What Is Convenience Sampling? | Definition & Examples (scribbr.com)

From this link you can check how to reduce bias.

Jorge R Hernández gave this answer here on RG

May 22, 2018

"You can use descriptive statistics such as: mean, median, standard desviation, percentile, Spearman correlation and non parametric tests like Mann-Whitney test. For more information see http://blog.minitab.com/blog/adventures-in-statistics-2/choosing-between-a-nonparametric-test-and-a-parametric-test"

The purpose of random sampling is to have a sample that mirrors the population to level of probability. If you have a large convenience sample and it is demonstrably similar to the population, there is probably no reason to do inferential statistics. You could just use descriptive statistics. If that is not the case, the strict statistical answer is "no" since all inferential statistics is based on random sampling. However, inferential statistics are used in these cases more than not used. This does not make it right.

My recommendation is to use descriptive statistics and describe the sample fully for which they apply!

Making inferences from nonprobability samples using standard statistical inference has no validity because the standard methods are derived from specific probability based assumptions. Thus the inferences are only useful in case the the underlying population has some of the same characteristics as the model from which the Statistical method was derived. Nonprobability samples usually give us no way to assess this. Best wishes, David Booth

In Survey Research, there is no such thing as a random sample. As James E. McLean pointed out, we expect a sample that is representative of the population of interest. But we can never be sure that the people who agree to answer your questions are similar to the people who refuse, or never get around to responding. We can never be sure that the people that you are able to ask are similar to those that you were unable to ask, etc. That's why it is so important to report in detail your survey protocol - the population of interest, the steps taken to define your sampling frame, recruitment method, response rate, etc. That way your reader can judge whether your sample is likely to be biased with respect to the topic under investigation.

Gebeyehu Jalu Negassa -

Your comment that "Making statistical conclusions from non-probability samples may be legitimate, but the validity of the inferences depends on the suitability of the model's underlying assumptions and how those assumptions affect the particular estimates" sounds like a direct quote I read somewhere, perhaps from Richard Valliant or J. Michael Brick, both of whom are accomplished statisticians on ResearchGate. In fact, Rick is giving the 30th Annual Morris Hansen Lecture this November. His paper will be "The Evolutuon of the Use of Models in Survey Sampling." I'm not sure which journal it will go to now, but many have gone to the Journal of Official Statistics. Morris Hansen dispised the use of models, but then William Cochran apparently did not, and we have learned more since then. Now Rick Valliant and coauthors and others have used both multiple covariates as well as pseudo-random sampling as methods for dealing with inference from nonprobability samples. Ken Brewer in his 2013 Waksberg Award paper that went into the journal Survey Methodology (the two journals mentioned here are the biggest in survey statistics) however noted that early use of covariates to find a "representative sample" included a colossal failure. So yes, this kind of thing is risky.

I have used very simple modeling with much more well known repeated sampling in official statistics, and find the use of convenience sampling a risk I would not know enough about. It would seem to me that in most situations, people using a convenience sample would not know enough about the population to have sufficient information to make these techniques work. But if you do have a lot of good auxiliary information, or i think better, a simple model with high correlation, you could consider it. For the newest on multiple covariate techniques you could visit the papers on ResearchGate by Richard Valliant (emeritus with Michigan) and/or possibly J. Michael Brick (Westat).

You said "...but I am not quite sure whether I am using inferential statistics or not." If you are using a sample to 'infer' something about a population, a mean or total perhaps, then you are using inference.

Best wishes - Jim Knaub

Here is a discussion I raised which is related:

https://www.researchgate.net/post/Comparison_of_Nonresponse_in_Probability_Sampling_with_Nonprobability_Sampling

Also, here is a paper on a use of nonprobability sampling for inference through regression/ratio modeling which is employed by the US Energy Information Administration (EIA): 

https://www.researchgate.net/publication/362370770_Application_of_Efficient_Sampling_with_Prediction_for_Skewed_Data