Misleading Graphs: The Chart That Starts at 97
The short version: a bar's length is its message, so bars must start at zero. A score that rose from 98.0 to 99.5 improved by about 1.5%. Start the axis at 97 and the second bar is 2.5 times taller, so it looks like +150%. That exaggerates the change about 98 times.
Slide 14 of the quarterly results showed the customer satisfaction index. Last quarter: 98.0. This quarter: 99.5. On the slide, the second bar towered over the first like a skyscraper next to a garden shed.
The board rose to its feet. The Chief Customer Officer said the word "transformational" twice. The consultants who had made the slide sent their invoice the same afternoon, and it was also transformational.
Cousin Kevin, who had made the spreadsheet behind the slide, noticed that the vertical axis started at 97. He decided this was not the moment.
The same two numbers, drawn twice
The real change is 1.5 points on a score of 98, which is an improvement of about 1.5%. But on the left-hand chart the bars are measured from 97, not from zero. The first bar is 1 unit tall (98 minus 97), the second is 2.5 units tall (99.5 minus 97). The eye sees a bar that grew 2.5 times, a jump of 150%.
Some chart designers measure this with a "lie factor": the size of the change in the picture divided by the size of the change in the data. Here it's 150% divided by 1.53%, a lie factor of about 98. A truthful chart has a lie factor of 1. Slide 14 was the most exaggerated thing in the building, and the building contains a sales department.
When a non-zero axis is fine
- Bars must start at zero. A bar says "this much", and its length is the whole message. Cut the bottom off and the message is false, however carefully the axis is labelled.
- Lines can start elsewhere. A line chart shows how something moves, not how big it is, so zooming in is fine when the numbers never get near zero, like body temperature or a stock index. The axis just has to be clearly labelled.
- Watch for a moving zero. The real giveaway is an axis that changes from slide to slide.
The following quarter
Next quarter the index fell from 99.5 to 97.6. Slide 14 had a new axis. It started at zero. Both bars were the same height, more or less, and the title said "Customer satisfaction remains stable". The board nodded. Nobody stood up. The consultants sent their invoice.
This is the part that should worry you more than the first one. A single exaggerated chart is a mistake. An axis that starts at 97 when the news is good and at zero when it's bad is a policy.
How to spot it in ten seconds
1. Read the bottom number on the axis first, before you look at the bars. If it isn't zero on a bar chart, the picture is lying about size.
2. Do the maths on the labels, not on the picture. New minus old, divided by old. 99.5 minus 98.0 is 1.5; divided by 98 it's about 1.5%. The picture said 150%.
3. Compare with the previous presentation. If the axis moved, ask who moved it, and in which direction the news was going at the time.
Where it costs you money
Every trading app does this automatically. Price charts zoom in to fill the screen, so a stock that moved 2% in a day looks like a cliff or a rocket. That's not dishonest, it's how line charts work, but it makes ordinary days feel dramatic and dramatic feelings lead to trades. Read the percentage change before you read the shape.
The moral
The data said "a little better". The chart said "a miracle". The chart got a standing ovation. Kevin has since been asked to make all future charts. His first one started at zero. It was returned with the comment "lacks energy".
The company, the index and the slides are an illustration, not data from a real organisation. Educational content, not financial advice.