You'll have to continue recruiting. If you have a liaison try to better understand why you can't find candidates? Did you ask questions or for information that they're uncomfortable with? Can you conduct the study without the third firm? If so, conduct your study and use the third firm as a limitation to your study, explain why, and form your recommendation for additional study around that limitation. I had the same issue and my problem was the word "Disabled" in my title. It was very offensive and I knew it was and begged my chair not to have me use the word. Out of over 300 people only 17 applied and that was not until after I explained why I used the word. In the end, I only had the minimum amount of people needed for the study. I couldn't lose one participant.

Try to prolong your study period from what you planned so that you can reach at minimum level. But please note that this can be done as such if your design is quantitative study as qualitative studies cannot necessarily need sample size determination rather we focus on data or response saturation.

Thank you Laverne A. Davis

Thank you Getasew Amogne Aynalem

I do appreciate your time and effort

Getasew Amogne Aynalem You don't saturate in qualitative and we do have a sample size minimum and maximum in qual due to data collection and analysis.

Dear Meteb Alotaibi , This is a problem that many researchers face. I think your sampling method is convenient now. In other words, the people who were available answered the questionnaire. It is best to try to find more participants. Otherwise, you can express this shortcoming as a limitation.

Thank you Omid Mahdieh I do appreciate your time.

Meteb -

Are you trying to estimate totals from establishment survey data? It is a little hard for me to tell. If you have auxiliary data, even administrative data such as number of employees, on the population which could serve as regressor data, then perhaps you could use a model-based approach. (See "The model based (prediction) approach to finite population sampling theory," Institute of Mathematical Statistics Lecture Notes - Monograph Series, Volume 17, 1992, 225-240, Richard M. Royall,

https://www.researchgate.net/publication/254206607_The_model_based_prediction_approach_to_finite_population_sampling_theory/.

The paper is available under Project Euclid, open access: https://projecteuclid.org/euclid.lnms/1215458849.)

I used the model-based approach here: an invited presentation to a statistical agency: 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

If you want to make inferences about a population from a sample, you can use a probability of selection (randomized) approach, a model-based approach, or a combination of these. If you use a convenience sample without modeling, then you are limited to talking about the data you collected. If you try to apply this to a wider population, then you don't know how this relates. You might speculate based on other information, but this may be highly problematic. You need covariates. Some have used a combination of model and psuedo-random sampling approaches (see Richard Valliant, for example).

This may be of interest:

Brewer(2014), "Three controversies in the history of survey sampling," Survey Methodology, Dec 2013 - article Ken Brewer wrote as a consequence of receiving the Waksberg Award: https://www150.statcan.gc.ca/n1/pub/12-001-x/2013002/article/11883-eng.htm

Cheers - Jim

Thank you James R Knaub for your comment and the materials you shared.

I do appreciate it

Thank you. ... One other thing, Meteb, in case it may be of any interest to you: I see that in Cochran(1977), on pages 135 and 136, he has some encouraging words to say about quota sampling, making it sometimes close to randomized sampling. His write-up in Cochran(1953), on page 105 is substantially different. Much of Cochran(1953) is often nearly repeated in Cochran(1977), but not in this case. (I do not have access to his second edition.)

................

Cochran, W.G.(1953), Sampling Techniques, 1st ed, John Wiley & Sons

Cochran, W.G.(1977), Sampling Techniques, 3rd ed, John Wiley & Sons