Charts and how they argue with you

You already know how to get an answer as a table. But people do not argue with tables — they argue with pictures. The trouble is that a picture comes with a built-in claim, and almost nobody reads that claim out loud. Before believing any chart, make the claim explicit: this chart says that A is bigger than B, or that A grows over time, or that A tracks B.

The three workhorses cover almost everything. A bar chart compares a few categories: sales by item. A line chart shows how one value moves over time: the queue length hour by hour. A pie chart shows how a whole splits into parts, and it is honest only when the parts really sum to one whole of something. Compare categories with bars, change over time with a line — mixing those two up is the most common wrong pick.

sales by item, units

juice      60 |################|
sandwich   55 |############### |
soup       40 |###########     |
salad      23 |######          |The sales data from the first lessons, drawn as bars.

Here is the oldest trick in the book. Same salad data, same week, two charts drawn from the very same five numbers. One says: calm, honest growth, nothing to see. The other screams: crash, drama, act now. The difference is only where the y-axis starts.

salad sales, one week

y starts at 0:        y starts at 20:
25 |     *            25 |     *
20 |    * *           20 |    * *
15 |   *   *          15 |   *   *
10 |  *     *         10 |
 5 | *                 5 |
 0 +------             0 +------
   M T W T F            M T W T F

same points, different storyTwo charts from identical data: the y-axis is the only difference.

The right chart starts its y-axis at 20, not at 0. Sales still fell from 25 to 10 — but that fall now fills the whole picture, so a drop of a bit more than half looks like a fall to almost nothing. Truncating an axis is not always a lie: sometimes 20 to 25 is exactly the interesting range. It becomes misleading when the zero matters and the chart hides where the scale begins.

Last piece: two numbers that move together. Two schools compare statistics for a year: the school with more laptops per pupil also has better exam results. Someone concludes: laptops cause results, buy more laptops. Before accepting any such claim, remember there is a third possibility.

The laptop school probably has the same hidden factor: money. Wealthier districts buy more laptops AND hire more tutors, feed pupils better, run libraries. The laptops may even help — but this comparison cannot tell, because it never measured the third factor. Correlation says these two numbers move together. Causation claims one turns the knob of the other, and that is a much stronger claim needing much stronger evidence.

So the data-analysis habit from all four lessons: query honestly, aggregate with care, and before you draw or trust a chart, ask what it is actually claiming, where its axes start, and what else could explain the pattern. The person who asks those three questions is already doing real data analysis.