Overviews, basics of sampling:
Ann Eshenaur Spolarich. Sampling Methods: A guide for researchers. American Dental Hygienists' Association August 2023, 97 (4) 73-77; https://jdh.adha.org/content/97/4/73 quick overview of the basics.
Anol Bhattacherjee Social Science Research: Principles, Methods, and Practices http://scholarcommons.usf.edu/oa_textbooks/3/ from 2012. See chapter 8 on sampling, starting on page 65.
Trochim's sampling section http://www.socialresearchmethods.net/kb/sampling.php of the knowledge base. Last revised in 2006.
Sampling methods http://www.statcan.gc.ca/edu/power-pouvoir/ch13/5214895-eng.htm discusses many types of sampling. Last modified in 2013, and listed as archived.
Statistical Methods for Sample Surveys http://ocw.jhsph.edu/index.cfm/go/viewCourse/course/StatMethodsForSampleSurveys/coursePage/index/ by Saifuddin Ahmed, 2009.
Pew Research Center has this http://www.pewresearch.org/methodology/u-s-survey-research/sampling/ overview of many issues about sampling, for the public to understand.
Specific types of sampling
Sampling https://www150.statcan.gc.ca/n1/edu/power-pouvoir/ch13/5214895-eng.htm Overview chapter. 2021.
Respondent Driven Sampling. Matthew Salganik. http://www.princeton.edu/~mjs3/rds.shtml This method uses snowball sampling, not to estimate population characteristics, but to estimate characteristics of a network of people in a hidden population (e.g., drug users, etc)
Respondent Driven Sampling http://www.respondentdrivensampling.org/ Douglas Heckathorn, Cornell U. Respondent Driven Sampling is a chain-referral method, or 'snowball' sampling that yields random samples of target populations and provides the means to calculate unbiased estimates of population parameters.
Yu, Chong Ho (2003). Resampling methods: concepts, applications, and justification. http://pareonline.net/getvn.asp?v=8&n=19 describes resampling methods
Fricker, R.D., Jr., has these two here http://faculty.nps.edu/rdfricke/frickerpa.htm
Sampling Methods for Online Surveys, Handbook of Online Research Methods, 2nd edition, N. Fielding, R.M. Lee and G. Blank, eds., chapter 14, London: SAGE Publications. To appear. (some time after 2013, website doesn't say when.
Sampling Methods for Web and E-mail Surveys, 2012 SAGE Internet Research Methods, J. Hughes, ed., London: SAGE Publications. Reprinted from The SAGE Handbook of Online Research Methods,
The UN has several papers
Expert Group Meeting to Review the Draft Handbook on Designing of Household Sample Surveys http://unstats.un.org/unsd/demographic/meetings/egm/default.htm The 2003 meeting has several documents about sampling.
Designing Household Survey Samples: Practical Guidelines (2008) http://unstats.un.org/unsd/demographic/standmeth/handbooks/default.htm#survey Click on "Survey" also on the same page, Household Sample Surveys in Developing and Transition Countries (2005)
WHO Step Part 2, Section 2, Preparing the Sample http://www.who.int/chp/steps/manual/en/index2.html
Probability and non-probability sampling
Online Nonprobability Samples. Jeremy Freese and Olivia Jin. 2025. Annual Review of Sociology. Vol. 51:109-128 (Volume publication date July 2025) https://doi.org/10.1146/annurev-soc-090524-043117 https://www.annualreviews.org/content/journals/10.1146/annurev-soc-090524-043117
This reviews some of the methods of dealing with non-probability sampling, and reviews research about how effective these are.
Evaluation of available techniques and their combinations to address selection bias in nonprobability surveys. Rueda-Sánchez, J.L., Ferri-García, R., Rueda, M.d.M. et al. AStA Adv Stat Anal (2025). https://doi.org/10.1007/s10182-025-00530-9
In this paper, we briefly explain most of these methods (to address selection bias) and conduct an extended study to compare their performances. Adjustments based on superpopulation modeling that use the whole population census for a set of covariates provide overall, the best or almost the best results ... but they require observing all individuals in the population for a set of common covariates with nonprobability sample. This makes it difficult to apply them with a sufficient number of variables in real situations.
Making online polls more accurate: statistical methods explained. Arletti Alberto , Tanturri Maria Letizia , Paccagnella Omar. Frontiers in Political Science, Vol 7, 2025. DOI=10.3389/fpos.2025.1592589 https://www.frontiersin.org/journals/political-science/articles/10.3389/fpos.2025.1592589/full
This paper provides an introduction to key statistical methods for mitigating bias and improving inference when non-probability sampling that likely has sampling bias. Methods include weighting (e.g., raking, propensity score adjustment), modeling (e.g., post-stratification), statistical matching, and a few others. ... All the models presented in the previous sections assume that the selection mechanism is entirely explained by the X covariates alone. If the selection mechanism is not entirely explained by X, then the estimated model might not provide accurate estimates of the population of interest. Importantly, there is abundant evidence that non-probability samples might suffer from non-ignorable selection
Integrating probability and non-probability samples through deep learning-based mass imputation. Chen, S., Xu, C. and Cutler, J. (2025). Survey Methodology, 51(2), 493-508. Paper available at http://www.statcan.gc.ca/pub/12-001-x/2025002/article/00007-eng.pdf. I got the paper here https://www150.statcan.gc.ca/n1/pub/12-001-x/2025002/article/00007-eng.htm
Use of nonprobability samples for official statistics, state of the art. by Danny Pfeffermann and Michael Sverchkov. Release date: June 30, 2025 https://www150.statcan.gc.ca/n1/pub/12-001-x/2025001/article/00008-eng.htm In StatCan Survey Methodology.
Probability-Based vs. Non-Probability Online Panel Surveys: Assessing Accuracy, Response Quality, and Survey Professionalism. Sylvia Kritzinger, Katharina Pfaff, Max Gschwandtner & Julia Partheymüller. 2025.
This is a preprint working paper https://osf.io/preprints/socarxiv/86tsv_v2
This paper says in their specific study, their non-probability sample was as accurate as a probability sample.
Raking Method as a Tool for Improving Representativeness in Non-Probability Studies. Víctor Juan Vera-Ponce, et al. (2025). International Journal of Statistics in Medical Research, 14, 223-236. https://doi.org/10.6000/1929-6029.2025.14.22
Raking, also known as iterative proportional fitting. The procedure iteratively adjusts sample weights so that the marginal distributions of selected variables match the known distributions of the target population.
Bunch of articles in 2025 issues of Journal of Official Statistics
Calibration Weighting for Analyzing Non-Probability Samples. Jae Kwang Kim. 2025. Journal of Official Statistics, Volume 41, Issue 3. https://doi.org/10.1177/0282423X251318104 https://journals.sagepub.com/doi/full/10.1177/0282423X251318104 Another way to weight samples.
Averaging Non-Probability Online Surveys to Avoid Maximal Estimation Error. Murray-Watters, A., Zins, S., Sakshaug, J. W., & Cornesse, C. (2025). Journal of Official Statistics, 41(2), 700-724. https://doi.org/10.1177/0282423X241312775 (Original work published 2025) https://journals.sagepub.com/doi/full/10.1177/0282423X241312775
One proposed method is for researchers to divide their sample among different ventors and then average. But still more research is needed on which vendors make similar / different errors. And currently, still need a standard randomized sample for comparison.
Combining Probability and Nonprobability Samples on an Aggregated Level. Aliste, S. F. V., Scholtus, S., & Waal, T. de. (2025). Journal of Official Statistics, 41(2), 619-648. https://doi.org/10.1177/0282423X241293751 https://journals.sagepub.com/doi/full/10.1177/0282423X241293751
In this paper, a method is proposed that combines estimators from a probability and nonprobability sample on an aggregated level.
Performance Measures for Sample Selection Bias Correction by Weighting. Liu, A.-C., Scholtus, S., Van Deun, K., & de Waal, T. (2025). Journal of Official Statistics, 41(2), 675-699. https://doi.org/10.1177/0282423X251318463 https://journals.sagepub.com/doi/full/10.1177/0282423X251318463
Evaluating the Impact of a Non-Probability Sample-Based Estimator in a Linear Combination with an Estimator from a Probability Sample. Čiginas, A., Krapavickaitė, D., & Nekrašaitė-Liegė, V. (2025). Journal of Official Statistics, 41(2), 649-674. https://doi.org/10.1177/0282423X251331346 https://journals.sagepub.com/doi/10.1177/0282423X251331346
On the Use of Auxiliary Variables in Multilevel Regression and Poststratification. Si Y. Stat Sci. 2025 May;40(2):272-288. doi: 10.1214/24-sts932. Epub 2025 Jun 2. PMID: 40476050; PMCID: PMC12140408. https://pmc.ncbi.nlm.nih.gov/articles/PMC12140408/
Using multilevel regression and poststratification on nonprobability samples.
More on non probability sampling, before 2025
Special issue for papers presented at the 29th Morris Hansen Lecture on the use of nonprobability samples. Survey Methodology Volume 50, Number 1 (June 2024).
https://www150.statcan.gc.ca/n1/pub/12-001-x/12-001-x2024001-eng.htm
Handling non-probability samples through inverse probability weighting with an application to Statistics Canada’s crowdsourcing data. Jean-François Beaumont, Keven Bosa, Andrew Brennan, Joanne Charlebois and Kenneth Chu (2024) https://www150.statcan.gc.ca/n1/pub/12-001-x/2024001/article/00004-eng.htm
This article focuses on inverse probability weighting methods, which involve modelling the probability of participation in the non-probability sample.
Validating an Index of Selection Bias for Proportions in Non-Probability Samples. Hammon, A., and Zinn, S. (2025) International Statistical Review, 93: 499–516. https://doi.org/10.1111/insr.12590. https://onlinelibrary.wiley.com/doi/full/10.1111/insr.12590
This index can capture the impact of different sample selection mechanisms on target statistics.
The return of non-probability sample: the electoral polls at the time of internet and social media. Di Franco, G. Qual Quant 58, 3811–3830 (2024). https://doi.org/10.1007/s11135-024-01835-8 I downloaded this article here https://link.springer.com/article/10.1007/s11135-024-01835-8
This paper looks at some possible methods and approaches for adjusting non-probability samples.
This paper concludes "Arguably the most pressing need is for research aimed at developing better measures of the quality of non-probability sampling estimates"
More Accurate Estimation for Nonrandom Sampling Surveys: A Post Hoc Correction Method. Takunori Terasawa, Kwansei Gakuin University. Posted: 29 May 2024. https://papers.ssrn.com/sol3/papers.cfm?abstract_id=4847598 This is the non peer reviewed version. The peer reviewed version is here, but not free to read: https://www.sciencedirect.com/science/article/abs/pii/S2772766124000582
This study introduces a post hoc statistical correction method that uses an existing probability sample survey as reference data. Uses propensity scoring to indicate how likely each survey respondent represents the population, and they get weights based on the scoring.
Population Sampling: Probability and Non-Probability Techniques. Prehospital and Disaster Medicine. Stratton SJ. 2023;38(2):147-148. doi:10.1017/S1049023X23000304 https://www.cambridge.org/core/journals/prehospital-and-disaster-medicine/article/population-sampling-probability-and-nonprobability-techniques/1B2C94894C95BF6C7C49B62A490B4520 A summary of the types and issues with non probability sampling. Basically, non-probability sampling has biases and cannot be generalized to the larger population.
Sample Size Determination for Survey Research and Non-Probability Sampling Techniques: A Review and Set of Recommendations. RAHMAN, Md. Mizanur. Journal of Entrepreneurship, Business and Economics, [S.l.], v. 11, n. 1, p. 42-62, feb. 2023. ISSN 2345-4695. https://www.scientificia.com/index.php/JEBE/article/view/201 click on the page numbers to see the article.
This is an interesting article. The explanations of non probability sampling are pretty good. However, it is unfortunate that sample size determination is in the same article, because, actually, if the sample is non probability, then the sample size really doesn't matter. Even if your sample is the right size, the sample is non-probability and so the results are still likely biased and can't be generalized.
Using Non-Probability Sampling Methods in Agricultural and Extension Education Research. Alexa J. Lamm, Kevan W. Lamm. 2019. Journal of International Agricultural and Extension Education Volume 26. Issue 1. https://newprairiepress.org/jiaee/vol26/iss1/5/
A very nice explanation of post survey weighting.
American Association for Public Opinion Research has a bunch of reports http://www.aapor.org/Education-Resources/Reports.aspx including one non-Probability Sampling, June 2013. Reviews of different kinds of non probability sampling and when it may be okay to use them.
Sampling, Nonrandom http://www.blackwellreference.com/public/tocnode?id=g9781405131995_chunk_g978140513199524_ss1-1 Andrew Hayes, in International Encyclopedia of Communication. not free, but should be interesting if you can get it.
Non-probability sampling https://www150.statcan.gc.ca/n1/edu/power-pouvoir/ch13/nonprob/5214898-eng.htm overview of types and uses, and says non-probability sampling can be used for questionnaire testing and some preliminary studies during the development stage of a survey.
A couple of R packages for non-probability sampling
nonprobsvy -- An R package for modern methods for non-probability surveys. Łukasz Chrostowski, Piotr Chlebicki, Maciej Beręsewicz. 2025. Working paper. arXiv:2504.04255 https://arxiv.org/abs/2504.04255
The R package NonProbEst for estimation in non-probability surveys. Rueda, María del Mar and Ferri-García, Ramón and Castro, Luis. The R Journal. 12(1), 406-418. https://doi.org/10.32614/RJ-2020-015 https://journal.r-project.org/articles/RJ-2020-015/
I list this out of order because it says the main methods of adjusting for non-probability sampling: "There are three important approaches: the pseudo-design based inference (or pseudo-randomisation (Buelens et al. 2018)), statistical matching and predictive inference." And then explains them very briefly. I just thought it would be nice to see this.
Sample Size
Ahmed, Saifuddin. 2009. Statistical Methods for Sample Surveys http://ocw.jhsph.edu/index.cfm/go/viewCourse/course/StatMethodsForSampleSurveys/coursePage/index/ by See lecture materials, lecture 3 on sample size.
Smith, Richard L. 2010. Basic concepts in statistics. http://www.unc.edu/~rls/s151-2010/s151.html see class 23, standard approach to sample size.
Wikihow has an explanation http://www.wikihow.com/Calculate-Sample-Size
Lots of sample size calculators on line. Here are a few examples
National Statistics Service, Australian Bureau of Statistics http://www.nss.gov.au/nss/home.NSF/pages/Sample+size+calculator includes explanation of what each part is. This assumes a simple random sample.
WHO Step http://www.who.int/chp/steps/resources/sampling/en/ sample size calculator. There is also an explanation of sample size, in Part 2, Section 2, Preparing the Sample http://www.who.int/chp/steps/manual/en/index2.html
Specific studies
A two-step approach to simultaneously correct for selection and misclassification bias in nonprobability samples from hard-to-reach populations. Christoffer Dharma, Peter Smith, Travis Salway, Dionne Gesink, Michael Escobar, Victoria Landsman. 2025. American Journal of Epidemiology, Volume 194, Issue 11, November 2025, Pages 3267–3272, https://doi.org/10.1093/aje/kwaf132
The Importance of Non-Probability Samples in Minority Health Research: Lessons Learned from Studies of Transgender and Gender Diverse Mental Health. Transgend Health. Turban JL, Almazan AN, Reisner SL, Keuroghlian AS. 2023 Jul 28;8(4):302-306. doi: 10.1089/trgh.2021.0132. PMID: 37525831; PMCID: PMC10387152. https://pmc.ncbi.nlm.nih.gov/articles/PMC10387152/
"we review the strengths and limitations of probability and non-probability samples ... We conclude that both types of studies provide important and actionable data about mental health inequities."
A new technique for handling non-probability samples based on model-assisted kernel weighting. Beatriz Cobo, Jorge Luis Rueda-Sánchez, Ramón Ferri-García, María del Mar Rueda. 2025. Mathematics and Computers in Simulation, Volume 227, Pages 272-281, ISSN 0378-4754, https://doi.org/10.1016/j.matcom.2024.08.009. https://www.sciencedirect.com/science/article/pii/S0378475424003094
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