1.20 Sampling, standard error and confidence intervals
You can put an honest error bar on a number.
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The standard error says how much a computed number would wobble if the data were collected again, and confidence intervals put that wobble on display. Bootstrapping extends the idea to statistics no formula covers. It sits early in statistics because an error bar is the difference between a number and a statement you can stand behind. The famous confusion is what a ninety-five percent interval means — it is a statement about the procedure across repetitions, not a probability about this particular interval containing the truth.
Work through these
Population vs. sample; sampling bias
A sample stands in for a population, and how it was drawn decides whether it can. Bias introduced at collection cannot be repaired by any later analysis.
Standard error and how it shrinks
The standard error describes how much a sample average would vary between samples, and it shrinks with the square root of sample size. That square root is why doubling accuracy costs four times the data.
Confidence intervals and what they do not mean
A confidence interval is a statement about the procedure rather than about the specific interval you computed, which is the part almost everyone gets wrong. Being able to state it correctly is the item.
Bootstrapping when the formula is unavailable
Resampling your own data repeatedly gives an error estimate when no formula applies. It is a general technique that removes a great deal of distributional worry.
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