Welcome to Wednesday night live from New York!

Tonight, we will continue discussing narrative, but this time with the idea of combining numbers in various forms with that narrative. To do this, we will also extend the design principles we recently considered.

Sound good?

But first, let’s remind ourselves how tonight’s material fits into the overall course.

As with last week, we will be focused on narrative, but closer to the intersections with data.

Here’s our deliverables timeline.

Next week you’ll be turning in homework 3.

Your memos will become valuable for the groups I assign you to in getting started on your projects. We’ll begin to discuss those group projects once you turn in your memos.

Ok, We’ve already been guided by various authors who explain that we cannot truly give meaning to our communications without comparisons, right? It’s that important.

From the references I’ve given you, Millar offers some related principles that help with comparison and context. She starts with the first concept I was taught in engineering school. The most basic and essential concept we must have with our numbers.

Units.

Here, we display the number 25. What does 25 mean?

25 what?

It isn’t enough to just provide a category of potential units, like temperature, for example. We need to communication specific units of measurement.

So, first, numbers communicated without units don’t mean anything.

Along with units, we can provide context about our numbers to give them more meaning. The who, what, when, and where. Let’s consider one of Miller’s examples.

In her examples, she provides three versions of information, each an improvement over the previous one. Now I’ve lightly edited her examples to further clarify my points.

So starting on the left, let’s read:

“There were 25 million deaths.”

Don’t yet look to the right. So, first, what are the units?

[DEATHS].

Yes, deaths. Of what? Who or what died? So this sentence offers no context to help us understand what 25 million means.

How about the middle version? Ah, we learn a little more. We learn some who or what, and we learn some when, and we learn something about the where.

“During the fourteenth century, 25 million people died in Europe.”

But this middle version still doesn’t seem all that useful on its own, right? Why did they die? The fourteenth century in the whole of Europe is incredibly broad in time and space and category of subject!

Let’s consider Miller’s third version, here on the right. I have slightly edited it.

[READ FROM SLIDE]

Ah, now we get some sense of cause and effect! We get more specificity of scope in time and space. And, finally, we are given something to compare this number with to get an understanding of scale.

Numbers need context and comparison for us to understand their significance. I think Millar’s helps us see this point. It does for me, and I hope it does for you.

When we discuss examples together, by the way, we should be thinking about how we can use the ideas in our own communications. So how can we apply this concept in our work? What about how you an apply these ideas, like to your memos?

Perhaps we can step into the shoes of our audience, read the sentence, and ask ourselves what about it we understand on its own, separating out what we otherwise know. Does the sentence on its own explain what it is in a fair context and why it’s important? For every sentence we write. Does that make sense?

Let’s look at another of Millar’s examples, this one focusing on the need for comparisons.

What does the left example tell us?

From the left example, you cannot tell whether 2001 was a typical year, unusually warm, or unusually cool, right?

Her middle example clarifies that 2001 was a warm year, as well as reporting the average temperature.

Finally, the right example points out not only that temperatures for 2001 were above average, but also just how unusual that departure was. So this communication now provides statistical context that we commonly want to know: a magnitude and direction from some average, and where in the distribution this value rests. Does that make sense?

Questions?

Let’s consider a third example. Now you recall our discussions from Doumont about using messages, not just information? Keep that in mind.

Ok, with that in mind, here is a third example.

From left sentence, it is difficult to assess whether total US expenditures on health care are high or low, stable or changing quickly. To most people, $1.1 trillion sounds like a lot of money, but the key question is “compared to what?”

If the audience knew the total national budget, they could do a benchmark calculation, but you will make the point more directly if you do that calculation for them.

In the middle example: This simple translation of total expenditures into a per capita figure takes a large number that is difficult for many people to fathom and converts it into something that they can relate to. Readers can compare that figure with their own bank balance or what they have spent on health care recently to assess the scale of national health care expenditures.

In the right example, and again, I’ve lightly edited the example. This description reveals that health care expenditures in the United States were the highest of any country and reports how much higher compared to the next highest country. By using percentage of GDP as the measure, this comparison avoids the issue that countries with smaller populations would be expected to spend fewer total dollars but could still have higher per capita or percentage of GDP expenditures on health.

Now sometimes the content itself will be unfamiliar to our audience. We need an entirely different frame of reference to help them understand why the content we communicate is important. Throughout human history, we’ve understood new things through things we know.


Ok, let’s try to use the ideas we’ve discussed so far, and reconsider our class example draft memo. Is it ready for communication, or does it need further revision.

Let’s take a poll to start this discussion.

[ACTIVATE POLL]

[DEACTIVATE, DISCUSS]

So we’ve been thinking about context to providing meaning for numbers. Where else can we find such context?

What’s a metaphor?

Yes, so a metaphor uses whatever is both familiar and analogous to what we want to communicate. The familiar thing, we call the source domain, and that thing will be used to explain what’s less familiar. And the less familiar thing, the target domain.

Let’s consider metaphors in a short data story.

Let’s consider metaphors in the context of an excerpt of a data story called The Last Rembrandt.

The Last Rembrandt was a collaboration to use machine learning to analyze paintings by Rembrandt, and then use the results of that machine learning to 3D print a new painting in the style of Rembrandt’s work.

So let’s look at some of the language they used to describe the data analytics concepts.

We’ll look at this language in a moment, But first, let’s watch the video — the data story — then we’ll look at the langauge I’ve pulled out.

[SCROLL DOWN TO REVIEW THE WEBSITE / WATCH THE VIDEO]

Ok, here’s the excerpt from the website we just reviewed, along with a link to the original material.

Let’s take a moment to read this excerpt. As you read, look for metaphors, things that may be arguably more familiar that are used to explain.

Ok, anyone need more time?

What did you all find? How were they used? What were their purposes?

[DNA, POOL, MAP, …]

Now the source domains for these metaphors are so familiar to most of us, that they can be used in contexts like this without explaining them first. Others do require some initial explanations, though. So let’s consider an example of that.

[PLAY THE VIDEO, SCROLL BACK UP]

I pulled this metaphor from R.J. Andrews’s book, Info We Trust, from which I’ve included the citation to in the references.

In his book, he uses artifacts of music to explain data information.

Does anyone have a vinyl record collection? Nostalgic now that we probably all stream music. Anyone know how vinyl records were made? On the left, I’ve quoted Andrews setup of this metaphor. Let’s read it together:

“How do we think about the albums we love? A lonely microphone in a smoky recording studio? A needle’s press into hot wax? A rotating can of magnetic tape? A button that clicks before the first note drops? No! The mechanical ephemera of music’s recording, storage, and playback may cue nostalgia, but they are not where the magic lies. The magic is in the music. The magic is in the information that the apparatuses capture, preserve, and make accessible. It is the same with all information.”

So the key transition here is the word information, using to for music information, and later for other, data information.

It is the same with all information.

Now that he has described the metaphor, let’s see how he uses it. I’ve pulled a few quotes from his book where he references back to the metaphor. Let’s read them:

“When you envision data, do not get stuck in encoding and storage. Instead, try to see the music.”

What is he doing? What’s he explaining here? Do you think it’s an effective way to help you think about data differently?

Let’s look at his next reference back:

“Looking at tables of any substantial size is a little like looking at the grooves of a record with a magnifying glass. You can see the data but you will not hear the music.”

Now this quote is also a bit of a dig on data organization we’re about to discuss. Again, same question. What do you think about the use of the metaphor in explaining data tables?

Finally, he says,

“Then, we can see data for what it is, whispers from a past world waiting for its music to be heard again.”

What might he mean by that?

Doesn’t it also seem to make his data discussions a little more interesting?

I wanted to share this with you as an example of a metaphor that needs to be setup but once it is, we can refer back to that more familiar thing to explain something newer.

Speaking of comparison, let’s consider another example from Millar.

The left sentence,

“Mortality and age are correlated”,

doesn’t say whether age and mortality are positively or negatively related or how much mortality differs by age.

The middle sentence,

“as age increases, mortality increases,”

is better in that it specifies the direction of the association, but the size of the mortality difference by age is still unclear.

The right sentence,

“among the elderly, mortality roughly doubles for each successive five-year age group,”

explains both the direction and the magnitude of the age/mortality association, which, again, are the type of statistical thinking we commonly use.

Are these discussions of examples so far helping you think about ways to add context, meaning, when reporting numbers? Questions so far?

I want to focus on another aspect of comparison. We can compare numbers in multiple ways. Let’s look at another example from Andrews book.

We can put two numbers side by side. We can talk about an additive difference. Or a multiplicative difference.

Especially with smaller numbers, humans tend to reason easier in an additive way. Like counting. In this example,

“the Apollo program crew had one more astronaut than Project Gemini.”

His second sentence uses multiplicative reasoning.

“Apollo’s Saturn Five rocket had about seventeen times more thrust than the Gemini-Titan II.”

“Seventeen times more”, which can be harder to process.

Notice, also, that both these comparisons fail to provide a critical bit of information. A baseline for comparison. Is one more important when there were only three astronauts? What about if there were originally 1000 astronauts? So the baseline is important.

In the bar graph, notice that we get a baseline and a sense of scale of the difference. Graphical comparisons can be effective in this way.

Now in all these examples, we have been talking about ways to add context to help us understand data. Millar gives us an overall strategy for summarizing data.

First, generalize the overall pattern.

Then provide one or more examples in the data table or chart as instances of the pattern. As she explains here, doing this helps to anchor the generalization to specific numbers. And it helps to link the narrative and data display together.

Finally, explain exceptions to the data pattern. Again, do this by comparing direction and magnitude of the exceptions with the overall pattern and note whether the difference is changing. As with the pattern, link discussion of the exception to a specific example in the data display.

Does that make sense?

Great, let’s now focus on organizing information with grids and typography.

When I say typography, most people think about what font we should choose. Times New Roman? Comic Sans?

That’s not what I’m talking about, and typography involves all aspects of laying out text visually.

Even the pdf versions of the memos we’ve considered have a visual organization about them. That’s part of typography.

At the document level, our best tool for organizing information is the grid.

The seminal reference on the systematic use of grids comes from Josef Muller-Brockman, in his text, Grid Systems in Graphic Design. And in it, he explains the importance of grids. Let’s read what he says together.

[READ QUOTES]

While grids organize information on the document scale, other aspects of typography organize the content itself. Let’s consider how another helpful author explains why we should pay attention to typography.

Matthew Butterick, in his text Practical Typography, says,

“Most readers are looking for reasons to stop reading. . . . Readers have other demands on their time. . . . The goal of most professional writing is persuasion, and attention is a prerequisite for persuasion.”

By the way, sounds just like what Doumont said, right?

Butterick continues,

“Good typography can help your reader devote less attention to the mechanics of reading and more attention to your message.”

The more we consider each aspect of communication, the more we will find this is true, and attention to every detail will improve our communications.

Further, as we begin to blend sentences and paragraphs with data and data visuals, learning how to optimize readability becomes even more important.

Let’s see how all this comes together in one of our example memos.

To create the pdf version of your example memos — and indeed to create these visuals for you all semester! — I started with a grid structure. In typography, grids are methodological ways we can organize information.

The memos used a very simple grid to align information. I’m showing you it here. I placed gridlines that defined sections of the PDF memos, which was the delivery of the communication.

The spaces around the gridlines can be used for either content or white space — also called negative space — that separates content. To see, let’s layer in the content, along with identifying what typographic best practices we used.

Here, we’ve layered in the content of one of the memo examples into the grid lines.

Along with placement, I’ve followed several other of Butterick’s typographic recommendations for page-sized communications. These recommendations include the font size for each section, the space between lines, and the line length.

All these are important to reduce our audience’s cognitive load.

All these are used to further the purpose of readability from the viewpoint of our audience.

Let’s see a grid used in another context. Actually, you’ve been looking at it all semester!

Here is the grid I’ve used to make all your class slides this semester.

Grids are used in most exemplary communications for visual organization.

Grids are used to organize data graphics. This example is actually a different version of the same author and same data we previously saw visualized when discussing layers, well data from a different year, but the same variables about popularity in music.

Let’s see the grid she used …

And here’s where I’ve identified a grid. Notice how it’s used.

Next, let’s consider organizing lots of numeric data and how these concepts relate to grids.

For lots of numeric data, some of our best tools are tables, in various forms.

We’ll start with some insight from Edward Tufte on exactly what they are for.

Let’s see what he says about tables, which I’ve quoted on the left:

“The conventional sentence is a poor way to show more than two numbers because it prevents comparisons within the data. The linearly organized flow of words, folded over at arbitrary points (decided not by content but by the happenstance of column width), offers less than one effective dimension for organizing the data.”

What do you understand him to mean by

“folded over at arbitrary points”?

[STUDENT ANSWER]

Yes, he also gives us an example of this issue, which I show here on the right: Let’s consider the first version, top right: again, I’ll read it with you:

“Nearly 53 percent of the type A group did something or other compared to 46 percent of B and slightly more than 57 percent of C.”

Now if we compare that approach to the second version, which leads to an easier comparison and why?

[STUDENT ANSWER]

Right, the information is aligned in a way that allows our eye to scan the three numbers side-by-side.

Notice that the three groups are alphabetized, too. That issue will come up again in a few minutes, but as Tufte notes, alphabetical orderings are usually not optimal. The ordering depends on what question we want to know. In this case, we’re comparing the three numbers and want to know which is highest, which is lowest.

For that, as seen in the third version, we can order highest to lowest and even without comparing the numbers we know just based on relative location that the top one is highest, for example. So it makes it easier, reduces cognitive load.

Now this example only has three numbers. Sometimes we need more. Why? Tables are hard to improve when our audience wants to look up exact numbers. So how should we think about arranging them?

What about grids?

Grids helped us on the document level, right? Even for a memo, in organizing information.

And they do the same all the way down to individual numbers to create tables.

Here’s another example grid. Recall we can use some columns to place information and other columns or rows or gutters to separate information. Ok, but more specifically, what else can we think about when deciding where to place the numbers?

Perceptual psychology can help us here. Next we’ll review a couple of principles we’ve covered, and more later when we dive into graphics.

The first I want to discuss is the Gestalt principle of proximity.

“Gestalt”, as a reminder, is German for “unified whole”. So our mind tends to see individual things as part of larger groups. Patterns. And in the 1920s scientists studied the ways, or causes, for us seeing these patterns. Proximity is one of these.

I’m demonstrating this principle here. And we’ve considered this before. On the left, I’ve spaced the individual dots closer horizontally than vertically. Do you see a pattern?

[STUDENT ANSWER] We see rows of dots.

Exactly. And on the right, I’ve spaced the individual dots closer vertically than horizontally. Again, what do you notice?

[STUDENT ANSWER] We see columns of dots.

That’s right. And seeing patterns helps our eye track across the information.

By the way, do you see this principle of proximity at work in any other way on this visual?

[STUDENT ANSWER] grouping a left block of dots from a right block of dots.

Good. Ok, so use this principle in placing numbers on the grid.

I’ve placed numbers on the grid. What do you notice about them?

[STUDENT ANSWER]

Numbers are closer vertically than horizontally, creating the perception of columns of numbers. And on a higher level three groups of columns.

Finally, notice the alignment of the decimal place. Now this is important for comparing the magnitude of numbers, and it these numbers were not all between 0 and 10 we would notice this more.

I’ll invite you to on your own after class, make all these numbers equidistant and see how the column groups and groups of columns disappears.

So we may perceive these groups, but what do the numbers mean?

[STUDENT ANSWER]

No idea, right? Because nothing has been labeled. We don’t even know their units! Before adding annotation to this table to explain the numbers, I’d like to introduce a second Gestalt design principle.

Just like we can separate information types using proximity, we can separate information types using similarity in other attributes, like color, or its channels. We’ve discussed this principle before, too, remember?

What do you see here?

[STUDENT ANSWER]

Now in this example I’ve made all dots equidistant, so the principle of proximity isn’t being used.

So their color attribute does all the work in creating what we perceive as rows. Pretty cool right? We can intentionally assign attributes to create perception of groups!

Let’s use this principle of similarity to improve our table.

Now that I’ve annotated the table, we get the sense that the audience isn’t us. It’s maybe for someone like the analytics executive at the Los Angeles Dodgers baseball team. Remember that class example memo?

We’ve added a title, and various labels, and a note. The intended audience is presumed to know what a “Bayesian model” is, what an “expectation” is, the rules of baseball and a half-inning, what a “count” is, what a “gamestate” is.

So according to the title, the numbers represent the expected increase in game score for the batting team given game state and count.

For your own understanding, in baseball a count is described as the number of balls and strikes. So 0-0 means 0 balls and 0 strikes.

And for gamestate, 123 colon 0 means a runner on 1st base, 2nd base, 3rd base with no outs.

Make sense? You can look this stuff up on Wikipedia to help you follow these examples, if you need.

Some of you may have also noticed that I used a slightly different shade of color for annotations than numbers. It’s hard to see this with the grid lines though, right?

Let’s remove those gridlines!

Because gridlines are just for design, they should be invisible.

So here’s our basic example. We can do more with this, depending on its ultimate purpose. Like we can assign color to the numbers to create a heat map that gives us a sense of which values are relatively high or low.

I’ll show you more examples in the next couple of weeks as we continue to explore uses of graphics.

We don’t need to go through this visual, but I’ve annotated the table here to remind you of the names of common table component names, just as I’ve done with common graphic components.

Ok, we’ve made a rectangular shaped table for the dodgers’ example.

Do tables have to be shaped as a rectangle of numbers?

Let’s look at a couple of examples of other arrangements to get us thinking about other possibilities.


First, I want to introduce you to what has been called a stem-and-leaf diagram. It’s an odd-shaped grouping of numbers, right?

A stem-and-leaf diagram has attributes of a table, and those of a histogram, which we’ve seen in earlier graphics explorations.

The numbers on the left of the vertical lines are referred to as a stem, and the numbers to the right, the leaves. It is the combination of these that tell you what the numbers are.

Now if you hover your cursor over each number, we see that the stem represents the left-most digit of a number that is common to all the leaves in its row. So the first row, we read 01 or 1, 02, or 2, and in the stem with a 3, we read 31, 32, 33, and so forth. Make sense?

The benefit of this type of encoding is that it shows you density of the numbers in a more compact way than a table, and shows your exact values, unlike a histogram.

Harris’s textbook, Information Graphics, the wikipedia of graphics, has an entry for understanding these stem-and-leaf diagrams and variations on them. I’ll leave it to you to get the motivation to read up on them in his book.

Ok, let’s look at one more idea related to tables.

This example comes from an old newspaper from the New York Times. It’s basically a table where each number has a label.

But we get a sense of comparison of the values in the white cells in relation to the black cells. The black cells represent actual economic growth in some category. The White cells were predictions of what the growth might be. So if the white cells were above the black cells, it’s prediction was too high. And those below, too low. Make sense?

I showed you these last two examples, just to get us thinking creatively about arrangements of tabular data, and how we can present it in various ways.

Now that we created a table, where should we put it in relation to our narrative? That’s what I want us to discuss next.

Let’s discuss both where to put a data display like a table or graph, and how we can link it to narrative.

Going back to Edward Tufte’s influential book, he explained, and I’m quoting from him on the left, that

“data graphics are paragraphs about data and should be treated as such.”

What does that mean to you?

[STUDENT DISCUSSION]

On the right, I’m showing you a couple of pages from Edward Tufte’s text. And his text tries to exemplify what he says. On these two pages, he puts (mock ups of) graphics in the main paragraphs right after the sentence discussing or introducing them.

If you think about it, this is the Gestalt principle of proximity manifested in another way. The sentence and graphic are close in space or proximity to be better understood together.

Make sense?

We’ve discussed this example before. Again, I’ve pulled this example from the Los Angeles Times.

To place it into context, this graphic is part of a story about crime in California in 2013. What do you notice in terms we’ve been discussing tonight?

[DISCUSS] context, comparisons, and annotations

My focus today is on the liberal amount of words directly on the graphic to explain it.

So consider first, placing your data tables and graphics directly into your paragraphs and second, directly annotating the data.

Again, the proximity of the two — in both ways — helps us understand.

How else can we link words and data? Can we somehow use the Gestalt principle of similarity again?

Let’s look at another example.

I’ve pulled this example on the right from an excellent article from Matthew Kay and Jeffrey Heer.

On the left, I’ve removed all the hues of color from their original, which I’m showing on the right.

Which is easier to understand what narrative is related to what data markings?

To place this graphic into context, it’s in a discussion about the influence of something called censored data on the model estimate. So you know, censoring data means that data above or below some amount are just reported as the maximum or minimum measured rather than the higher or lower actual value. Does that make sense?

Let’s see how the principle of similarity is used here to link words and data encodings. What do you notice?

[STUDENT DISCUSSION]

So applying the same coloring to both words and the related data can help us more!

We have yet another way of organizing our narrative and data that can give us further improvement in understanding.

It’s use of parallel structure, what I call a rhetorical figure. Let’s see parallel structure in action generally.

This example comes from another excellent book, written by Paul Rosenbaum, titled Observation and Experiment. He’s discussing the pitfalls of something called a matched-pair observational study. If you were in my research design class, or if you’ve taken one of the other sections, you would discuss the meaning of this concept. Does anyone have a sense of what this is?

[STUDENT ANSWER]

We won’t get into the reasons for constructing a matched-pair study here, except I’ll say that we try to isolate what difference in an independent variable, say X, has on a dependent variable, say Y.

We try to isolate this difference by selecting observations that have other attributes most similar to each other. If both variables are the same in all attributes except the X, then maybe we can infer the correlation between X and Y.

So that’s what Rosenbaum is discussing in this short but dense paragraph on the right about the figure on the left.

Let’s see how he writes or composes it. Notice he starts each sentence the same way, which I’ve bolded.

And the structure of each sentence is similar. This is parallel structure, and helps us understand their relationships of information across sentences.

Now we can apply parallel structure, in a way, across words and data visual.

Millar describes that in one of the readings from her I gave you.

Let’s see what she says.

We accomplish something like parallel structure between words and data by first, organizing the data display to accomplish the point of the display, and second explaining the data display using the same organization.

So if our question is about which category is higher than the others, we can order the categories by their value. If we do that, we should describe the data in that same order. Let’s see an example.

I’ve pulled this example from Millar’s article, you’ve seen the visual before, but, and this is another tip: I’ve modified the bar chart here because she did not use best practices in presenting those charts.

We’ve talked about making text horizontal when possible, and rotating the data markings to accommodate, right?

So my tip is we need to read broadly and get lots of perspectives because no single author has all the best answers.

If you compare this bar chart to hers, you’ll see the main difference is that I’ve rotated mine so that the category labels are on the y axis and the values are on the x axis. The reason I did this is that we read horizontally, and long labels on the x axis make reading them problematic.

Ok, aside from that, let’s consider the chart and the narrative. Notice, the categories are arranged high to low. Now Millar’s narrative describing that Figure are also in that order.

“Housing was the highest expenditure category, followed by …”

Make sense?

Great. If you consistently try to apply all the principles we’ve discussed today, your communications will improve.

Let’s try to bring these additional ideas into our table example, placing it into the narrative and linking it.

To go with our example table, I’ve written this example narrative. Take a moment to read it. It wasn’t written for you, it was written for someone in baseball.

Anyone need more time?

How many of you found it difficult to follow how to use our example table?

Let’s try another approach.

So, again, I’ve setup the example to show you the concepts we’ve been discussing in practice.

Here I’ve placed the table directly within the narrative, and I’ve used color to link specific narrative to the data, thus using both principles we’ve just discussed.

Even though the content is probably dense for those of you who are unfamiliar with baseball, do the application of these principles make it easier to follow the narrative on how to use the table?

Notice, also, does the narrative sort of follow Millar’s advice to first describe something generally, then show an example?

Cool. I hope this example has been helpful in thinking about ways we can apply the principles we’ve been discussing.

Ok, that’s plenty for us to think about for tonight. I look forward to reading your memos next week!

Here are the major resources I recommend for your reference related to our discussions tonight.

That’s all for tonight.

I’ll stay on for any questions. Otherwise enjoy the rest of your day or night!