Math Says Yes
Concept

Confidence Intervals

A confidence interval is a range produced by a method that captures the true value a stated share of the time across repeated samples. It describes uncertainty in the estimating method, not a personal guarantee that one already-computed interval contains the truth.

Lessons

Point estimates shown with horizontal uncertainty ranges.
Uncertainty Needs Ranges
A measured number is usually a best estimate with sampling wobble around it, so honest comparisons need ranges as well as point estimates.

Related Facts

Data Tricks
4 min · medium
Several interval bars around a target line, with most bars crossing the target and one missing it.
A 95% confidence interval is not a 95% promise
A 95% confidence interval means the method works 95% of the time in repeated samples, not that this exact range now has a 95% chance of holding the truth.
Risk & Decisions
4 min · easy
Two poll bars with overlapping margin-of-error brackets.
A three-point poll lead can still be a tie
If a poll says 51% versus 48% with a plus-or-minus 3 point margin of error, the headline leader may not really be ahead.
Data Tricks
5 min · medium
A horizontal range bar with a center dot on the left, and a dashed threshold line with a marker crossing it on the right.
P-value vs confidence interval: what each one tells you
A p-value asks whether the data look surprising under a null model. A confidence interval asks which effect sizes remain plausible.

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