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Random & Probability Sampling

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Source: Top Hat, Creative Commons: http://commons.wikimedia.org/wiki/File:Chapeauclaque.png; Pool balls created by the author

This tutorial is on random and probability sampling methods. And so you might be wondering, what does this term random actually mean? It's going to be a term that we use a lot. And so you might be wondering, what exactly does it mean?

Does it mean unusual? Does it mean haphazard? No, it actually doesn't mean either of those two things.

Unusual is the way that it's sort of used in everyday speech like, oh my goodness, I can't believe that someone was wearing the same pants as me, that's so random. That doesn't actually fit the real mathematical definition. It also doesn't work when you say that something that was haphazard was random. Just because it isn't done with a discernible order, doesn't necessarily mean random.

What random does in fact mean in a mathematical sense is that it's unpredictable in the short term, but consistent in the long run. So if we want to select participants in such a way that every member of that population has an equal chance of being selected for the sample, we can do that. We can also weight certain people so that they might be more likely to be selected for the sample. But any time you set it up like that where it's predictable long term but you still don't know exactly what you're going to get any individual sample, that's called a probability sampling plan.

So an example of a random sample might look like this, where here's the 15 billiard balls from a pool table, and you place them all on a hat, and you shake the hat, and voila, here's a sample of five. We took ball number 1, 5, 7, 10, and 14. This is another sample of five. And not all the balls are different than the previous example, but this sample is just as likely as that first one was, which is just as likely as this one, which is just as likely as that one, which is just as likely as this one. Now, this might seem unusual what happens here.

What happened here was we got balls 9, 11, 12, 13, and 14. All of which happened to be striped billiard balls. Now, we didn't get any solid. And if all we knew was this sample of five, we might be led to believe that all the balls in there were striped, which wouldn't be the case.

However, this can happen every once in awhile. It doesn't happen all that much. But this certainly can happen even though we took this randomly-- we did a probability sampling plan. The reason being, this sample of five is just as likely as any other sample of five to be chosen.

So what have we learned here? That sometimes the sample that you get doesn't accurately reflect the population. That will happen occasionally. Although most of the time, we've done our best in order to make sure that we do get an accurate snapshot of the population.

So we don't know exactly what's going to happen. Might we get something that's unrepresentative? Yes. But the vast majority of time it will be representative.

So to recap, the best method for selecting a sample that's representative is we using a random sample and a probability sampling plan. Now, this won't always get you a representative sample. But often you will get one when you do random samples. So the terms that we've used in this tutorial are random sample, random selection, and probability sampling plan.

Good luck. And we'll see you next time.