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Probability & Statistics/what's the point of sample size?

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Question
Clyde, thank you very much for answering my question on prevalence and sample size.

I admit, it got me curious -- why ISN'T sample size important? There seems to be so much fuss about getting the right sample size.

Answer
Well, it is important, to a point. But there are two reasons why it's not something that creates problems for poll-makers, survey-givers, etc.:

1. The error is generally not dependent on the population size. This means that if you do a survey in Rhode Island, you need to survey about 10,000 people to get it right within 1%. Then, if you do the same survey nationwide, you do not need to increase the sample size to get the same 1% error estimate.

2. Because the error is roughly 1 / √(N), where N is the sample size, you can really do a fairly good job with a (relatively) small sample. 10,000 people, for example, is a very small sample when you consider a population of 5 million, 30 million, 1 billion, etc. Even in a small population, if you have 4000 people and you survey 500 of them your figures are good within 4% (and 4% of that population is only 160 people, which isn't that bad relatively speaking).

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Clyde Oliver

Expertise

I can answer all questions up to, and including, graduate level mathematics. I do not have expertise in statistics (I can answer questions about the mathematical foundations of statistics). I am very much proficient in probability. I am not inclined to answer questions that appear to be homework, nor questions that are not meaningful or advanced in any way.

Experience

I am a PhD educated mathematician working in research at a major university.

Organizations
AMS

Publications
Various research journals of mathematics. Various talks & presentations (some short, some long), about either interesting classical material or about research work.

Education/Credentials
BA mathematics & physics, PhD mathematics from a top 20 US school.

Awards and Honors
Various honors related to grades, various fellowships & scholarships, awards for contributions to mathematics and education at my schools, etc.

Past/Present Clients
In the past, and as my career progresses, I have worked and continue to work as an educator and mentor to students of varying age levels, skill levels, and educational levels.

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