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# Sampling Error and Sample Size

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Author: Ryan Backman
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Identify the relationship between sampling error and sample size.

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Tutorial

## Video Transcription

Hi, this tutorial covers sampling error and sample size. So let's start with some motivation here. So the average height of an adult male in the United States is 70.2 inches. So since we're talking-- since this represents the mean of a population, we're going to denote that as mu, so mu equals 40 point-- excuse me-- 70.2.

So now that we've established this as our population mean, now, let's consider two samples. So one is a sample of 10 randomly selected US adult males. So in this case, n is equal to 10, n being our sample size. And two, a sample of 1,000 randomly selected US adult males. So again, we're dealing with n, so n in this case would be 1,000.

All right, so now, let's think about the mean of sample number one and the mean of sample number two. Now, we didn't actually calculate means here, but think about what we would expect the mean for sample one to be and what we do what we would expect the mean of sample two to be. Now, here's a question, if you had to bet \$1 million, which sample mean would you say is closer to that population mean?

OK, so again, thinking about sample number one, sample number two, if we were to calculate means, and you had a bunch of money to bet, would you think that sample mean one would be closer to the population mean, or sample number two would be closer to the sample mean? So just think about that for a sec.

Now, I hope you said the mean of sample number two so you'd get some return on that bet. And this is why. So as the sample-- excuse me-- as the size of the sample drawn from the population is increased, so if we went from a sample size of 10 to a sample size of 1,000, the variation of the sample statistic goes down. Also, the sample statistic becomes a more accurate estimate of the population parameter.

So with that bigger sample size in our case, so that sample size of 1,000, we would expect that mean, that sample mean to be a lot closer to your population means, so a lot closer to 70.2. Whereas with the small sample, we would probably expect that the population or that that sample mean might not be as close to your population. So as you probably know, a large sample is always desirable. So there is that important relationship between sample size and sampling error.

So let's make sure we have a good definition of both of those. Sample size is the size of a sample of a population of interest, abbreviated n, and your sampling error is the error that comes from a random sample to estimate a population parameter. You're always going to have a little bit of error because you're not going to be able to get a totally representative sample from your population. So there's always a little bit of an error associated with that.

Now, as the sample size increases, the sampling error decreases. So as n increases, sampling error decreases. And obviously, since we're dealing with an error, we want a low sampling error, so we want to take as large of a sample as possible.

Now, a couple of things about sampling error. A margin of error-- you may have heard that term before-- a margin of error is a calculation of a probable sampling error. So if you're looking at a political study, and a certain candidate has 44% of a sample with a margin of error of 3%, they're saying that that 3% is a probable sampling error.

Now, a sampling error does not include non random errors like biased sampling, bad survey language, or measuring errors. So when they're talking about sampling error, usually defined as that margin of error, they're assuming that none of these other errors came into play. So the margin of error usually only is a calculation of your sampling error.

All right, so the key thing here is just to make sure that you want to take as large of a sample as possible, because as your sample size increases, your sampling error decreases. All right, so that has been the tutorial on sampling error and sample size. Thanks for watching.

Terms to Know
Sample Size

The size of a sample of a population of interest.

Sampling Error

The amount by which the sample statistic differs from the population parameter.