One of the most common errors in interpreting polls and surveys is the presumption that because something has a really huge sample size it is more meaningful. Or indeed, meaningful at all. Size isn’t what makes a poll meaningful, it is how representative the sample is. Picture it this way, if you’d done an EU referendum poll of only over 60s you’d have got a result that was overwhelmingly LEAVE… even if you polled millions of them. If you did a poll and only included people under 30 you’d have got a result that was overwhelmingly REMAIN… even if you polled millions of them. What matters is that the sample accurately reflects the wider population you want them to represent, that you have the correct proportions of both young and old (and male & female, rich & poor, etc, etc). Size alone does not guarantee that.
The classic real world example of this is the 1936 Presidential Election in the USA. I’ve referred to this many times but I thought it worth reciting the story in full, if only so people can direct others to it in future.
Back in 1936 the most respected barometers of public opinion was the survey conducted by the Literary Digest, a weekly news magazine with a hefty circulation. At each Presidential election the Digest carried out a survey by mail, sending surveys to its million-plus subscriber base and to a huge list of other people, gathered from phone directories, membership organisations, subscriber lists and so on. There was no attempt at weighting or sampling, just a pure numbers grab, with literally millions of replies. This method had correctly called the winner for the 1920, 1924, 1928 and 1932 Presidential elections.
In 1936 the Digest sent out more than ten million ballots. The sample size for their final results was 2,376,523. This was, obviously, huge. One can imagine how the today’s papers would write up a poll of that size and, indeed, the Digest wrote up their results with not a little hubris. If anything, they wrote it up with huge, steaming, shovel loads of hubris. They bought all the hubris in the shop, spread it across the newsroom floor and rolled about in it cackling. Quotes included:
- “We make no claim to infallibility. We did not coin the phrase “uncanny accuracy” which has been so freely applied to our Polls”
- “Any sane person can not escape the implication of such a gigantic sampling of popular opinion as is embraced in THE LITERARY DIGEST straw vote.”
- “The Poll represents the most extensive straw ballot in the field—the most experienced in view of its twenty-five years of perfecting—the most unbiased in view of its prestige—a Poll that has always previously been correct.”
You can presumably guess what is going to happen here. The final vote shares in the 1936 Literary Digest poll were 57% for Alf Landon (Republican) and 43% for Roosevelt (Democrat). This worked out as 151 electoral votes for Roosevelt and 380 for Landon. The actual result was 62% Roosevelt, 38% for Landon. Roosevelt received 523 in the electoral college, Landon received 8, one of the largest landslide victories in US history. Wrong does not nearly begin to describe how badly off the Literary Digest was.
At the same time George Gallup was promoting his new business, carrying out what would become proper opinion polls and using them for a syndicated newspaper column called “America Speaks”. His methods were quite far removed from modern methods – he used a mixed mode method, mail-out survey for richer respondents and face-to-face for poorer, harder to reach respondents. The sample size was also still huge by modern standards, about 40,000*. The important different from the Literary Digest poll however was that Gallup attempted to get a representative sample – the mail out surveys and sampling points for face-to-face interviews had quotas on geography and on urban and rural areas, interviewers had quotas for age, gender and socio-economic status.
Gallup set out to challenge and defeat the Literary Digest – a battle between a monstrously huge sample and Gallup’s smaller but more representative sample. Gallup won. His final poll predicted Roosevelt 55.7%, Landon 44.3%.* Again, by modern standards it wasn’t that accurate (the poll by his rival Elmo Roper, who was setting quotas based on the census rather than his turnout estimates was actually better, predicting Roosevelt on 61%… but he wasn’t as media savvy). Nevertheless, Gallup got the story right, the Literary Digest hideously wrong. George Gallup’s reputation was made and the Gallup organisation became the best known polling company in the US. The Literary Digest’s reputation was shattered and the magazine folded a couple of years later. The story has remained a cautionary tale of why a representative poll with a relatively small sample is more use than a large poll that makes no effort to be representative, even if it is absolutely massive.
The question of why the Digest poll was so wrong is interesting itself. Its huge error is normally explained through where the sample came from – they drew it from things like magazine subscribers, automobile association members and telephone listings. In depression era America many millions of voters didn’t have telephones and couldn’t afford cars or magazine subscriptions, creating an inbuilt bias towards wealthier Republican voters. In fact it appears to be slightly more complicated than that – Republican voters were also far more likely to return their slips than Democrat voters were. All of these factors – a skewed sampling frame, differential response rate and no attempt to combat these – combined to make the Literary Digest’s sample incredibly biased, despite its massive and impressive size.
Ultimately, it’s not the size that matters in determining if a poll is any good. It’s whether it’s representative or not. Of course, a large representative poll is better than a small representative poll (though it is a case of diminishing returns) but the representativeness is a prerequisite for it being of any use at all.
So next time you see some open-access poll shouting about having tens of thousands of responses and are tempted to think “Well, it may not be that representative, but it’s got a squillion billion replies so it must mean something, mustn’t it?” Don’t. If you want something that you can use to draw conclusions about the wider population, it really is whether it reflects that population that counts. Size alone won’t cut it.
* You see different sample sizes quoted for Gallup’s 1936 poll – I’ve seen people cite 50,000 as his sample size or just 3,000. The final America Speaks column before the 1936 election doesn’t include the number of responses he got (though does mention he sent out about 300,000 mailout surveys to try and get it). However, the week after (8th Nov 1936) the Boston Globe had an interview with the organisation going through the details of how they did it that says they aimed at 40,000 responses.
** If you are wondering why the headline in that thumbnail says 54% when I’ve said Gallup called the final share as 55.7%, it’s because the polls were sometimes quoted as share of the vote for all candidates, sometimes for share of the vote for just the main two parties. I’ve quoted both polls as “share of the main party vote” to keep things consistent.