As I commented previously when we had a poll on the ages of HNers, the data can't be relied on to make such an inference. That's because the date are not from a random sample of the relevant population. One professor of statistics, who is a co-author of a highly regarded AP statistics textbook, has tried to popularize the phrase that "voluntary response data are worthless" to go along with the phrase "correlation does not imply causation." Other statistics teachers are gradually picking up this phrase.
-----Original Message----- From: Paul Velleman [SMTPfv2@cornell.edu] Sent: Wednesday, January 14, 1998 5:10 PM To: apstat-l@etc.bc.ca; Kim Robinson Cc: mmbalach@mtu.edu Subject: Re: qualtiative study
Sorry Kim, but it just aint so. Voluntary response data are worthless. One excellent example is the books by Shere Hite. She collected many responses from biased lists with voluntary response and drew conclusions that are roundly contradicted by all responsible studies. She claimed to be doing only qualitative work, but what she got was just plain garbage. Another famous example is the Literary Digest "poll". All you learn from voluntary response is what is said by those who choose to respond. Unless the respondents are a substantially large fraction of the population, they are very likely to be a biased -- possibly a very biased -- subset. Anecdotes tell you nothing at all about the state of the world. They can't be "used only as a description" because they describe nothing but themselves.
http://mathforum.org/kb/thread.jspa?threadID=194473&tsta...
For more on the distinction between statistics and mathematics, see
http://statland.org/MAAFIXED.PDF
and
http://escholarship.org/uc/item/6hb3k0nz
I think Professor Velleman promotes "Voluntary response data are worthless" as a slogan for the same reason an earlier generation of statisticians taught their students the slogan "correlation does not imply causation." That's because common human cognitive errors run strongly in one direction on each issue, so the slogan has take the cognitive error head-on. Of course, a distinct pattern in voluntary responses tells us SOMETHING (maybe about what kind of people come forward to respond), just as a correlation tells us SOMETHING (maybe about a lurking variable correlated with both things we observe), but it doesn't tell us enough to warrant a firm conclusion about facts of the world. The Literary Digest poll
http://historymatters.gmu.edu/d/5168/
http://www.math.uah.edu/stat/data/LiteraryDigest.pdf
is a spectacular historical example of a voluntary response poll that didn't give a correct picture of reality at all.