Two million votes still picked the wrong president
In 1936 the Literary Digest surveyed over two million people and forecast a Republican win—then lost badly. Magazine and phone lists leaned Republican, so sheer size could not save a biased sample. Good sampling is about representativeness, not just volume.
Sampling selects a subset from a statistical population to estimate traits of the whole. Statisticians chase unbiased, representative samples because a full census is often too costly, too slow, or impossible—like measuring every star. Survey weights can correct design features such as stratification. Business, medicine, and acceptance sampling of production lots all rely on the idea.
Pierre Simon Laplace estimated France's population in 1786 with a sample and a ratio estimator, even bounding error probabilistically with Bayes' theorem and a uniform prior. Alexander Ivanovich Chuprov brought sample surveys to Imperial Russia in the 1870s. Singapore's Elections Department has used sample counts since 2015, citing roughly a four percent margin of error at ninety-five percent confidence—while reminding the public that only the returning officer's full count is official.
Defining the population is half the work: a production batch, checkout lines over time, or even a roulette wheel's long-run behavior, as Joseph Jagger studied in Monte Carlo. Sometimes the sampled frame only partly overlaps the group of interest. A probability sample gives every unit a known positive chance of selection, enabling unbiased totals via weights. Equal-probability designs are self-weighting; methods include simple random, systematic, stratified, probability-proportional-to-size, and cluster sampling.
Nonprobability methods—convenience, quota, snowball, purposive—leave some people with no chance or unknown chance, blocking honest sampling-error estimates. Interviewing whoever answers the door favors homebodies. Nonresponse can quietly turn a probability plan into a nonprobability mess. The Digest disaster remains the cautionary tale: large and wrong beats small and careful every time.
Source: Sampling (statistics)
