Estimation and Inference

How to learn about a population from a sample: the five main sampling methods and what they mean for sampling error, why sample size and a single population matter, the central limit theorem and the standard error of the sample mean, confidence intervals for the mean (z vs t), and bootstrap and jackknife resampling.

1. 1. Populations, samples and sampling errorWe study a sample because examining the whole population is impossible or too costly, and the price we pay is sampling error.Free13 min
2. 2. Stratified and cluster samplingStratified sampling draws randomly from every subgroup to guarantee representation and precision; cluster sampling picks whole subgroups to save time and money.14 min
3. 3. Convenience and judgmental sampling, and choosing a methodNon-probability samples are chosen by convenience or expert judgment: quick and cheap, but at real risk of not representing the population.12 min
4. 4. Sample size and mixing populationsMore data reduces sampling error, but with diminishing returns, and only if every observation comes from the same population.12 min
5. 5. The central limit theoremWhatever the shape of the population, the mean of a large random sample is approximately normally distributed around the true mean, with variance $\sigma^2/n$.Free13 min
6. 6. The standard error of the sample meanThe standard error measures how precisely a sample mean estimates the population mean: $\sigma/\sqrt{n}$, or $s/\sqrt{n}$ when $\sigma$ is unknown.Video · 6 min13 min
7. 7. Confidence intervals for the meanA confidence interval turns a point estimate into a range: point estimate ± reliability factor × standard error.15 min
8. 8. Bootstrap and jackknife resamplingResampling builds the sampling distribution of a statistic by computer from the one sample you have, with no analytical formula needed.14 min