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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.

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    $\begingroup$ Note that this is vaguely similar to rejection sampling. However, in the method you describe, note that your resulting sample size is actually a random variable. Depending on what kind of analyses you have in mind, this may or may not introduce some complications. For example, in many (but not all) GLMs, the sample size is effectively random, but the inference is done conditionally (and this approach can be justified rigorously). $\endgroup$
    – cardinal
    Oct 27, 2011 at 17:38
  • $\begingroup$ @cardinal Thank you for the reference to rejection sampling. I am wondering what type of complications would be introduced? If the new sample can be described as a random sample of another population, can't I "virtually" ignore the fact that it was obtained through resampling? $\endgroup$
    – Antoine Vernet
    Oct 28, 2011 at 7:37

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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.

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    $\begingroup$ Randomness is more than equal prior chances. For example, one team in Spain could have been randomly selected. Assuming equal team sizes, this gives all soccer players the same chance of being included in the sample, but it's a stretch to assume that a single team is truly representative of all players in the country. $\endgroup$
    – whuber ♦
    Oct 27, 2011 at 20:44
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    $\begingroup$ (...)but it's a stretch to assume that a single team is truly representative of all players in the country... especially if that country is Spain! :) $\endgroup$
    – cardinal
    Oct 27, 2011 at 20:48
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    $\begingroup$ @whuber- you are right. To be precise, not only equal prior chances, but also equal chances given the rest of the sample. This will exclude the team-sampling-scheme. $\endgroup$
    – JohnRos
    Oct 27, 2011 at 21:46
  • $\begingroup$ @JohnRos. Thanks for the precision about the relation between randomness and representativity. $\endgroup$
    – Antoine Vernet
    Oct 28, 2011 at 7:32
  • $\begingroup$ @whuber Thanks for pointing that equal prior chances are necessary but not sufficient. $\endgroup$
    – Antoine Vernet
    Oct 28, 2011 at 7:33
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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?

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  • $\begingroup$ I agree with the points you make, but where does it say that the players were contacted or attempted to be contacted? The OP could just have, say, some summary statistics for a random subset of players from Europe. $\endgroup$
    – cardinal
    Oct 27, 2011 at 17:46
  • $\begingroup$ @John Doucette Thank you. These precautions make sense to me, but strictly speaking, they are not statistical precautions but design ones, which leads me to think that assuming there is no known bias for the subpopulation, selecting people in that subpopulation in your sample leaves you with a random sample. As for the data, the example is fictitious, I was just trying to get away from the children in classrooms in schools type of example. $\endgroup$
    – Antoine Vernet
    Oct 28, 2011 at 7:24

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