Misleading Graphs: Why the Axis Matters

Full transcript

Word for word what is said in the video — the same text as the subtitles. Times are minutes:seconds into the video.

0:00Same two numbers, two stories ▶

One town, one month of buses: the average delay of bus seven and bus four, side by side. Bus four's bar stands twice as tall as bus seven's. A complaint writes itself: bus four is twice as late. The bus company answers with a chart of the very same two numbers: hardly any difference at all. By the end of this video: how the same two numbers tell both stories.

0:27Isn't a chart just the numbers? ▶

A headline can steer you with a single word, and a chart, or graph, can do it without any words at all. Most of us treat a chart as the numbers, simply drawn: if the numbers are right, the picture must be right too. Yet the complaint and the bus company use exactly the same two numbers. So the story is not in the data: it sits in how the chart is drawn. You will leave with one habit for every chart you meet, and three cases to check.

0:55A bar's length is its number ▶

Start with the plainest chart there is: a bar, standing on zero. In a bar chart, the length of the bar is the number it shows. A bar for six minutes should stand exactly twice as tall as a bar for three minutes. You could check that with a ruler, but your eye does it for you, without asking. So for every bar chart, ask one thing: if a bar looks twice as tall, is its number twice as big? That only works when the bar starts at zero, so keep an eye on where a bar starts.

1:24How much later is bus 4? ▶

Back to the two buses, this time without the numbers on the bars. You know a bar may not start at zero, so look at the bars alone: how much later is bus four, would you say? Hold on to your first answer for a moment.

1:38The axis slides, the numbers stay ▶

Here are the numbers: bus seven runs six minutes late on average, and bus four six and a half. That is half a minute more, about eight percent, and not twice. The bar looks twice as tall because the axis does not start at zero: it starts at five and a half minutes. Above that mark, bus seven shows half a minute and bus four a whole one: that is the twice your eye saw. Now watch the bottom of the axis slide down to zero, while every number stays exactly where it is. The two bars become almost the same height, and the bus company's story appears: hardly any difference. Slide it back up, and the complaint returns, with not a single number changed. And zoom out far enough, all the way to thirty minutes, and even six minutes late starts to look small. All three pictures come from the same two numbers: the drawing picked which story you see first. So should every axis start at zero, then?

2:30Bars from zero, lines may zoom ▶

For bars, yes: their length is the number, so only a bar that starts at zero shows eight percent more as eight percent taller. A line chart is different, because it shows change rather than size. Here is the noon temperature over that same month, drawn on an axis from zero. The warm-up from about thirteen degrees to about nineteen looks like a gentle slope. And zero degrees is not "no temperature", so it does not have to be on the axis. Start the axis near the data, and the warm-up is easy to see. But even here your eye makes the change look bigger, so read the numbers on the axis.

3:05Knowing is not enough: the habit ▶

Did your first answer still lean towards twice, even though you knew the axis might be cut? That is normal: in five experiments, more than four in five people saw a bigger difference with a cut-off axis. People with lots of experience with data fell for it too. The same went for people who had it explained right before, if a little less. And it is often not a trick at all: many charting programs cut the axis off by default. So the fix is not knowing, it is a habit. Before you read the shape, read the axis: where it starts, and where it ends.

3:39Two scales on one chart ▶

One more case to check: two scales on one chart. On the left, the noon temperature; on the right, the average delay of both buses that day. The two lines climb almost on top of each other, and a new headline is ready: hot days make the buses late. But look at the right axis: it covers less than half a minute. From the first week to the last, the delay rose by about eight seconds, on top of more than six minutes. Stretch the right axis to two minutes, and the same delay line barely climbs. Neither range is wrong for a line on its own. How closely the two lines match is set by whoever picks the scales. Temperature and delay really do rise a little together, but first ask last video's question: could the season be pushing both? The cleanest fix is two charts side by side, each with its own axis, and you read both.

4:27One look back ▶

Back to video eight: twenty-eight students and their minutes to school, drawn as two hills and as one slope. Which one setting turned the two hills into a single slope? The bin width: a choice in the drawing, just like the range of an axis today.

4:42In one picture ▶

So, in one picture: the same numbers can tell more than one story, depending on how the chart is drawn. A bar's length is its number, so a bar axis starts at zero. A line chart may zoom in, but your eye still makes the change look bigger. Two scales on one chart can make almost any two lines look like partners. And the one habit for every chart: read the axis before you read the shape,

5:05Next time ▶

because that is where the story gets chosen. Next time, the course goes back to the question every dataset starts with: what kind of data is it? And if a chart has ever steered you, tell me in the comments which one. And if you want to keep learning, subscribe, the next video will find you. Until then: happy learning.