T-61.271 Information visualization

Visualization project 27

Misleading visualizations

13 January 2003

Henrik Ingo
47010e
hingo@cc.hut.fi

Abstract

The Post-Enron world with it's tough requirements on reliable financial reports has left US accountants and CEOs without choice. They will now have to tell us the truth and nothing but the truth about their companies financial status. Or do they?

While the art of creative accounting may have come to an end when it comes to the actual numbers in the the book, there are still other ways in which a financial report could mislead it's reader into believing that everything is going great.

This paper suggests various ways to make "better than reality" charts, while at the same time preserving correctness with the underlying statistics. Each technique is briefly evaluated in terms of a lie factor and whether or not it fulfils the requirement of embellishing the truth while at the same time not getting caught.

Some real world examples are also evaluated in the same way.

This essay is hereby released into the Public Domain. To view a copy of the public domain dedication, visit http://creativecommons.org/licenses/publicdomain or send a letter to Creative Commons, 559 Nathan Abbott Way, Stanford, California 94305, USA.

Some images used as illustrations are part of the CorelDraw 8 Clipart gallery and yet others have been copied as citations from publications where they first appeared. While it's ok to copy and distribute them as part of this essay or any future modified version of it, they are not public domain in themselves.

This essay is available on the web at http://www.cafe-seed.net/~hingo/kirjoituksia/misleadingvisualizations.html

1. Introduction

The past year we have seen some surprising turns in the world economy. After a couple of cheerful years of so called New Economy, stockbrokers were issuing warnings of an expected downturn. And down we went.

But what happened then? Enron. And with them almost overnight one of the worlds biggest auditing firms Andersen simply ceased to exist. Enron had been supporting the Republicans. And when I say supporting, I don't mean that the employees used to cheer for the politicians during congress meetings - no, you know what kind of supporting I mean. But when shortly after that the Democratic Party backing WorldCom announced that they had accounted for 7 billion of dollars that didn't have any counterpart in Real World dollars, even Mr W got a bit upset. "From now on any dot-com that funds the Democrats will have to report their earnings truthfully, or else..." he declared.

So with the threath of facing 20 years of jail - merciful as he is, W didn't, at least yet, threaten with the chair he has back home in Texas - accountants all over the USA are now faced with the dull prospects of only accounting for money that actually exists, as we used to do back in the good Old Economy days. But that of course poses some new challenges. "How are we going to make the investors like us, if we have to tell them the truth?" some might ask. One might even argue that if this kind of creative accounting had not been allowed during the last years, we might never have seen any of the New Economy that, after all, was a happy time wasn't it?

But maybe all is not lost, my friends. Even if the actual numbers will now have to be truthful, there still are some tricks a dot-com might turn to. This paper discusses the art of making charts that lie, while being technically correct. Accountants all over the world will be delighted to find, that it's possible to make a financial report that at the same time is 100% correct but also looks good. It is kind of like painting pretty pictures next to a horrible story. The logic of using such misleading graphics in forthcoming financial reports would therefore be:

1. When given a choice, most readers will rather look at the colorful graphics of a report than the actual numbers presented in a dull table.

2. It is possible to make such graphics look much better than the underlying statistics, while at the same time preserving their integrity - or shall we say at least technical correctness.

In the following pages we will learn some techniques, to make such charts. Each technique is presented separately, as a kind of building block. It's left to the reader to combine suitable techniques in order to achieve the best possible results for his financial report. After presenting the various techniques of deception, some real world examples are also investigated.

This paper was written as part of a course in Information visualization, at Helsinki University of Technology. Most ideas are drawn from or have at least been inspired by the two coursebooks"The Visual display of quantitative information"[2] by Edward Tufte and "Information visualization: perception for design"[3] by Colin Ware. Most basic tricks have their roots in Tufte while the more advanced tricks that play with the shortcomings in the psychology of our vision are from Ware.

It is my humble wish that it may help US accountants to save the world economy.

Question:
(totally unrelated to the topic of the paper)

If the financial boost during the so called New Economy was only a boost on paper - that is, none of the fuzz actually existed as real money - is it then also true, that the current depression is also only a depression on paper, since there never really was any money to be lost?

2. Basic concepts and tools

Before we start looking into the various techniques, let's start with introducing a couple of concepts, that will be used in evaluating the techniques.

The Lie Factor

The lie factor is a concept that is introduced in Edward Tuftes book "The Visual display of quantitative information"[2]. The idea of the lie factor is to express in numbers, how much a graphic deviates from the actual data it should represent. The formula for calculating the lie factor is thus:

(1)

For instance, if we have a simple table with two numbers:

The basic bar chart would then become:

Since this is an accurate representation of the data, the lie factor equals one. On the other hand, the artist in charge of making charts might for some weird reason decide to "emphasize" the second bar in the chart:

Now the second bar is much taller than the first one, even though both claim to represent the value 100. If we assume that the size of the first bar is correct we can now calculate the lie factor for year 2002:

(2)

A good rule of thumb to remember: Truthful charts always have a lie factor of one, whereas any other lie factor indicates a misrepresentation.

The Psychological Lie Factor

As we shall see, it is quite feasible to make charts that have a lie factor of one, but still manage to fool the eye into seeing something that wasn't in the data. These charts are technically correct but they lie anyway. In these cases we will talk about a psychological lie factor, which would be defined as something like:

(3)

The "looks like" part will often only be a subjective estimate, but nevertheless this will be a useful concept in evaluating how much a graphic manages to fool the viewer.

The Thumbs rating

Finally we will rate each technique with a thumbs-up or thumbs-down figure, possibly with handcuffs added.

Table 2: The Thumbs rating

This rating will characterize how the technique relates to the two questions:

• How well does the graphic perform in "beautifying" the actual data?

• Will the artist go to jail or not? I.e. is the graph technically correct?

In terms of the lie factors, the artist will typically avoid handcuffs and jail, if the lie factor is one. The thumbs up rating on the other hand, will be given to graphics where either the lie factor or the psychological lie factor is not equal to one.

Another funny side note:

It is perhaps worth noting, that what we normally would regard as a good graphic, would here receive a thumbs down rating, because of the fact that it represents the data as truthfully as possible. In this essay, that is not a wanted feature.

On the other hand, such a graphic would avoid the handcuffs, so honesty is not that bad after all.

3. Manipulating the axes

The first set of techniques, is based on manipulating the axes to better suit our needs. Let's go straight to it.

Pick your own interval

To demonstrate these techniques, let's play with some figures from our favourite stockmarket company Nokia¹.

In an ordinary graphic, these numbers become two equally heigh bars:

The bars look similar. Even though Nokia did quite well, increasing it's sales by 3%, it isn't obvius from the chart. It's probably okay if we emphasize that growth just a little:

Who says that the scale has to start from zero? Nothing important happens before 30 billion euros anyway. With focusing on the range 30 000 - 31 200 we have made year 2001 stand out as a major year of growth, instead of being practically equal to it's predecessor, as the first chart might have led us to think.

So what about the lie factors? Technically there is nothing wrong in what we have done. The numbers on the Y-axis are there, and the bars are exactly the height of the values they are supposed to represent. The chart comes out with a lie factor of one! When comparing the two charts above, it is however obvious, that the second one is more positive than the first one. Even though we can clearly see the correct numbers to the left, our eyes tell us that the bar to the right is 3,16 times higher than it's left companion. The psychological lie factor will therefore be 3,16/0,03 = 105!

The graph will therefore be awarded a definitive thumps-up and no handcuffs! A simple but powerful technique, that is in fact often used in advertising.

De-emphasize with a large interval and stretching

The previous technique has one major drawback. It can only be used to over-emphasize data that actually exist. If sales had gone down during 2001, we could not have saved ourselves using this technique. The same technique can however be reversed. We can choose an overly broad interval. That will not turn profits into losses, but it will de-emphasize the downward trend into something that seems to be very flat. This could have been useful in reporting Nokias net profits for the same time period:

Table 4: Net profits for Nokia 2000-2001

	2000 (EURm)	2001 (EURm)	Change %
Net profit	3938	2200	-44

But with a different scale it's not that bad:

To hide the decline we have streched the x-axis which made the bars thicker and thus helps de-emphasize their height.

But hey, wait a minute! Why do those bars start from a negative 4000? There is really no good reason, nor even a mediocre excuse. The only reason is, that it was really hard to get those bars equally high. And even if I cheated a little, the right one still looks shorter than the left one.

So even if the chart is still technically correct, the cheating is too obvious and what's even worse, the decline in profits is still visible. This technique might be handy in some cases, but to cover up a decline by almost 50% is too much to ask. We are forced to give a negative verdict: thumbs down and caught for cheating!

When to use a negative scale

There are situations, when negative numbers might be excused. Suppose Nokias profits continue to decline, and turn into losses in 2002. (At the moment of writing this doesn't seem very likely, but let's imagine they do.) Let's say that for 2002, Nokia would report a loss off 500 million euros:

Declining profits is bad enough, but if a company starts to lose money it's even worse. The worst thing to do is to start emphasizing that with red color! This might be a situation, where it is tempting to drop the x-axis downward, so that all bars at least point up:

We won't go into the discussion about the lie factors for this graph (I'm trying to avoid the need to introduce the concept of a negative lie factor), but it is obvious that it makes a difference whether something points up or down. Whether we are still on the safe side legally is a tough call. Now when we actually have negative values in our data, it might be okay to have a negative axis. The judge might let it pass, but I'll leave the handcuffs on just to be safe.

Picking the most suitable scale

Above we have used techniques where we pick a suitable begin and endpoint for our axes and also stretch them according to our needs. One last thing to consider, is the scale itself. If you've paid attention in a statistics class, or even explored your spreadsheet application (Excel), you might have heard about something called a logarithmic scale. A logarithmic scale is typically used to present data, that grows or otherwise changes exponentially. It has an effect of emphasizing the variations in small values (from 1 to 10) and and de-emphasizing the variations of larger values (100 to 1000). Consider the development of the Nokia stock over the past 5 years²:

The curve seems to be rather smooth until the end of 1999 when it suddenly starts rising. During 2000 the ups and downs are extreme, but towards 2002 the curve smoothens again. The New Economy bubble is evident. Or is it...

What bubble? Sure the stocks seem to rise during 1998, but other than that this curve seems very smooth. What's happening here?

The former chart shows the development of the literal value of the stock. The latter chart on the other hand, shows the relative development. Let's say that Nokia drops 10% during one day and see what it looks like on the first graph. If the drop happens in January 1998, it's likely to go almost unnoticed in the graph, since the change is less than 0,5$. But if it happens during January 2001 it will certainly be noticed, because now it's more than one interval on the y-axis.

On the latter chart both of these 10% drops, as well as any other 10% change, would be of exactly the same size. That's because the logaritmic size shows relative changes, while the linear scale shows absolute changes.

So, what does all of this mean? The former chart is what we recognise from the economic news and press. But in times like these, why not use the second chart? "I don't know about you guys, but we here at Nokia have certainly not seen any bubbles burst. Our curve is as smooth as ever!"

So what about the handcuffs? Again we are not doing anything wrong, altough you could argue that the log10 scale means a psychological lie factor of 10. In any case the scientists do it all the time, so it must not only be right, it's probably also intelligent and cool! The only dishonesty is simply that people are used to seeing the first chart. Thumps up and no handcuffs!

Real World example: Yahoo!'s daily stock quotes

The problem with picking a suitable scale and interval for the axis, is that you always have to pick something. What is right and what is cheating is not always easy to say.

Take this graph from Yahoo as an example. It's a curve of one days exchange rates for Nokia:

At first sight it looks like Nokia had a rough day. But then you look at the scale of the y-axis and realise that all variation was within 35 cents and what's even more, at the end of the day we are pretty much back to the same level where we started in the morning. I don't know much about the stock market and it could be that 35 cents is very significant but at least it's still much less than the interval Nokia had the previous day, which was almost a dollar:

Yet the curves look very much alike at first sight.

What's happening here? Yahoo scales each graph, so that only what's significant will show. That is a valid excuse, it would not make much sense to have a constant scale for all days and different companies, since some curves would surely not fit on the screen at times of turmoil while others would look like a dead straight line. Scaling into what's significant is the best option if we want to maximize the amount of information in the graph.

But there is still a pitfall. This approach guarantees that all charts will look like there was a storm at the stock exchange, even when the curve is in fact very flat. A thumbs up to Yahoo for making sure that every day on the stock market looks exciting. And no handcuffs for the (very much so) valid excuse.

4. Artistry

One obvious way to achieve our goal of beautifying the actual data, is straigthforward: Simply draw a picture that looks the way you want it. This is the category that Tufte calls "the Pravda school".

I think the Sovjet artist definately deserves a thumbs up!

The graphics in this section should be accompanied with the subtitle "all characters and events in this movie are fictious, and any resemblance to actual persons or events is purely random". Obviously, all charts in this chapter will have a thumbs rating with handcuffs on. That follows directly from the definition.

The magnifying glass

A typical thing to do, which at first thought sounds like something perfectly normal, is to emphasize this years figures. Let's look at our second most favorite stock company: Sonera³.

Talk about technology bubble! Less than a third is left from the profits of 2000. But don't worry, zooming in on 2001, it doesn't look all that bad after all:

This is the wet dream of Enron accountants! Just stretch the bar in both directions until it's big enough. The slope in the bottom line provides a hint for the viewer, that we have broken the scale at this point and moved in for "a closer look". This is a standard way of drawing in perspective, so the reader might even think this is ok. But it's not. The lie factor for this graph is
(2,75 cm / 409 EURm) / (2,95 cm / 1506 EURm) = 3,4
and the stretching of the x-axis and the brighter red add some more for a psychological lie factor. Click click, on with the handcuffs.

The artistry category could be expanded by many more masterpieces. In fact once the artist gets going, the charts will be much more decorative. But the idea will always be the same as in this basic bar chart.

5. Confusing dimensions

One type of artistry that deserves to be given it's own category, is the play with dimensions.

Is this 1d or 2d?

What about exchanging the dull bars with something more interesting? Like a bag of money, for instance. Here are the same results from Sonera again:

It's the same bar chart but fancier. What we are doing here is playing with the viewers mind. How much money does the big bag represent? It's hard to tell really. The bag looks tall, but on the other hand it looks slim. A slim year 2000? What if we make both height and width dependent on the profit:

Whoa! That year 2000 really was something after all! Note that the bags are exactly as tall as in the first chart, but the effect is rather different this time.

Let's try some other variants. If we really want to have 2-dimensional moneybags, it would be more correct if the area of each bag represents the value, rather than the radius:

Suddenly year 2000 doesn't look that different from the others.

Or is it 3d?

But since we are dealing with moneybags, shouldn't the size of the bag reflect the amount of money that's in it? Or if we put it in the language of geometry, shouldn't the value be relative to the volume of the bag? Let's try that too:

As you might have guessed, the bag with 1506 million euros shrinks even further. That we have added a 3-dimensional lighting effect doesn't help, the 1506 million euros look awfully small.

Looking at the above charts, we can conclude that playing with dimensions greatly affects what the viewer sees in a graphic.

So what about the lie factors? The thing is, all charts are correct in their own way. The problem is to know from which dimensions the variables should be read. So it's really up to the viewer. To make an extreme example, if we interpret the bags in the second chart as true 3-dimensional bags, we get a lie factor of

...which must be some kind of a record!

But as a more general summary, we can conclude that

• The first chart with moneybags is the one most like bar charts. It confuses the viewer, but whether it emphasizes or de-emphasizes things isn't immediately clear and may depend on the data and type of image used. To me it looks like this chart is emphasizing the loads of money made in 2000, but that could be subjective.

• The second chart is obviously an exaggeration. In fact, because we have used the same variable in two dimensions, it's almost knocking on the border of being illegal, but we'll judge it still being on the safe side.

• Using true 2d and especially 3d images, is a great way of smoothening.Year 2000 is greatly de-emphasized.

• Personally, I find the true 2d chart to be the most intuitive one, and thus most truthful, but the first chart is probably the one to be generally acceptable, because it is basically a normal bar chart with pictures. The first chart is also most likely to be seen in artistic charts, because both Excel and OpenOffice contain a feature to use images as bars.

In short, a great package of tools for both growing and shrinking things as needed. And all of it completely on the legal side!

A deceitful perspective

While we are at the subject of 3d imagery, let's delve into two other useful techniques in the same category. Look at the same Sonera bars once more, now with a 3d effect courtesy of OpenOffice Calc:

Those OpenOffice people have done a nice job with their 3d effects. It's even possible to rotate the chart so that you get another perspective. Here is another chart that is almost like the one above:

So, what has changed? In the first chart, the perspective is such that we are looking at the bars from a very low viewpoint. In the first graph, it is as if we are about the same height as the four low bars, while the tall bar of year 2000 is way higher than anything else. In the second version we are looking down on everything, and also the bar for 2000 looks shorter than us.

And the judgement for this technique? There is a difference, but one bar that is three times the height of everything else will stand out no matter how you twist it. Having seen the moneybag tricks, we are not impressed with this anymore. In a very tight situation this technique could be used to give a psychological hint of what should be considered high and what low. But we will give it a thumbs down. No lying in this technique though, so there is no harm in using it if you think it does something for you.

A background with perspective

For our last trick in this category, let's switch back to the numbers from Nokia we already had in the beginning. You have already seen them, but here they are again:

Ok, so the bar for 2001 might still look shorter, but the image in the background does soften the drop a little bit. The effect comes from the perspective in the picture. If we interpret the bars as being part of the landscape, it would seem that the lower bar is short but close to us, while the upper bar is very big but distant. If interpreted like that, we could use the boardwalk to estimate that a psychological lie factor is something between 4 and 5. (The lower bar would have to be 3 times bigger just to match the upper in reaching the boardwalk.)

Unfortunately however (for Enrons accountants that is) most people are not so stupid as to fall for this trick. Most of us simply ignore the background and interpret the bars correctly, as if the background was not there at all:

Even if we couldn't make the shorter bar look taller, the perspective in the background does bend reality a little, so I think it's worth a thumbs up.

I don't know if you noticed, but I had to cheat a little again. In order for the perspective thing to work at all, I had to make the upper bar thinner than the lower. Without this adjustment, the trick simply doesn't work. Even if the length of the bars is still intact, tampering with the bars in this way is in my opinion going too far. So we put the handcuffs on again.

6. Distractions

3 dimensional backgrounds is not the only irrelevant thing we can add to our charts to confuse the reader. The ultimate trick in the distractions category - only to be used by the truly desperate - would of course be adding not only a beach but also a bunch of topless chicks! Or perhaps that would seem too desperate?

A suitable placement for the labels

In any case, I don't have pictures of topless women (sure, and you couldn't find any on the Internet either...) so I'll show you a different trick. You have seen these moneybags from Sonera:

The bars/bags are exactly the same, but is there a feeling of a positive trend in this picture, that wasn't there in the original:

The difference is, in the original the labels that tell us the actual value of each year are all down at the bottom. In the modified version above, There is an upward trend - the last value of 409 is actually higher than it's predecessor 1506.

There is no motivation in the data for placing the labels as I did, but it doesn't feel completely wrong to do it either. And is the viewer confused? The bags are still there, and it's obvious that the last bag is much shorter than it's predecessor. But when reading the values, the reader scans the numbers from left to right and the eyballs follow the numbers making a slight upward tilt, giving a subtle feeling of something going upward - a positive trend.

But it's only a subtle feeling and in fact the reason why I chose the moneybag chart for this trick is that simple rectangular bars would have been strong enough to cancel that effect. The height of a rectangular bar is something very obvious and in addition it's something we are all very used to interpret. The moneybags are not as easy to interpret and while the reader is processing this new type of chart in his mind the eyeballs start making the upward tilt. In short, an unclear graphic gives more weight to the effect of placing the labels intentionally wrong.

If you are still not convinced, consider this variant where the values are placed at the top of each bag:

When reading the numbers, you have to considerably lift your eyes to reach the high number of 1506, leaving no doubt that it's way bigger than the other ones. It's obvious from these three charts that the placing of labels makes a difference (in fact it's the reason why I chose to move the labels to the bottom in the 2d/3d experiments). If you want to emphasize year 2000, use the last version. If you want to create a feeling of a positive trend, use the first one.

No lying involved, the lie factor is an even one. It's hard to give a numeral estimate on a psychological lie factor, but it's obvious that the trick works. And another reason to give a thumbs up: this trick will not upset your mom and dad. Stay clear of naked women as long as possible!

7. Simply hide the ugly details

In this category we will examine techniques that don't distort anything. We simply hide the things we don't want to show. And there is more than one way to do it.

No context

An important property of a chart is to have enough context to be able to interpret the chart meaningfully. But in this essay we don't want the viewers to interpret anything meaningfully. Suppose we are a bit embarrased by the two-thirds decline in profits for Sonera. Why don't we just cut out the possibility to do any comparison:

Okay, that looks a bit ridiculous, I just wanted to make my point. Some other data would probably have fitted this technique better. For instance we could break up the 2001 result into each quarter and then we would have had four bars to show the same data as above. Our readers would be satisfied with so many bars to look at and no one would remember what happened in 2000.

Charts that suit this technique very well are lines and curves of all kind. Do you remember the boom and bust in the chart of Nokia's exchange rates over the last 5 years. We already made that bubble disappear once, but I can assure you that there really was no bubble. Those mobile companies are a safe and solid bet on the stock market:

Bar charts with only one bar is going too far, but used with the appropriate amount of good taste and careful consideration, this technique will be your friend in many tough situations. And best of all, it's all 100% true.

Or too much

The other way to go, is to provide more information than anyone can take down:

Also known as the "They will never know what hit them" technique. Lucky for us, the turnover has increased even in 2001, providing for a steadily growing curve on top. Since you can't really figure what's going on with the other lines, this will give an overall impression of "something was going up, even if I couldn't tell what it was".

The spagetti that results from the 9 other lines can also be interpreted positively: "Lot's of activity in this telecom". Or in more layman terms: "Those guys at Sonera are really some hard workers." (Because they have produced so many curves that just looking at them makes me tired.)

The only downside with these techniques, is that if you make things too unreadable, the reader might fall back to reading the actual numbers in the financial statement again and we were trying to use graphics to prevent them from doing that.

Another useful and 100% truthful technique. Just don't overdo it or you'll lose everything.

Real World Example: Oikotie ad in Helsingin Sanomat

Chart 29: Helsingin Sanomat advertising for it's Oikotie website. Other websites in the graph are "Etuovi", "Autotalli", "Jobline", "Uranus".[1]

This full page ad appeared in the daily newspaper Helsingin Sanomat on 12th November 2002. The graph shows the development of visitors per month for some Finnish websites, where users can sell or buy apartments, cars and announce job opportunities. The chart is intresting to us, because it actually uses several of the techniques we have just presented.

Firstly the fact that this is a full page ad, provides for some really phenominal stretching of the Y-axis. Not only is www.oikotie.fi leading the race, it's doing that with a margin of 7 centimeters to it's closest competitor "Etuovi" and a whopping 27 centimeters above level zero!

But the chart also employs the "Not enough context" technique, which is a very common thing to do in advertising. I mean you wouldn't buy such an expensive ad if it weren't to tell some carefully selected positive facts. In this case we are faced with a timeseries with only four datapoints, covering a period of only four months, June - September 2002. If we also take into account that in Finland this is the time for everyones holidays, this data would probably not be worth much in a more serious study. But as an advertisement it's great.

But even more engineous than the scarce datapoints, is the fact that we are not comparing apples to apples here. The slogan below the chart says: "Guess the business is where the people is". Now Oikotie is a service for buying and selling apartments, cars and jobs. But the names of the other websites indicate, that they are doing only one of the three: Etuovi (front door) is probably for trading apartments, while Autotalli (garage) obviously is about cars and Jobline... well you get the picture.

So Oikotie may have the largest number of visitors alltogether. But what if I want to buy a car? This chart doesn't seem to tell me what the best place to do that is. While Oikotie on top probably is not the worst of choices, we don't know whether it's a very good car trading place, or whether most of the traffic there is actually about apartments. Anyway, following the logic of the slogan, we could then continue to conclude, that the second best place to sell your car is the "front door" service, which obviously cannot be true.

Thus this chart seems to actually mix in too much and too little context at the same time! It's a definite thumbs up.

8. Optical illusions

So let's move to our final category, optical illusions. This is the category of real magic, where our eyes start to see things that don't exist at all.

Grayscale tricks

Our eyes are used to adapting to different levels of illumination. We have adequate vision in an almost dark room and on the other hand we have no problem adjusting to the brightest summer day. But this capability can also be abused. Even when you know it's a fact, it's difficult to admit that the four bars in the next picture are of the same level of gray:

No matter how hard you try, it will always look as if the left bar is darker than the right. This is because our eyes immediately adjust to the background, and thus the same bar will look different against different backgrounds.

So, how can we use this to create more deceitful charts? Actually, within our topic, it's kind of difficult. The idea in itself is simple, you could use an image in the background (like we did with the beach and perspectives) where suitable areas would be darker or lighter. But the problem is, to use this technique we would have to encode our datavalues into grayscales. Now that might be possible if we were drawing maps, but for financial data it would be rather exotic:

The unorthodox encoding is likely to confuse the viewer so much, that the trick itself is completely wasted. I myself have problems understanding what I'm trying to do with that picture!

But we can use this effect, known as crispening, in another kind of trick. Consider Nokia's net profits once more. A basic bar chart, but colored with grayscale gradients:

The shade of blue is added simbly because it looks good. But what are we trying to do? The size of the bars is intact and the height of the bars is also perceived correctly. But if I were to ask you to point out the 50% height of both bars, the varying background will add some challenge.

In our rational minds, we try to cut the bars in two halves, but our eyes see something else. Our eyes easily fixate on the spots where the gray shade of the bar equals the gray of the background. Approximately these spots are:

If you previously felt that the right bar was mysteriously strongly rising even though you knew it's the shorter one, this was why. The spots where its' brightness equals the background are higher than corresponding spots on the left bar, giving a feeling that somehow - although it's still shorter - it is rising very steeply. Another thing that adds to the effect is that on both bars the spot his a bit higher on the right side than the left, creating a feeling of an "upward trend". This comes from the fact that the background lightens towards right, and the bars are quite wide so the lighting is different on the left and right sides.

And how should we rate this? I must say I was expecting more from this. Maybe it's just that I don't know how to do it correctly, but the effect is not as powerful as I had hoped. But it's doing something isn't it? Maybe I'm just imagining something that isn't there at all, but I'm inclined to give it a very small thumbs up for good effort if nothing else.

Texture variations

Another effect where our eyes lie to us, is variations in texture. An example would be the picture below:

The texture seems to become smaller (or thicker) towards right. But there are two circular areas that differ from this overall pattern. It seems like at the left there is an area with quite a small texture while the area at the right has a larger texture.

This is in fact a trick similar to the four identical gray bars that seem to differ in brightness. The two circles in the picture are completely identical. Their texture size just seems to be different, because our eyes get confused when the background is not constant.

So, could this effect be useful? Let's try with the net profits from Nokia again:

Not impressed? Me neither. But the background seems to have some kind of effect, if you compare it to what the plain bars would have looked like:

In any case this is not exactly what we were heading for anyway. If we compare with the original example, also the bars should be texturized:

The only real effect seems to be that the bars, especially the right one, become hard to spot at all. Once you get a hold on them, they look the same size as always.

Ruling: We are not impressed. Even the grayscale tricks were better than this.

9. Summary

What have we seen? A plethora of techniques that can be used to distort reality in charts. Some were really astonishing, while others failed miserably. Most techniques seem to be useful in either emphasizing a positive trend that actually exists, or de-emphasizing negative trends. It proved to be difficult to find techniques that could actually make losses look like gains. Closest to actually turning reality upside down, was chart 28 in the "Too much context" category. There we needed one good looking curve under which to hide all the negative ones:

The coolest effect in my opinion was the play with the moneybags in different dimensions. It's still hard to accept that these charts actually show the same thing:

But the prize for best overall effect goes to chart 4 in "Pick your own scale". The jury especially praises the technique for it's large flexibility and simplicity. It is very easy to implement, fits a large range of different data and gives you flexibility in how far ou want to go:

Finally the prize for "Greatest disappointment" is awarded the "Optical illusions" category. Maybe it was my inexcperience with such graphics that was the problem, but nevertheless: we had great expectations and saw absolutely nothing: