What is a probability-weighted sample for a survey?

When law departments are surveyed at random, and a single lawyer responds from each participating department, any given lawyer in larger department has a smaller probability of responding than a lawyer in a smaller department. More precisely, the probability of a lawyer being included in the survey is inversely proportional to the size of the department in a random sample of law departments, if lawyers within a department are selected with equal probability and there are no non-responses.

However, composition of the sample is affected by non-response. One source of non-response is non-availability: no one answers the phone, no one receives the message on the answering machine, or no one answers the email or letter. It seems reasonable to suppose that in a larger department it is more likely that someone will be in the office.

Statisticians have developed methods to correct for this bias, one of which is to create a probability-weighted sample. With these methods, large law department lawyers have the same influence as smaller law department lawyers.