I am collecting data using a web-based survey from online social media users and one demographic criterion I am monitoring is the nationality of the respondents. However, I am faced with the problem of getting an unbalanced sample (e.g. more respondents from one geographic region than the other). Are there statistical ways of working with biased samples?
If you know what your study population is, you could weigh your observations according to what you know about their share in the study population. I think it is a more severe problem that participants of your survey are systematically different from your non-participants. It seems you lack any information on the latter, making it impossible to tell whether there is a difference and what it is. A good read on sampling is Henry, Gary. T. (2009): Practical Sampling. Bickman, Leonard and Debra J. Rog (eds.): The Sage Handbook of Applied Social Research Methods. Los Angeles: SAGE: 77-105.
As Ingo writes, the mail problem is that you only know about people who respond to your survey, and don’t know about non respondents. So you do need to find out any info about the demographics of social media users in general, and compare your sample. In the meantime, in any reporting, carefully describe your respondents, and only write “the people who responded to this survey said … Also, you can report the responses from the people in the one region separately, and combine all others.
Can you advertise your survey in multiple ways to get more respondents? What is it about? If you advertise it through your academic affiliation, you may get more respondents, since people may see it as more legitimate.