sample representativeness

#1
Is there a statistical test to show that a sample is representative of a population? or is just fufilling some criteria, ie sample source, data collection methods, screening criteria, etc. This is for a retrospective clinical study.
 
#2
AFAIK You should go through two things: power calculation and sampling methods. Power calculation methods deal with the sample size which must be neither too small, nor too large. They are also relevant to the power of the statistical test.
Prior to the study on human subjects, one should determine how many participants are needed to provide a sufficient test power without involving too many humans which may become unethical sometimes, when a novel technique is being tested, and may become unnecessary and resource-killing.