The comforting number
A 95% confidence interval feels like a promise about the number in front of you. It is not. It is . Run the same procedure on many samples and, if every assumption holds, about 95% of the intervals it produces will contain the true value. This interval either does or it doesn’t — the probability already collapsed.
The gap between the promise and the practice is where the trouble lives. When a small, skewed sample is fed through the textbook formula, real coverage can fall to the low eighties while the label still reads 95% — the assumptions quietly failed, and the number stayed confident anyway.
Read that chart as a warning, not a ranking. The methods that do better are the ones that lean less on assumptions the data can quietly violate. An interval is only as honest as the model that drew it.
Uncertainty is not the enemy of knowing — it is the grammar of it. An interval that admits what it doesn’t know is worth more than a point estimate that pretends it does.
So the next time you meet a tidy ±3 point margin, ask the quieter question the label skips: 95% of ? The answer is usually more interesting than the interval.