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by jonathanleane 972 days ago
It's not a 6% higher risk, it's nearly double the risk - i.e. 7% vs 13.2%.

"Dementia occurred among 96 of 730 participants (13.2%) with adult ADHD and 7630 of 108 488 participants (7.0%) without adult ADHD."

1 comments

For those who might not know, this is the difference between "percentage" and "percentage points". It is not 6% higher, it is 6 percentage points higher.

This really matters for things with a very low probability.

> It is not 6% higher, it is 6 percentage points higher.

And the difference between the two is?

A percentage always reflects a ratio between a quantity and another reference quantity. When you say a value is 6 percent higher, you are saying it went from X to (X + X*(6/100)) = (X*106/100) = 106% of the value you had before (whatever it was).

When you say it is 6 percentage points higher it means you had a percentage Y% and it is now (Y+6)%, a value which cannot be determined unless you know Y, never mind the reference absolute value it relates to.

In this particular case you can say it went from 7% to 13.2%, so if you ignore "%" as the unit the actual change is from 7 to 13.2; a ((13.2-7)/7) ≈ 0.8857 = 88% change. Had the original percentage been say 67%, a 6.2 p.p. change would have increased the percentage to 73.2%; a much smaller ((73.2-67)/67) ≈ 0.0925 = 9% change.

Had the change been "six percent of seven percent", the new value would be 7+7*(6/100) = 7.42 (percent).

TIL thanks! Upvoted you and the other reply. Appreciate the breakdowns!
https://www.stat.fi/meta/kas/prosentti_vs__p_en.html

"Per cent means one hundredth of something. Percentage point is used when comparing percentages to one another. For example, when inflation drops from three to two per cent, inflation decreases by one percentage point and 33.3 per cent."

This is a nice simple explanation of it. It's also why stock holders use "points" instead of "dollars." A stock share going up $1.50 is amazing if it was a penny stock, and absolutely not worth mentioning if it was say, Tesla. But the points have the same meaning for either stock - one is just a lot higher of a point than the other, even though the dollar change was the same.