grained elements of the user’s experience, like variable navigation, style, and content. There are a bunch of different possible explanations for #3’s performance that should be investigated and visualized, but it’s clear that #3 is the victor here.

The client is pleased with your work

You created an excellent visualization that enabled New Army to quickly and simultaneously assess all the variables they tested in their experiment.

And you evaluated that visualization in light of a bunch of different hypotheses, giving them some excellent ideas about what to test for in the future.

Orders are coming in from everywhere!

Because of the new website, traffic is greater than ever. Your visualization of the experimental results showed what they needed to know to spruce up their website.

Even better, New Army has embarked on a continuous program of experimentation to fine-tune their new design, using your visualization to see what works. Nice job!