Misleading line graphs

Thrill Soda hired a marketing company to help them promote their brand against Yummy Cola. The company gathered the following data about consumers' preference of soda. So they have, year by year, percentage of respondents who preferred Yummy Cola, percentage of respondents who preferred Thrill Cola, and then these are people who had no preference. So in 2006, 80% liked Yummy, only 12% liked Thrill, and 8% didn't like either one or didn't have any preference. And so actually just from here you see that many, many more people liked Yummy Cola than Thrill Cola, actually every year over year. So, Thrill Cola definitely has something. They have an uphill battle. But then they said the advertising company created the following two graphs to promote Thrill Soda. And so let's see what's happening over here. And let's think about whether this is misleading or not. So if we look at this graph over here, in 2006, sure enough, 80% liked Yummy Cola. Then in 2007, 76%. Then it keeps going to then 77%, then 73%, then 73% to 68%. So this is accurate data. It actually represents the data that's given right over here. I'll do it in the same. It actually represents this data very faithfully. Then right over here, if we look at this chart, Percentage of People who Prefer Thrill Soda, so over here in 2006, 12% preferred Thrill Soda. 2007, 19%. 2008, 19%. Then we go up to 20%, 21%, and 25%. So the graphs are actually accurate. They're not lying. These are actually the data points of the percentage who prefer Thrill Soda. Now what's misleading is if someone were to just look at these two graphs without actually looking at the scales over here, they'll see two things. They'll say, oh, look, you see a declining trend. And that's what line graphs are good for, for seeing trends. They say, look, I see a declining trend in the percentage of people who prefer Yummy Cola. And I see this increasing trend in the percentage of people who prefer Thrill Cola. And that's true. You have a declining trend here. And you have an increasing trend here. But what's misleading here is the way that they've plotted the scales. These scales are not the same. So when you look at this, you say not only is there an increasing trend of people who prefer Thrill Soda, but the way they set up the scale, it looks like the trend is above. The human brain is tempted to compare these and to say, look, not only is this an upward trend, but it's above this trend right over here. Even in 2006, this data point looks higher than these data points right over here. But the reality is that it's only because the scale is distorted. Now this is the oldest trick in the book when plotting line graphs. It all depends on the scale. So this just looks good because they used this scale that went from 0 to 30 as opposed to 0 to 100. The better thing to do, or the more genuine thing to do, or the more honest thing to do, would have actually been to plot them on the same graph. Although if they did that, that wouldn't have painted a very good picture for Thrill Soda. So if we plotted on the same graph Thrill Soda, let's try that out. And actually, this is even worse. You actually wouldn't even be able to plot Thrill Soda on this graph because they started this graph right over here at 50%. They didn't even start it at 0%. So you actually would not even be able to plot Thrill Soda on this graph. If you did, you would have to extend this graph all the way down. So you would have to extend this graph all the way down to-- so this would have to be 40%. This would be 30%. This would be 20%. This would be 10%. And then down all the way over here would be 0%. And then the Thrill Soda graph would be all the way down here. So it was like 12%. And it goes all the way up to like 25%. So the Thrill Soda, it would have looked something like this. The graph would have looked something like this, which is nowhere near. If you plotted these on the same scale, on the same graph, then it would have still been pretty obvious that-- even though the trend is downward-- a lot more people prefer Yummy Cola to Thrill Cola. So there's two very disingenuous things going on over here. One is the actual scale. For this amount of distance on this scale, they represent 10%. So whatever the gain is, it looks like it's a huge gain. And over here, on that same amount, they're actually representing a larger amount. They're representing closer to 15% or 16%. And then the main thing is they started the scale here at 50%. So they're not showing how many people really prefer, how large 80% or even 70% really is. And over here, they start at 0% and they just have a larger scale. So it makes it look like out the gate, a lot of people prefer, or a comparable amount of people prefer, Thrill and that the trend is up. But the reality is still way more people prefer Yummy Cola. So this was a little bit-- or actually a very, very, not-so-honest way of representing the data. Or I guess you could say they're misrepresenting the data.