Estimation is the branch of statistical inference concerned with using sample data to say something trustworthy about an unknown population parameter, whether that's a single number (point estimation) or a defensible range (interval estimation). It sits at the hinge between descriptive statistics, which only summarizes the data you already have, and the rest of inferential statistics — hypothesis testing, regression, experiment design — all of which lean on the same habit of quantifying uncertainty that estimation teaches. Practitioners reach for it constantly: sizing a poll's margin of error, reporting a clinical trial's effect with a credible range instead of a bare average, or deciding how large a sample a study actually needs before collecting a single row of data. The single most useful mental model to carry into the tables below is that a confidence interval is a property of the procedure, not of any one interval you compute — before sampling, the process has (say) a 95% chance of producing an interval that traps the true parameter; after sampling, that specific interval either contains it or it doesn't, and no amount of re-reading the numbers changes which. Everything that follows — which formula to reach for, how wide the interval will end up, and which of the many "95% confident" claims people make are actually true — falls out of taking that distinction seriously.
What This Cheat Sheet Covers
This topic spans 13 focused tables and 76 indexed concepts. Below is a complete table-by-table outline of this topic, spanning foundational concepts through advanced details.
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Table 1: Foundations of Point and Interval Estimation
Every confidence interval starts from the same handful of building blocks: a parameter you can't observe directly, a statistic computed from data you can, and a way to size up how much that statistic is likely to wander from sample to sample. Get these definitions straight first, since every formula in the tables below is just a different way of combining them.
| Concept | Example | Description |
|---|---|---|
x̄ = (1/n)Σxᵢ | A single value computed from sample data used as the best guess for an unknown population parameter. | |
population mean $\mu$ vs. sample mean $\bar{x}$ | A parameter describes the whole population and is fixed but unknown; a statistic is computed from a sample and changes from sample to sample. | |
$\bar{x} \pm \text{margin of error}$ | A range of plausible values for the parameter, built around the point estimate to convey the estimate's uncertainty. | |
$SE(\bar{x}) = \dfrac{s}{\sqrt{n}}$ | The estimated standard deviation of a statistic's sampling distribution; it shrinks as sample size grows. |