The minimum sample size required for statistical analysis of results from survey according to the size of population was calculated. However, the no. of survey respondents was lesser to that of minimum sample size. Do we have to get to the survey again or is there any statistical correction methods that we could apply in our analysis?
There is no hard and fast rule about when a sample is "too small." Instead, that judgement always has to be be made against some desired property of the results, such as the size of a standard error or the desired power for a statistical test. If your sample is smaller than than you planned, then you will larger standard errors and less power than you desired, but you can still use that sample.
If you have a small sample, Bayesian methods are extremely useful. Even if you do the survey again, Bayesian methods will allow you to "update" your first results with new evidence in a rigorous maner. See for example:
http://jeffgill.org/publications/bayesian-methods-social-and-behavioral-sciences-approach
or:
https://books.google.com.bo/books?id=GTJUt8fcFx8C&printsec=frontcover&dq=Bayesian+methods&hl=en&sa=X&ved=0ahUKEwjD2-Kv_LznAhWPILkGHW2OBq84ChDoAQg4MAI#v=onepage&q=Bayesian%20methods&f=false
I am consultant with expertise on Bayesian methods and I can be of help if needed.
There is no hard and fast rule about when a sample is "too small." Instead, that judgement always has to be be made against some desired property of the results, such as the size of a standard error or the desired power for a statistical test. If your sample is smaller than than you planned, then you will larger standard errors and less power than you desired, but you can still use that sample.
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