An Interval Says More
How precise is that number, really?
The idea
A confidence interval shows the range of values the data is compatible with, which a single estimate hides.
In the real world
An estimate of 12% with an interval from 2% to 22% is a very different finding from 11% to 13%.
Going deeper
A confidence interval shows the range of values the data is compatible with, which is information a point estimate throws away.
Two studies both reporting 12% can carry entirely different amounts of information: an interval of 11–13% constrains the answer tightly, while 2–22% is compatible with nearly nothing and with a very large effect. Only the first supports a decision that depends on the size of the improvement. Quoting the range alongside the estimate costs one clause and prevents a whole class of overconfident conclusions.
Where it stops applying
Confidence intervals are frequently misinterpreted as containing the true value with 95% probability, which is not what they state. They also assume the model and sampling were sound.
Why it matters
It tells you whether a result is precise enough to act on, which the headline number cannot.
Try this today
When quoting a figure from a test, quote its range too.
Test yourself
Two studies both report a 12% improvement. One's interval runs 11% to 13%, the other's 2% to 22%. Why treat them differently?
Show the answer
The first is compatible only with a modest, real improvement. The second is compatible with almost nothing and with a very large effect, so it barely constrains the answer. Identical point estimates can carry completely different amounts of information.
Learn this in the feed Answering from memory, then again days later, is what makes it stick.