Mathez  -

Are you looking at continuous data?  My expertise is basically in continuous data, but much of what is below will also relate somewhat to other data. 

If you do not have regressor data on the entire population to use for modeling, then you need randomization to make more valid inference than you could with a purposive sample and no regression model.  If you have both regressor (auxiliary) data and probability design-based sampling, then you could use model-assisted design-based sampling and estimation.

At any rate, whatever you do, stratification/grouping of your data into categories so as to reduce variance is often useful.

Variance and bias, sampling and nonsampling error, are important considerations.

Within a stratum or group, if you have nonresponse, you might weight in the spirit of response propensity groups. 

Perhaps you may want to research some of the terms above on the internet.

I did a great deal of work with quasi-cutoff  (multiple attribute cutoff-like) sampling for highly skewed establishment survey data where good regressor data are available, but I suspect that you do not have regressor/auxiliary data available.  If you do, you may find something helpful on my ResearchGate profile pages, but otherwise, you might find something useful in the report at the attached link that I got from Mike Brick's ResearchGate pages.  He and others did that report, and he was the Washington Statistical Society  (ASA chapter) presenter for the WSS President's invited seminar in 2014.  I attended that seminar. It was excellent. 

 https://www.researchgate.net/publication/273561892_Summary_Report_of_the_AAPOR_Task_Force_on_Non-probability_Sampling

As for design-based and model-assisted design-based methodologies,  using probability (random) sampling, there are a number of good textbooks. I'll suggest a few below.  Most, including the first few here, are basically just design-based, where probability comes from the sampling, whereas I've seen it noted that a model can perform a similar function. In either case, "representativeness" is important. That is why stratification is a great tool not only in design-based methodologies, but also for all purposive sampling, with or without a regression model. Model-assisted design-based methods can help greatly in compensating for random sampling that happens to be 'unfortunate,' such as predominately large or small responses.  (For no reason known to me, we call regressor data "auxiliary" data when we refer to model-assisted design-based methods.) 

Cheers - Jim

Cochran, W.G(1977), Sampling Techniques, 3rd ed., John Wiley & Sons.  (pages 158-160 on model-based method)

Blair, E. and Blair, J(2015), Applied Survey Sampling, Sage Publications.

Lohr, S.L(2010), Sampling: Design and Analysis, 2nd ed., Brooks/Cole.

Särndal, CE, Swensson, B. and Wretman, J. (1992), Model Assisted Survey Sampling, Springer-Verlang.     

Brewer, KRW (2002), Combined survey sampling inference: Weighing Basu's elephants, Arnold: London and Oxford University Press.  

Article Summary Report of the AAPOR Task Force on Non-probability Sampling

Dear Mathez,

Yes, you still can do the puposive sampling for quantitative analysis. In quantitaive analysis, you have two techniques such as parametric and non-parametric techniques involved. Basically, probability sampling is suit to parametric tecnique since the this application need normality data for an analysis. Since purposive sampling is one of the non-probability sampling, i prefer non-parametric technique such as mann whitney test, wilcoxon, fisher exact test, kruskal wallis test and etc.

Mathez - -

Actually you do not need normality for sampling of any kind. Normality is really associated with the Central Limit Theorem, and with distributions of 'errors,' and with estimated residuals in regression, where it might sometimes be desirable.  I worked many years with establishment survey data, and they are by nature highly skewed.  It is a commonly held misconception that data distributions in general should be "normal."

Also, parametric vs distribution-free statistics would be a separate issue entirely.  I also worked in that area extensively.

Cheers - Jim 

I have published extensively in this with many years of success, and so has Jaap in another area,  but unfortunately some irresponsible down voter does not have a clue. So we have two experts vs a clueless down voter.  

James do not worry

Actually no one want to do it hard way and look for easy short cut. I mean these people are like Statistical clerk who want ready made algorithm for problem they face and when faced with a new situation....

So it is not surprising to have down voters.

We can not understand the objective of your survey research study. In general, if your study is to get a sampling estimation of a population, then  the probability sampling techniques should be used; and if your study is to develop a model for generalized application or find a rule for your studying objectives, then the purposive sampling (non-probability) can be used.

Consider

 An Introduction to Model-Based Survey Sampling with Applications,

Ray Chambers and Robert Clark, 

Oxford Statistical Science Series 37, 2012.  

There they still make a great deal of use of randomization. 

To me, the real key is a good regressor or regressors for the entire population, and grouping data categories such that one model applies to each group. 

Consider the sampling comparisons in examples found here:

 https://www.researchgate.net/publication/261947825_Projected_Variance_for_the_Model-based_Classical_Ratio_Estimator_Estimating_Sample_Size_Requirements  

Consider model groupings here: 

https://www.researchgate.net/publication/262066356_Quasi-Cutoff_Sampling_and_Simple_Small_Area_Estimation_with_Nonresponse

Consider these reflections on this specialized area for Official Statistics:

 https://www.researchgate.net/publication/261472614_Efficacy_of_Quasi-Cutoff_Sampling_and_Model-Based_Estimation_For_Establishment_Surveys_and_Related_Considerations

In particular, note this reference found there:

 Karmel, T.S., and Jain, M. (1987), "Comparison of Purposive and Random Sampling Schemes

for Estimating Capital Expenditure," Journal of the American Statistical Association, Vol.82, pages 52-57.

Conference Paper Projected Variance for the Model-based Classical Ratio Estim...

Article Quasi-Cutoff Sampling and Simple Small Area Estimation with ...

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

You need regressor data on the population for the following, which was for continuous data for cross-sectional surveys (here, finite populations), in each application:

 https://www.researchgate.net/publication/319914742_Quasi-Cutoff_Sampling_and_the_Classical_Ratio_Estimator_-_Application_to_Establishment_Surveys_for_Official_Statistics_at_the_US_Energy_Information_Administration_-_Historical_Development

Better use probability sampling technique.

Actually I am having the same question and am therefore very much interested in the answers that you get.

Great insights I have found here.I was in the same dilema

This is informative

You may use purposive sampling for your quantitative research if your objective is to generalize the data to develop a model or module for example if you're doing need analysis before starting your research. There are some types of purposive sampling. one of them is expert sampling where we choose the experts in our field to know the needs of your model or module development. So that we can use the purposive sampling method to choose the experts to answer your questionnaire.

Hi

Could I get some references that confirm of using Purposive Sampling for Quantitative research and inferential statistics??

I was in similar dilemma.

I have the same question, these are helpful responses. Thanks.

I really needed answer to the same question. Your responses are helpful. Thank you.