Claim
Percent and percentage point are different units
If a rate moves from 4% to 5%, that is a rise of one percentage point and a rise of 25% in relative terms. Both descriptions are true. One sounds like a rounding error and the other sounds like a crisis, and which one gets printed depends on who is printing it.
The defense is a habit: whenever you see a percentage change, ask what it changed from. A doubling of a small number is still a small number. A one point fall in a large number can be enormous. Neither of those is a trick, and someone choosing between the two descriptions is making an argument.
Evidence
The four graph moves, all documented for seventy years
Darrell Huff catalogued most of these in How to Lie with Statistics in 1954 and nothing has been added since. A truncated axis, where the scale starts at 94 rather than zero, turns a flat line into a cliff. A chosen start year picks the trough or the peak and draws from there. A swapped denominator changes the population under the numerator, so the same count becomes a rate of something else. A change of units mid-argument compares numbers that are not comparable.
All four are legal, common and detectable in about five seconds each, once you look at the axes and the date range before the shape of the line.
Claim
Relative risk without absolute risk is close to useless
A claim that something raises your risk by 50% tells you nothing until you know the starting figure. Fifty percent on a one in a million risk is one and a half in a million. Fifty percent on a one in ten risk is a genuine problem.
So every relative risk needs its base rate attached to be interpretable, and health reporting almost never attaches it, because the relative figure is the larger number. When you cannot find the absolute figures, that absence is itself informative: the people publishing chose the frame that makes the effect look biggest, which tells you something about the paper you have not read yet.
Evidence
Numeracy collapses when identity is engaged
The unsettling part is that this is not about education. Dan Kahan and colleagues published a study in Behavioural Public Policy in 2017, sometimes called the motivated numeracy paper, in which people were given the same table of data to interpret in two framings.
When the numbers described the effect of a skin rash treatment, participants read the table correctly at a rate that tracked their numeracy. When identical numbers described a contested policy, the most numerate participants got it wrong most often in the direction of their prior commitments. Skill did not protect anyone. It provided better tools for reaching the conclusion they already wanted, which is a finding worth holding against yourself rather than against your opponents.
Action
Audit three charts
Find three charts today from any source, including ones you agree with. For each, write down the answers to four questions. Where does the y-axis start. What is the first year shown, and why that year. What is the denominator. Is the change given in percent or percentage points.
That is about four minutes per chart. Then note which of the three you had instinctively believed before you checked. The point of including charts you agree with is that the technique only works if it runs in both directions, and almost nobody applies it to material that flatters them.
Caution
Debunking is not the same as knowing
This day hands you a set of tools that feel powerful, and the failure mode is the man who can dismantle any number and cannot state any position, because everything is flawed if you look hard enough.
That is a form of laziness with the appearance of rigour. Every real dataset has limitations, and pointing at them is not a rebuttal. The question is always whether the flaw is large enough to change the conclusion, and answering it requires you to say what you think the truth probably is and with how much confidence. Day 7 is where that gets recorded.
Aside
Where the axis rule is wrong
I gave you the standard advice that a truncated y-axis is a distortion, and it is not always. For a series that moves within a narrow band, such as a body temperature, a mortgage rate or an unemployment rate, starting at zero can hide everything that matters and is worse than truncation.
The honest rule is that the axis should be chosen to show the variation that is relevant, and that you should notice when the choice is doing argumentative work. This is one of those places where a rule taught as a simple fraud detector turns out to require judgment. Treat the truncated axis as a prompt to check, not as a verdict.