Confidence Intervals

“A point estimate looks exact; an interval shows how much it could move under the procedure.”

01 / PLAINLY

What it means, plainly

A confidence interval pairs an estimate with a range produced by a procedure. Its width conveys how much precision that procedure offers under its assumptions.

02 / CONTEXT

A little more

In frequentist terms, a 95% interval procedure would cover the true parameter in about 95% of repetitions under its assumptions. The observed interval also conveys model-based precision.

03 / WHY IT MATTERS

Why it matters

It shows which values remain compatible with the model instead of letting a point estimate look perfectly exact.

04 / EXAMPLE

A familiar example

An estimated difference of 4 with an interval from 1 to 7 says more than reporting 4 alone.

05 / LIMIT

What it does not mean

Once calculated, it is not generally correct to say the fixed parameter has a 95% probability of lying inside.

06 / NOTICE

Notice it in your day

Compare an estimate of 4 with intervals from 3 to 5 and from −2 to 10. Describe the change in precision without judging only by the center.

FINAL NOTE

The idea worth keeping

Inspect width, assumptions, and compatible values, not only whether a threshold is crossed.

QUESTIONS / 02

Questions people still have

What does interval width communicate?

The precision supplied by the procedure under its model and assumptions.

What does 95% mean in the frequentist reading?

Across many repetitions, the procedure would cover the true parameter about 95% of the time under its assumptions.