If you post a survey on Google docs and wrap it up when you get 100, it would be convenient sampling. But of course you can make it quota sampling if you make sure that you get quota on specific criteria - age group, gender, user-nonuser of x and so on. A more difficult question is whether it can be made probabilistic - say SRS or stratified? This is difficult because those who respond are perhaps different in some relevant characteristics from those who did not.

So, a test that can establish that those who responded are not significantly different on relevant characteristics can help answer whether the sample can be treated as probabilistic. A validation sample on an adequate scale that is collected offline with the same instrument can be compared for differences in statistics if any.

I suppose, one may also use tests of randomness and tests of normal distribution etc. as easier substitute or complementary procedures.

Raj

@Raj: Thanks, your comment really helps. I am supervising several undergrads; some of whom used online survey exclusively. I'll tell them to gather more samples offline as comparison to test for differences.

Imam -  

Random sampling has to take place at the design stage to be able to use the corresponding randomization-based estimation and any inferences that depend upon randomization. Purposive sampling is a very broad category which includes the convenience sampling noted above. As indicated by Raj, purposive sampling is subject to sometimes a great deal of bias. However, there is another possibility. If you have regressor data available on the entire population, then you can take advantage if regression modeling to use what is called "prediction."  This is not forecasting, it is taking the relationship between the data you have ( y data) and one or more sets of regressor data (x), and using that relationship to fill in for the missing y data.  One needs to be careful to stratify the data by any distinctive category to help reduce any bias (increasing 'representativeness').  Using such regressor data makes model-based inference possible.  

In survey statistics, we can used design-based methods (randization), model-based methods, or model-assisted design based methods. Only the strictlyod-based methods can do without randomization, and only if you are careful to stratify. 

For regressor data on the entire population, you can use a variety of innovations. As long as there is an  x datum to pair with each y datum, and x data for the remainder of the population. The model-based classical ratio estimator (CRE) can not only estimate totals or means, but also variances, when we do not even have an individual x datum for each missing y datum. You just need a lump sum of x corresponding to the missing y's.   That is, if you did a sample survey of some entities for y data, and knew the corresponding x data for those entities, and a sum of all x data from a census survey or some other source, you could use prediction.   

Attached are links to some documents that might help. The titles may be with regard to applications that do not sound like your topic, but the idea is that if you can use prediction, they may show you methodology that you can use in the future. (I realize that your question was written some time ago.)    

Hope that helps.  -  Jim     

Article Efficacy of Quasi-Cutoff Sampling and Model-Based Estimation...

Article The Classical Ratio Estimator (Model-Based)

Technical Report A Note on Estimating Impact of Data Collection Mode Change f...

Data CRE Prediction 'Bounds' and Graphs Example for Section 4 of ...

Hmmm. I went through the above before I submitted it, and fixed some typos.  I see that for some reason, the editing was ignored. Could be software at my end. Whatever. I saved what I had. Perhaps it will work now: 

Imam -

Random sampling has to take place at the design stage to be able to use the corresponding randomization-based estimation and any inferences that depend upon randomization. Purposive sampling is a very broad category which includes the convenience sampling noted above. As indicated by Raj, purposive sampling is subject to sometimes a great deal of bias. However, there is another possibility. If you have regressor data available on the entire population, then you can take advantage of regression modeling to use what is called "prediction." This is not forecasting, it is taking the relationship between the data you have ( y data) and one or more sets of regressor data (x), and using that relationship to fill in for the missing y data. One needs to be careful to stratify the data by any distinctive category to help reduce any bias (and increasing 'representativeness'). Using such regressor data makes model-based inference possible.

In survey statistics, we can use design-based methods (randomization), model-based methods, or model-assisted design based methods for inference. Only the strictly model-based methods can do without randomization, and only if you are careful to stratify.

For regressor data on the entire population, you can use a variety of innovations, as long as there is an x datum to pair with each y datum, and x data for the remainder of the population. The model-based classical ratio estimator (CRE) can not only estimate totals or means, but also variances, when we do not even have an individual x datum for each missing y datum. You just need a lump sum of x corresponding to the missing y's. That is, if you did a sample survey of some entities for y data, and knew the corresponding x data for those entities, and a sum of all x data from a census survey or some other source, you could use prediction.

Attached are links to some documents that might help. The titles may be with regard to applications that do not sound like your topic, but the idea is that if you can use prediction, they may show you methodology that you can use in the future. (I realize that your question was written some time ago.)

Hope this helps. - Jim.   

If you don't know how many people are reviewing it and if you do not use criteria to eliminate people who should not be answering the questions, then you are convenience sampling in my opinion. If you meet sample size requirements by bulk, without any predetermined estimate on your target sample size, or criteria that asks for people with a Management Title in the field of nursing or whatever, the research design is NOT a priori. 

I had assumed that someone doing a convenience sample would still not use a respondent who is out-of-scope.  But now that Beth mentions it, that does sound like a concern, and I only assumed a definition for convenience sampling.  Being out-of-scope would be a serious problem. My concern, however, was that without an a priori random sampling design, for design-based sampling, or regressor data and good stratification where needed, for model-based methodology, you cannot obtain much useful information.     

The problem is that some authors does not explicitly describe their sampling method. Simply saying that it's purposive or quota might satisfy some reviewers, but it would not provide necessary description for repeat testing in other context...

That would be a serious problem.  Perhaps what Raj said might help:  "A validation sample on an adequate scale that is collected offline with the same instrument can be compared for differences in statistics ...."