Is there a need to calculate sample size in non-probability sampling? AND What is the rationale?
https://www150.statcan.gc.ca/n1/edu/power-pouvoir/ch13/nonprob/5214898-eng.htm
1. Sample sizes larger than 30 and less than 500 are appropriate for most research.
2. Where samples are to be broken into sub-samples;(male/females, juniors/seniors, etc.), a minimum sample size of 30 for each category is necessary.
3. In multivariate research (including multiple regression analyses),the sample size should be several times (preferably 10 times or more) as large as the number of variables in the study.
4. For simple experimental research with tight experimental controls (matched pairs, etc.), successful research is possible with samples as small as 10 to 20 in size."
Reference
Sekaran, U., 2003. Research methods for business: A skill building approach. John Wiley & Sons.
No non probability samples don't lend themselves to mathematical statistics methods. David Booth see Scheaffer Mendenhall and Ott, Elementary Survey Sampling.
Thank you, Professors, for your valuable answers
David Eugene Booth Suraj Kapoor Chuck A Arize
Sample size calculations generally assume no bias. However, with nonprobability sampling, bias is often a problem. People have used covariates for techniques which employee either pseudo-weights or regression modeling. See, for example Elliott, M.R., and Valliant, R.(2017), "Inference for Nonprobability Samples," Statistical Science, 32(2):249-264,
https://www.researchgate.net/publication/316867475_Inference_for_Nonprobability_Samples, where the paper is found at
https://projecteuclid.org/journals/statistical-science/volume-32/issue-2/Inference-for-Nonprobability-Samples/10.1214/16-STS598.full (Project Euclis, Open Access).
Sometimes a single regressor in a ratio model is best when the correlation is strong. For a discussion of sample size in one such type of case, see https://www.researchgate.net/publication/261947825_Projected_Variance_for_the_Model-based_Classical_Ratio_Estimator_Estimating_Sample_Size_Requirements
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In conclusion:
The idea is to see how large a sample is needed to reduce standard error to a given level, while minimizing bias.
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Note that when bias overwhelms your problem, increasing sample size may not help at all. Typically you might increase your sample in one subpopulation and not others.
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