Voluntary response sample

In a voluntary response sample nobody gets selected. The researcher opens a channel, a link, a call-in line, a mail-back form, a review page, and the sample is whoever decides to use it. That self-selection is systematic rather than random: people who take the trouble to answer an unsolicited invitation tend to hold stronger views than the people who ignore it, so the sample overrepresents both ends of the opinion scale and thins out the indifferent middle.

A school newspaper posts a link asking the school's 1,600 students whether the dress code should change. 300 answer and 240 of them say yes, so the poll reports $\hat{p} = \frac{240}{300} = 0.80$ (p-hat). Suppose that among the 1,300 students who ignored the link, 455 would have said yes, a rate of 0.35. The true proportion is $\frac{240 + 455}{1600} = 0.434$. The poll is off by more than 0.36 while displaying 300 responses, which is a respectable-looking number.

"That is a 19 percent response rate" is the misreading worth killing. It is not a response rate. A response rate is answers divided by people selected, and nobody here was selected. The 1,300 silent students are not nonresponse; there was no sample for them to fail to respond to. The distinction decides the repair: nonresponse is attacked by chasing a known list of chosen individuals, and this poll has no such list, so there is nothing to chase and no way to patch the number after the fact.

It is also not a convenience sample, though both skip randomization. The difference is who did the choosing. In a convenience sample the researcher grabs whoever is easiest to reach; in a voluntary response sample the respondents put themselves forward.

Size is not the fix. An open poll with 100,000 answers is still self-assembled and still centered on whatever the motivated fraction believes, so the extra data only tightens the scatter around a wrong value. The repair is to select first: draw a random sample from a list of the population, then pursue the people you drew.