A random probability sample is the "gold" standard of survey research. The maths behind a random probability sample are that it satisfies two criteria: every unit in the population has a chance of being selected for the sample; and the probability of selection for any unit in the population is either known or could be calculated. Effectively, everyone in the population has a known and non-zero chance of being selected.
Probability samples should be used whenever point estimates (e.g. means and percentages) need to be generalised to the population and / or where accuracy is paramount, in particular for the very large central government-funded national surveys (e.g. the Labour Force Survey) and those for media measurement (e.g. NRS PAMCo ,(a large scale study of newspaper and magazine readership undertaken by Ipsos Connect).
In practice, Quota samples have been found to be as accurate as random probability samples, on many key variables, and cost less to execute, and therefore they form the basis of most of Ipsos' commercial surveys. However, Random probability samples are, strictly speaking, the only ones from which we can generalise to a larger population within known limits (i.e. undertake a test statistical significance of each result). All other samples, including quota and other purposive samples, cannot strictly have confidence intervals calculated for them, as they are not based on a random sample, and therefore the probability of selection for each respondent cannot be calculated.
Do remember that it is very difficult to obtain a random sample with most internet samples as one would not know what the extent is of the population of users from which the sample is drawn nor would have a reliable sampler frame or list of all members of the population in order to determine the probability of each unit is to appear in the sample.
Ipsos Point Of View
Probability samples should be used whenever point estimates (e.g. means and percentages) need to be generalised to the population.
Because the sample has been selected at random we can be confident that the sample will be sufficiently representative of the population, so that, with appropriate weighting, the point estimates from the sample should be fairly precise estimates of the true population measures. Even if the sample is selected with unequal probabilities, then selection weights – calculated directly from the known probabilities of selection – will adjust the sample to represent the population.
Random Probability samples should ideally be used whenever a client needs to produce the most accurate data possible, including the minority of people in Western countries who are not online, where coverage spread is particularly important, and where results need to be generalised to the population as a whole.
Fieldwork for random probability samples
Although the process of selecting a random probability sample (RPS) "in the office" of units from a population is no more difficult than selecting a quota sample, the fieldwork for the former is considerably more complex, costly and involved than for the latter. Indeed, executing random probability samples well is difficult and requires experience.
If a unit is drawn through an RPS, then it is necessary for the interviewer to obtain a response from that unit, otherwise the randomness and associated accuracy of the sample would be jeopardised. It is not possible for that unit to be substituted with another unit nearby, even if it / they appear very similar to the interviewer. For face-to-face fieldwork, an interviewer would need to call back to the address a number of times and at different times of the day. If obtaining an interview is still unsuccessful, then it would be necessary for the client team (or even the client) to approve of a sample re-issue or accepting this as a "non-response".
There also exists the question of "who to interview" within households selected through RPS. The selection of the right person within the household is still part of a scientific process and will also need to be carried out in a random probability way – i.e. with known selection probability. A number of methods exist to allow this, such as routines within the CAPI system and the person with the next birthday.