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Sampling Error and Sample Size

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This tutorial talks about sampling error and sample size. Sampling error is the error that comes from using a random sample to estimate a population parameter. Now, errors can arise because random samples aren't always representative.

So for example, if I had a population of two males and six females and was taking samples of size two, it is possible that, when I take my sample, I select just the two males. Now, if those two males are super different from these six females, then I would end up with a non-representative sample, and that can affect the results that we get.

Sampling error does not include non-random error. So errors that come from biased sampling, bad survey questions, or measuring errors are not incorporated into sampling error. Additionally, calculating the margin of error is creating a probable sampling error. So you're able to give an idea of what you expect that your sampling error will be based on a variety of factors.

Now, with sample size, as your sample size goes up, the variation in the sample statistic decreases, and your accuracy in estimating the population parameter increases. So when you have a larger sample, the variation between those samples, between the sample statistics decreases, which gives you greater accuracy in estimating what the population parameter looks like because you're less likely to get samples entirely of those extreme or end measures.

So in the last example, you're less likely to get the sample with just those two guys if you're taking a larger sample. So if you did a sample size of three or four, you would have to get some of the females involved, and that would decrease the variation in your sample statistic and increase the accuracy in estimating the population parameter. Because of this, when it's practical, a larger sample size is preferred. This has been your tutorial on sampling error and sample size.