Random Sample vs. As Large a Sample as Possible? I'm struggling to differentiate scenarios where you would use random sampling vs. getting as large a sample as possible. For instance, one thing I am trying to test is the notion that being in a "home" arena boosts player performance.
I have collected individual football game data for every game over the past 10 years. I have over 34000 observations of players performance during this time span. Would it have been more prudent for me to take a random sample of say, 1000 players over the past 10 years?
I just don't understand why, in the above scenario, I'd take a random sample of 1000 when I can just take all of the players performances from the past 10 years.
 A: From your description, your 10-year "sample" seems to have exhausted an important population of interest. Usually, the purpose of a random sample is to learn about the population from which it was drawn. 
A small truly random sample is typically better than a large haphazard sample that may be atypical of its population in important ways. But with modern technology it is sometimes possible to look directly at the whole population, and no sample (not even a random one) can beat that.
However, when you claim to have looked at a whole population, you should make sure you have really done that. In the US we have a Census every 10 years that seeks to count and ask basic questions of the entire US population (everyone living in the US, citizen or not). But some people are not easy to find and question. That may include people who are homeless, are reclusive, seek privacy because they are in the country illegally, and so on. As a check on whether the Census is really complete, the Bureau of Census sometimes takes very careful random samples in various small areas and compares sample results with purported population results.
Some statisticians have suggested that it may be more efficient and accurate to do a large and meticulously careful random sample than to try to find everyone. For some purposes, they seem to be right. However, the US Constitution requires a "complete enumeration"---and does not define "meticulously careful random sample."
