Subsample of a random sample: random sample? Let's say you have a large random sample of soccer players in Europe but you are only interested in what happens in Spain. Could you reduce your sample to players in Spain and still call it a random sample (but of a different population)?
If not, how would you call that subsample and which specific precautions should you take to be able to make inferences on the population of spanish soccer players?
My feeling is that using that subsample would be fine as long as it is large enough, but maybe I am missing something.
 A: Generally speaking, what you really want from a sample, is to be "representative". Random sampling is a good way to go since it allows all subjects the same probability of being sampled; In the hope that all attributes and attribute-relations existing in the population will exist in the sample. Making it "representative". 
In your case, if you believe all Spanish players had a a-priori equal chance of being drawn in the (sub)sample, then it is "random".  
Regarding size considerations: A single observation can still be a "random sample". Larger samples are needed when you want more precision, and especially when you are looking for rare relations in the population, which might not be present in a small sample. 
A: Assuming there are no biases in the sampling technique, this should be fine. Some questions to ask might be:
-> Was the survey conducted in Spanish if requested? (Language bias)
-> Was the survey conducted over the phone or in person? If over the phone, and cell phones were excluded, are Spanish players more or less likely to own cell phones than players in the rest of Europe, and for what reasons? 
-> Was the rate at which Spanish players refused to answer survey questions different from the rate for players as a whole?
-> Overall, what proportion of Spanish players were sampled?
Without knowing the exact composition of the data it's hard to say more. Are there any specific issues you're concerned about?
