Knowing without asking everyone: how did the sampling method win out in the 20th century?

To know what the plov in the pot is like, a cook does not eat all of it; he tastes a spoonful. But there is one condition: first it must be stirred well. Otherwise you taste only the rice on top and conclude that "there's no meat". The main discovery of 20th-century statistics was the scientific proof of this simple rule.

What did Neyman prove about sampling?

In June 1934 the Polish statistician Jerzy Neyman gave a paper at the Royal Statistical Society entitled "On the Two Different Aspects of the Representative Method". The paper was published in the society's journal. It compared two approaches: - Purposive selection: the researcher chooses groups that "look like the average" himself - Random, stratified sampling: the population is divided into groups and a random selection is made from each group

Neyman showed the advantage of random stratified sampling and also proposed a way of assessing how reliable the result is. According to the Encyclopedia of Mathematics, it was in this very paper that the idea later called the confidence interval appeared in a limited form.

Stratified sampling (prepared by the author, hypothetical figures). The "Navro'z" retail chain wants to survey 500 of its 10 000 customers.

Within each group customers are selected at random. If all 500 people were surveyed only at the shop in the centre, the village customers would not be heard at all.

Why did the 1936 poll get it wrong?

Before the 1936 US presidential election, the "Literary Digest" magazine conducted a very large postal poll and predicted that Alf Landon would win. In the event, Franklin Roosevelt won by a wide margin.

Two reasons are usually given (as in the Emory University material): - The names were taken mainly from telephone directories and car registration lists. In 1936 telephones and cars were more common in well-off families, and low-income voters were under-represented - Only part of the ballots sent out came back, and those who responded were not like those who did not

Later researchers (including D. Lusinchi, 2012) discuss how the first reason was not the only one, as previously thought, and how non-response also played a major role. Either way, the lesson is the same: the result depends on whom you ask and who responds.

In the same election George Gallup, with a much smaller but well-planned sample, correctly predicted Roosevelt's victory. The magazine later closed, while Gallup's name became famous in the field of polling.

How did calculating machines change?

As the history page of the US Census Bureau states, the bureau used updated versions of Hollerith's machine up to the 1940 census. In 1951 the bureau signed a contract for the UNIVAC I electronic computer, and it was used to process part of the 1950 census and the whole of the 1954 economic census. So sampling theory and electronic computing came into force in the same period: it became possible to ask fewer people but to calculate the result faster and more accurately.

Then and now

The lesson is still relevant today: correctly chosen answers from a thousand people are worth more than a million answers collected the wrong way.