Presenting data correctly: perceptive priority
Presenting data correctly is tricky. That’s why we’ll never run out of stories for this blog. Today we’ll introduce a new term and two rules to follow if you don’t want to embarrass yourself the next time you present business data.
Let’s take a closer look at the example below from The Economist. Without much further thought, we assume that the chart is trying to show that the value from 2005 almost doubled in 2006. That is exactly what the height of the bar chart suggests because the column for 2006 is 1.7 times higher than the one for 2005.
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| The Economist 389 (2008), p. 49. A sevenfold exaggeration (click to enlarge) |
Lie factor: measuring the distortion (click to enlarge) |
That, however, is not the case. An increase from $83 to $94 billion dollars is only 13 %. The chart on your right, however, calculates the largest distortion that The Economist made. What happened here? To explain that, I have coined a new phrase: perceptive priority.
The length and height of bar charts, for example, have perceptive priority. The human eye compares the heights and uses them to derive the differences among the values. Our first rule for today, therefore, is: Make differences in length proportional to the values that you are presenting. Since The Economist chopped off the base line, the columns are no longer proportional to the values – and now everything is wrong.
Now let’s take a look at the same numbers in a line chart. The example on your left uses a zero base line while the one on your right does not. What’s most interesting? Perceptive priority now ensures that the information that we have gained from the bar chart is totally worthless. Line charts contain line segments which we use to help assess the meaning of the chart. There, we especially focus on the angles of the line segments to each other. The distance to the base line, however, isn’t very interesting. You can’t find any distortion here.
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| Redesign with a zero-to-maximum scale | Redesign with a minimum-to-maximum scale |
Now for our second rule: The angles in a line chart must be proportional to the relative changes of the values. Problems with distortion only come into play when the values vary greatly in size. In that case, the same angles can show very different relative changes. We have already explored an example for that in detail. With the data we have here, however, the options above both work.
The concept of perceptive priority illustrates that we cannot simply apply a rule that works for bar charts to line charts. What catches our eye first in a bar chart is the distance between the x-axis and the data points, whereas in a line chart it’s the gradient of the connecting lines. In a line chart, perceptive priority is always given to slope, not altitude.
To decide which of the options works better, we need to take additional criteria into account. We’ll examine them more closely in one of the next issues.
I like that term, perceptive priority. It is at once concise and descriptive, not just of the effect (priority) but of its cause (perception).
Saturday, February 7th, 2009, 4:12 pmNicolas, this is excellent. For years my intuition has told me that bar charts should have a zero baseline but line charts shouldn’t, and I’ve never thought of this explanation.
Another factor, I believe, is that measures of quantity tend to need a baseline (here the metaphor is a stack of items) whereas averages use a different metaphor – we are interested in a single point rather than a stack. Of course that begs a question – is it appropriate to graph averages as bars?
Tuesday, February 10th, 2009, 1:24 pmThank you! I agree: Averages look more like averages when shown as dots. Personally, wherever possible, I try to show the difference from the average instead of the average itself.
Tuesday, February 24th, 2009, 12:16 pmFirst of all, I have to say that I agree with the concept you are trying to put forth here … many times the graphs that media present are misleading and try to fool the public. But, I have to say that I object with some aspects of this … I would say that the axes need to allow one to clearly demonstrate a magnitude of the effect is meaningful and relevant. If you insist on always having a zero, you can miss meaningful changes. If the measures in question include the statistical variation (e.g. error bars), then you can graph the data based on meaningful differences. This is not included in your example.
Here are a few examples:
1) Body Temperature. Tylenol undoubtedly would have incredibly robust data in patients with fevers but the magnitude of the effect would be small. A graph that showed temperature based on F (or even C) using an absolute 0 would not be very impressive. But the meaningful range would probably only be from 95 deg to 105 deg.
2) Blood glucose. Normal mice have blood glucose values of ~160 mg/dL. The variability if very low with a coefficient of variation of ~5 %. Given that the intrinsic variability of the measure is low, then an increase of 20 % would be highly statistically significant (and functionally quite ill), but it would not be very “impressive” if you require someone to show a “0” on the graph.
3) Body weight. A body weight of 0 is irrelevant and therefore should not be included on a graph. If a group of mice (or people) start out weighing 40g (or 200 lb) and they all lost 5–10 % that would be very significant and very functionally important. But graphing it with a 0 would not suggest signficance. I have seen a lot of data where investigators show BW graphs in ways that UNDEREMPHASIZE parameters that are highly regulated. They see a 5 % weight loss and think is means nothing, but in fact it can be quite important.
Two other examples to consider … Again Temperature … We use Farenheit and Celcius, each of which have their own meaning of 0. You might extend your argument to say the only real measure of temperature is Kelvin and therefore all data should add 273 to it. In truth, Celcius and Farenheit just defined new 0 values based on practical experience. That is what one does if they cut an axes short.
Another example to consider would be time … what is 0 time? Going back to the big bang? Birth of Christ? 2009? Again, one usually selects at “time 0” that is relevant for the data being presented.
In both cases, as I think should be argued for scientific data, the person presenting the data needs to be fair about what they are presenting. Data with variances should be different than that without. There should be some consideration of RELEVANCE of the magnitude of the effect. However, I do agree that often popular media overlook this aspect of data presentation.
Thursday, October 22nd, 2009, 12:33 amAgreed! Perceptive priority primarily hints to the difference in interpreting bars/columns and line graphs. As shown in other postings, there are valid reasons for not using zero as a graphical basis (May you chop axes? No…you must! and The scale is your message)
Thursday, October 22nd, 2009, 4:44 pm