Sampling is the use of a subset of the population to represent the whole population or to inform about (social) processes that are meaningful beyond the particular cases, individuals or sites studied. Probability sampling, or random sampling, is a sampling technique in which the probability of getting any particular sample may be calculated. Nonprobability sampling does not meet this criterion and, as any methodological decision, should adjust to the research question that one envisages to answer. Nonprobability sampling techniques are not intended to be used to infer from the sample to the general population in statistical terms. Instead, for example, grounded theory can be produced through iterative non-probability sampling until theoretical saturation is reached (Strauss and Corbin, 1990).
Thus, one cannot say the same on the basis of a nonprobability sample than on the basis of a probability sample. The grounds for drawing generalizations (e.g., propose new theory, propose policy) from studies based on nonprobability samples are based on the notion of "theoretical saturation" and "analytical generalization" (Yin, 2014) instead of on statistical generalization. Researchers working with the notion of purposive sampling assert that while probability methods are suitable for large-scale studies concerned with representativeness, non-probability approaches are more suitable for in-depth qualitative research in which the focus is often to understand complex social phenomena (e.g., Marshall 1996; Small 2009). One of the advantages of nonprobability sampling is its lower cost compared to probability sampling. Moreover, the in-depth analysis of a small-N purposive sample or a case study enables the "discovery" and identification of patterns and causal mechanisms that do not draw time and context-free assumptions.
Non-probability sampling is often not appropriate in statistical quantitative research, though, as these assertions raise some questions --how can one understand a complex social phenomenon by drawing only the most convenient expressions of that phenomenon into consideration? What assumption about homogeneity in the world must one make to justify such assertions? Alas, the consideration that research can only be based in statistical inference focuses on the problems of bias linked to nonprobability sampling and acknowledges only one situation in which a non-probability sample can be appropriate --if one is interested only in the specific cases studied (for example, if one is interested in the Battle of Gettysburg), one does not need to draw a probability sample from similar cases (Lucas 2014a).
Non-probability sampling is however widely used in qualitative research. Examples of nonprobability sampling include:
Nonprobability sampling should not intend to meet the same type of results neither to be assessed with the quality criteria of probabilistic sampling (Steinke, 2004).
Studies intended to use probability sampling sometimes end up using nonprobability samples because of characteristics of the sampling method. For example, using a sample of people in the paid labor force to analyze the effect of education on earnings is to use a non-probability sample of persons who could be in the paid labor force. Because the education people obtain could determine their likelihood of being in the paid labor force, technically the sample in the paid labor force is a nonprobability sample for the question at issue. In such cases results are biased.
The statistical model one uses can also render the data a non-probability sample. For example, Lucas (2014b) notes that several published studies that use multilevel modeling have been based on samples that are probability samples in general, but nonprobability samples for one or more of the levels of analysis in the study. Evidence indicates that in such cases the bias is poorly behaved, such that inferences from such analyses are unjustified.
These problems occur in the academic literature, but they may be more common in non-academic research. For example, in public opinion polling by private companies (or other organizations unable to require response), the sample can be self-selected rather than random. This often introduces an important type of error, self-selection bias, in which a potential participant's willingness to volunteer for the sample may be determined by characteristics such as submissiveness or availability. The samples in such surveys should be treated as non-probability samples of the population, and the validity of the findings based on them is unknown and cannot be established.