Overviews, basics of sampling:
Sampling Methods. Site last modified December 2025. At National University Academic Success Center. https://resources.nu.edu/researchtools/samplingmethods General overview of typical probability sampling methods: simple random sampling, stratified sampling, cluster sampling and systematic 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.
Sampling methods, types & techniques. Qualtrics. January 2023. https://www.qualtrics.com/articles/strategy-research/sampling-methods/
Chapter 3: Sampling Methods. https://openbooks.library.unt.edu/cjresearchmethods/chapter/chapter-3-sampling-methods/ In Applied Research Methods in Criminal Justice and Criminology. Eric Fritsch, Chad Trulson, Ashley Blackburn. 2022. https://openbooks.library.unt.edu/cjresearchmethods/front-matter/applied-research-methods-in-criminal-justice-and-criminology/
Sampling https://www150.statcan.gc.ca/n1/edu/power-pouvoir/ch13/5214895-eng.htm Overview chapter. 2021.
Conducting Surveys. https://open.maricopa.edu/brownresearchmethods/chapter/conducting-surveys/ This is chapter 37, in Research Methods in Psychology, 4th edition, by Jessica Parsons; Rajiv S. Jhangiani; I-Chant A. Chiang; Carrie Cuttler; and Dana C. Leighton, 2019. https://open.maricopa.edu/brownresearchmethods/
This chapter has a description of the different methods used in probability sampling.
PEW has a short video explaining random sampling combined with weighting. Methods 101: Random Sampling https://www.pewresearch.org/methods/2017/05/12/methods-101-video-random-sampling/ May 2017
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.
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.
Specific types of sampling
Commentary: Respondent-driven Sampling in the Real World. Salganik, Matthew J.. Epidemiology 23(1):p 148-150, January 2012. | DOI: 10.1097/EDE.0b013e31823b6979 https://journals.lww.com/epidem/fulltext/2012/01000/commentary__respondent_driven_sampling_in_the_real.22.aspx
Respondent Driven Sampling. Matthew Salganik. http://www.princeton.edu/~mjs3/rds.shtml List of papers. 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).
Yu, Chong Ho (2003). Resampling methods: concepts, applications, and justification. Practical Assessment, Research & Evaluation, 8(19) http://pareonline.net/getvn.asp?v=8&n=19 describes resampling methods
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 site takes a while to load)
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://www.neolifescience.com/index.php/ijsmr/article/view/10192
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.
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.
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
More on non probability sampling, before 2025
The Efficacy of Propensity Score Matching for Separating Selection and Measurement Effects Across Different Survey Modes. Eliud Kibuchi, Patrick Sturgis, Gabriele B Durrant, Olga Maslovskaya. 2024. Journal of Survey Statistics and Methodology, Volume 12, Issue 3, June 2024, Pages 764–789, https://doi.org/10.1093/jssam/smae017 https://academic.oup.com/jssam/article/12/3/764/7648668
Unfortunately, their conclusion is: Our results show large differences in estimates for the same variables between parallel face-to-face and online surveys, even after matching on standard demographic variables. Moreover, discrepancies in estimates are still present after matching between surveys conducted in the same (online) mode, where differences in measurement properties can be ruled out a priori. Our findings suggest that PSM has substantial limitations as a method for separating measurement and selection differences across modes and should be used only with caution.
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.
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.
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.
Using Auxiliary Information in Probability Survey Data to Improve Pseudo-Weighting in Nonprobability Samples: A Copula Model Approach. Tingyu Zhu, Laura J Gamble, Matthew Klapman, Lan Xue, Virginia M Lesser. 2024. Journal of Survey Statistics and Methodology, Volume 12, Issue 5, November 2024, Pages 1338–1364, https://doi.org/10.1093/jssam/smad032 https://academic.oup.com/jssam/article/12/5/1338/7271452
Survey Weighting Explained: How To Ensure A Poll Is Truly Representative. Stephen Tracy. 2024. https://analythical.com/blog/weighting-data-explained
This isn't specifically about non-systematic sampling, but this article describes different methods of weighting, most of which, I think, are used with non-systematic sampling. In particular, see Demographic Weighting, Post-Stratification Weighting, Raking, Propensity Score Weighting, and Regression Weighting.
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.
Data Quality Metrics for Online Samples: Considerations for Study Design and Analysis. November, 2022 https://aapor.org/publications-resources/reports/ or directly here https://aapor.org/wp-content/uploads/2023/02/Task-Force-Report-FINAL.pdf From the American Association for Public Opinion Research.
Describes issues with non-probability sampling and methods for addressing non-probability sampling.
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. Last modified in 2021
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.
PEW Research Center has this short video: Methods 101: What are nonprobability surveys? https://www.pewresearch.org/methods/2018/08/06/video-explainer-what-are-nonprobability-surveys/ August, 2018. Mostly about online surveys.
PEW also has this: For Weighting Online Opt-In Samples, What Matters Most? The right variables make a big difference for accuracy. Complex statistical methods, not so much. 2018. https://www.pewresearch.org/methods/2018/01/26/for-weighting-online-opt-in-samples-what-matters-most/ But a very interesting page in this report is the following:
How different weighting methods work https://www.pewresearch.org/methods/2018/01/26/how-different-weighting-methods-work/
A couple of R packages for non-probability sampling
Unit 3: Statistical Analysis, Lesson 10 Power and Sample Size Considerations https://online.stat.psu.edu/stat507/Lesson10 Last updated January 2026
Part of this course. STAT 507 | Epidemiological Research Methods https://online.stat.psu.edu/stat507/
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
Wikihow has an explanation https://www.wikihow.com/Calculate-Sample-Size last modified in January 9, 2026
Conducting Power Analyses to Determine Sample Sizes in Quantitative Research: A Primer for Technology Education Researchers Using Common Statistical Tests
Research. Jeffery Buckley. Journal of Technology Education Vol. 35 No. 2, Spring 2024. https://jte-journal.org/articles/10.21061/jte.v35i2.a.5
Qualtrics has a couple of pages for very basic explanation and calculations
https://www.qualtrics.com/articles/strategy-research/calculating-sample-size/ Sample size calculator and intro to basics of sample size, March 2023
https://www.qualtrics.com/articles/strategy-research/determine-sample-size/ How to determine sample size. A few basic ideas. Feb 2024
Statistical primer: sample size and power calculations-why, when and how? Hickey GL, Grant SW, Dunning J, Siepe M. Eur J Cardiothorac Surg. 2018 Jul 1;54(1):4-9. doi: 10.1093/ejcts/ezy169. PMID: 29757369; PMCID: PMC6005113. https://pmc.ncbi.nlm.nih.gov/articles/PMC6005113/
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 and https://academic.oup.com/aje/article/194/11/3267/8170089
Social media sampling is an effective way to access hard to survey populations and low prevalence groups. Klinke, D., Jacobsen, J., Dierse, M., Faas, T., Gerstorf, D., Helal, H., … Specht, J. (2025). International Journal of Social Research Methodology, 1–20. https://doi.org/10.1080/13645579.2025.2564866 long link is this https://www.tandfonline.com/doi/full/10.1080/13645579.2025.2564866
They compare general probability social surveys to non-probability surveys using social media, for hard to reach populations. General social surveys usually don't get enough hard to reach populations. I'm still reading this one....
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
page last updated 1/28/2026
Last verified 1/15/2026