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Misleading Graphical Displays

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Source: Wind Capacity Graph created from public domain, http://en.wikipedia.org/wiki/File:US_Wind_Power_Capacity.gif Recycle Bin graph created with public domain clipart, http://openclipart.org/detail/169402/recycle-bin-by-netalloy Graphs @3:13 created by the author

This tutorial covers misleading graphs. There are a lot of different ways that grass can be misleading. When a graph is misleading, it comes from decisions and how the graph was created. And that affects how viewers are able to interpret data and what interpretations are made at first and what jumps out from the graph, what's most clear to us.

If the graph is misleading, then we're not presenting this information accurately. There's some error or some kind of way that the graph is pushing us to see something that we otherwise wouldn't notice if it was presented neutrally. We'll go through several examples.

Here is an example of a perceptual distortion. This can happen when you're using 3D charts. Because our eyes have a hard time reading 3D, it's harder to compare these two values.

OK, so this graph is showing the United States windpower capacity. And up on this side is megawatts, and over here is year. And the red is showing total capacity, and the green is showing what's new.

So first of all, it's really hard to see exactly what the heights of these bars are, particularly for these lower levels. Because of the angle that's required for a 3D chart, you can't really trace back. Should I trace back the front of the shape and say, oh, this level here is about 5,000? Or should I trace back the back of the shape and see that it's above 5,000? That's not easy to tell.

Additionally, it's hard to compare between two of them, because one is placed in front of the other. Because of that angle used to give the 3D view, you can't really compare the tops as easily. Perceptual distortions can also occur when you're 2D images in order to kind of represent bar height.

So here, we're showing something about recycling. Here's another problem with the graph. This axis isn't labeled. If the axis isn't labeled either with units or with words, then you have no idea what the graph is actually about. We're just making assumptions.

So let's say our graph was labeled with number of recycling stations. So this is talking about our school building. And we have more recycling stations as time goes by. That much is clear. The buckets are getting bigger.

But if we were just looking at a bar, it would start out this way, get taller, and get a little taller. There's a little bit of an increase between 2006 and 2007, and a larger increase between 2001 and 2006. However, by using a 2D graphic, when I increase the bucket to go from here to here, I'm increasing area as well as height. And because the area is increasing, the shape looks a lot larger than if I had just increased height.

So this is implying, and kind of tricking us to believe that there is lot bigger increase than there actually was. Here, we have a misleading graph because of the scale. So I mentioned before that if your axes aren't labeled, that's a problem. But the axes can also be labeled incorrectly. Sometimes you have uneven subintervals.

So if we have a graph, and it goes 2, 4, 8, 16-- yes, I am doubling between each of the intervals, but that means that it's uneven. Because this space here shows a space of 2, and to go from 2 to 4 is another 2. But from 4 to 8, that's 4. And from 8 to 1, that's 8. So it's totally not the same in between each of the spaces on the graph, which is going to distort our picture. That's a problem.

Also, if you change the width of the intervals, if you change from really narrow spacing to really wide spacing that's going to change what your graph shows. This here shows an example of it. On the y-axis, we have ours. It goes from 3, 4, 5, 6, 7. Evenly spaced. That's OK.

We have school, eat, play outside, watch TV, sleep, chores, and homework. The graph starts at three hours and goes up to seven hours. So if you just looked at this really quickly, you would see that school and sleep were the highest. They are super high. Nothing else comes close. Everything else is just barely hovering at the bottom here. So it's barely hovering right around zero.

Wait, that first line doesn't represent zero. That first line represents three hours. So because this graph didn't start at zero, they're tricking us into believing that almost nothing was spent on eating, playing outside, watching TV, chores, and homework. But actually, that's pretty close to three hours.

So here's a graph of the same situation, but it's corrected. So we're starting at zero. And now we can see eat, play outside, watch TV, chores, and homework. Those all show up. However, they've also changed the width of the intervals.

In this graph, it's jumping by two-hour intervals. On this graph, it was jumping by one-hour intervals. So the differences between these heights are also a lot less pronounced. Because-- here, let's pull it up so we can see-- here, it looks like a huge difference between how much you go to school and how much you beat. Here, not as big.

So this graph had two different things that were misleading about its scale. First of all, it didn't start at zero. Second of all, the intervals were squished to make a larger difference appear. Here's the correction. It starts at zero, and the intervals are spaced out appropriately for the data that we have so that you can see that there is a difference. But it's a moderate difference.

This has been your tutorial on misleading graphs. There's many ways to use a graph to mislead, so you need to be careful that you don't make those mistakes yourself. And you also need to be on the lookout for them. Perhaps a newspaper would do something like this. They would not start at zero in order to try to make you conclude that students spend all their time at school and don't spend any time eating. Or they spend all their time at school, they don't get to play outside at all.

But if you did it appropriately, you could see well, yeah, they spend a lot of their time at school. But there is some time for these other activities. Thank you.

Source: CAT, PUBLIC DOMAIN HTTP://OPENCLIPART.ORG/DETAIL/1198/CAT-SILHOUETTE-BY-LIFTARN HORSE, PUBLIC DOMAIN HTTP://OPENCLIPART.ORG/DETAIL/372/HORSE-SILHOUETTE-BY-JOHNNY_AUTOMATIC DOG, PUBLIC DOMAIN HTTP://OPENCLIPART.ORG/DETAIL/63865/DOG-SILHOUETTE-BY-LAOBC GRAPHS CREATED BY AUTHOR

This tutorial covers pictographs. Pictographs are a type of graph that has artwork embedded into it. So instead of using dots or lines or bars, we use little pictures that help us to represent what we're talking about. This one here from the US Census Bureau and International Database shows the world population. They have the years 1650, 1850, 1930, '75, '99, 2012, and 2070. These last two values they note are projected.

Now over here they tell us that this one little person thing equals one billion people. So we can start to translate these into numbers. So here with 1650, we don't have a full person. It's probably around half. So that is around half of a billion, 500 million. Now here with 1850, we have a full person. We have a billion people. Here with 1930, we have two people. So we have two billion people.

And then we can see that by 2070, we have 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 people. 10 billion people in the world are expected. Now what this helps to do and people would use a pictograph to more elicit a response from a reader. When you see the number of people literally getting bigger, it's easier to internalize the fact that the population is getting bigger. It can help to make the graph more interesting as well. Instead of using a bar, you, have a picture.

However, pictographs can be deceiving. We'll see how on our example in the next slide. So here's how we're going to make a deceptive pictograph and something that you need to be aware of. Now when we are doing our example, let's say we surveyed a ton of people about their favorite animal. And their choices were cat, horse, and dog. Now when we've surveyed them, we want to have each of our pictures represent a certain number. So we're I say each one of these represents 50 people.

Now let's say for cat, 200 people said they liked cats. So we have 50, 100, 150, 200. Then for horses, 100 people liked horses. 50, 100. For dogs, let's say that 150 people liked dogs. So 50, 100, 150. If you just looked at this graph real fast, I would look at it and I would see that the dogs, they come out the furthest. Most people like dogs.

But in actuality, dogs was 150, cats was 200, and horses was 100. So because the graphics aren't each the same size, we're kind of making dogs look like it pushes out ahead. We could have also spaced things out differently to make sure that cats looks like get pushed out ahead or to make dogs look even further. ahead. So things like that, whether or not your graphics are the same size, whether or not the spacing is the same, or even whether or not each graphic represents the same amount.

What if I had said instead of each of these being 50 people, cats was 50 people, the horse picture is worth 20 people, and the dog picture is worth 10 people. Then this graph would be way out of whack. We would have 200 cats lovers, and 40 horse lovers, and 30 people saying they prefer dogs. But it looks like dogs is the most.

So when you're doing a pictograph, or when you're reading a pictograph, pay attention really carefully to what each graphic actually represents and the size of the graphic. This has been your tutorial on pictographs.