The population being studied is well over one million. Unlike probability sampling, i guess there's no formula for computing the sample size in convenient sampling?
Still I wonder what would be a proper sample size in this method, with a valid and reliable reference?
Regarding references, which you requested in your question, the following URL takes you to a bibliography for a number of resources which I consulted for a project involving both design-based methods (i.e., using randomization), and model-based methods (regression/'prediction'), for an estimator which uses auxiliary data regardless. Some of these books may contain a few lines of relevance to you. I think that Cochran(1977) does, but it is basically just to say that you cannot expect to infer much of worth from a convenience sample. Thompson(2012) is rather comprehensive, but glancing at it just now, I saw no direct mention of convenience sampling.
https://www.researchgate.net/publication/317914104_Handout_Bibliography_for_Comparison_of_Model-Based_to_Design-Based_Ratio_Estimators_Poster
It is generally agreed that you cannot reliably infer to a population from a convenience sample. However, if you have regressor data, so you can model, that could work well, depending upon circumstances.
Generally speaking, I'd say you need to stratify your population, and endeavor to sample randomly from each stratum.
Regardless, stratification would be an improvement.
The following may be of interest:
Brewer, K.R.W. (2014), “Three controversies in the history of survey sampling,” Survey Methodology,
(December 2013/January 2014), Vol 39, No 2, pp. 249-262. Statistics Canada, Catalogue No. 12-001-X.
http://www.statcan.gc.ca/pub/12-001-x/2013002/article/11883-eng.htm
You can calculate non-probabiliy sampling as the conveinece comes in the scope of NPS. (NPS). Because NPS formula applies when u have more than 50,000 respondents.
In addition, there is no universal rule for convenience sampling, it depends on your study objectives and nature. However, NPS gives you a valid sample size. NPS available on google
Niloofar -
Sample size estimation, whether from use of randomization, prediction, or both, is really based on obtaining an acceptable (depending upon application) estimated relative standard error, with the implicit but very important assumption that bias is either completely estimable, or negligible, generally the latter.
The problem with convenience sampling is that the level of bias is not well known, often nearly a complete mystery, and can be very high. Thus, a random sample, depending upon population standard deviation and sample design, of just a few hundred out of a million may be adequate for your needs, but a convenience sample of a few hundred thousand may not be, and worse, you won't know that you may likely have highly inaccurate results.
You should at least try to stratify your population by characteristics that may impact relevant results.
If you have auxiliary data to form prediction (regression model application) groups, that could help.
Best wishes - Jim
Regarding references, which you requested in your question, the following URL takes you to a bibliography for a number of resources which I consulted for a project involving both design-based methods (i.e., using randomization), and model-based methods (regression/'prediction'), for an estimator which uses auxiliary data regardless. Some of these books may contain a few lines of relevance to you. I think that Cochran(1977) does, but it is basically just to say that you cannot expect to infer much of worth from a convenience sample. Thompson(2012) is rather comprehensive, but glancing at it just now, I saw no direct mention of convenience sampling.
https://www.researchgate.net/publication/317914104_Handout_Bibliography_for_Comparison_of_Model-Based_to_Design-Based_Ratio_Estimators_Poster
It is generally agreed that you cannot reliably infer to a population from a convenience sample. However, if you have regressor data, so you can model, that could work well, depending upon circumstances.
Generally speaking, I'd say you need to stratify your population, and endeavor to sample randomly from each stratum.
Regardless, stratification would be an improvement.
The following may be of interest:
Brewer, K.R.W. (2014), “Three controversies in the history of survey sampling,” Survey Methodology,
(December 2013/January 2014), Vol 39, No 2, pp. 249-262. Statistics Canada, Catalogue No. 12-001-X.
http://www.statcan.gc.ca/pub/12-001-x/2013002/article/11883-eng.htm
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