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Random & Probability Sampling
Common Core: 7.SP.1

Random & Probability Sampling

Author: Katherine Williams
Description:

Determine a representative sample when using random sampling.

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Tutorial

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This tutorial introduces the topic of random sampling. First, let's look at the word random. You've heard the word random used before in many contexts, but in statistics, it refers to something specific. It refers to something that's unpredictable, that there's no recognizable pattern.

So this picture here of the Christmas tree sprinkles. There's no pattern as to how the sprinkles fell. This one down here is diagonal, and then a straight down, and then diagonal the other way, and then straight up, and then kind of diagonal-- there's no pattern that you could follow or determine here. It's unpredictable as to how it fell on the tray.

With dice, it's the same thing. Because a 2 came up the first time, it doesn't mean a 2 is going to come up or can't come up the next time. There's no way to predict what will happen next. Now this picture here is very carefully organized. It's not haphazard. All the circles are in perfect rows horizontally and vertically. However, the coloring of each of the circles is totally random. There's no pattern as to how they go together, as to what color is chosen and where it goes, it's random, it's unpredictable, there's no pattern to it.

With a random sample, every member of the population has the same chance of getting selected. This is similar to rolling a die. When you roll a die, every number from 1 through 6 has the same chance of coming up. You have the same chance of getting a 1 as you do a 5. The same is true of a random sample. If you number your people in your population from 1 through however many there are, every single person would have the same chance of having their number pulled.

The advantage of doing a random sample is that it's the best way to get a representative sample. Now if you recall, a representative sample is one where the population and the sample have the same set of relevant characteristics. This helps us to ensure that our sample accurately reflects the population.

When you're trying to do a random sample, you need to come up with a probability sampling plan. This is pretty much your method of how you're achieving a random sample. Some non-probability sampling plan, some non-random samples we looked at in other tutorials. Convenient samples and voluntary samples or self-selected samples are both not random because not every member has the same chance of being selected.

In a convenient sample, the researcher is taking the people that are easy or convenient to get to. So not every single person in the population has the same chance of getting picked. People that are easier to sample or sampled more often, so they have a higher chance than the other people in the population.

Similarly, a self-selected sample is also non-random in a non-probability sampling plan. In a self-selected sample, people choose whether or not to be part of the sample. So not everyone has the same chance of being selected. The people who are more interested in being selected, who put themselves up to be part of the survey, they are selected more often.

So in summary, when following a probability sampling plan to select a random sample, every member of the population has the same chance of getting picked. And remember, random just means that it's unpredictable, that there's no pattern to it. It doesn't mean that it's haphazard or unorganized.

Terms to Know
Probability Sampling Plan

The way to collect a random sample that guarantees a certain likelihood for each member of the population to be selected

Random Sample

A sample that has been selected in a manner where every member of the population has some predetermined chance of being selected for the sample

Random Selection

The method of obtaining a random sample