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Random and Systematic Errors

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This tutorial is going to teach you about random and systematic errors. Now, both of these are different types of errors. Random errors are things that just happen and aren't really your fault. Systematic errors are things that maybe you could have controlled for.

When we sample from a larger population, we don't know if what we get is going to be exactly what the population looks like. So for instance, suppose that there was 100 individuals, 20 of them were college students. And we'll call this our population.

Suppose we took a sample of five of them. What would you expect to happen. Well, since 20% or one out of five individuals in the population is a college student, you would expect exactly one of those five to be a college student.

However, that doesn't always happen. You might get no college students. In fact, you might even get all five of them being college students. Just because you expect to get one doesn't mean that you're going to actually get one.

So for instance, let the individuals 1 through 20 be the college students and 21 through 100 be individuals who aren't in college. Using a random number generator, you might get a simple random sample of individuals 85, 27, 17, 94, and 74. One out of five of those is a college student.

Another simple random sample might look like this. And again, one out of five is a college student. But you might get a simple random sample that looks like this.

Here, the second person, number five, and the fifth person, number 20, are college students out of our sample of five. So it's a 40% college students in our sample. What went wrong?

I mean really, nothing went wrong. Random errors just happen sometimes. Random error occurs when the sample, just by chance, doesn't match up perfectly with the population.

In the last example, we had two simple random samples give us one out of five college students before we got one that didn't give us one out of five. Random error is not a mistake that you've made. And as such, it's not anything you can correct for. It just happens sometimes.

Can we avoid it? Well, no. But you can lessen the effect by increasing the sample size. When you increase the sample size, you're going to get a more representative group. You're going to get a better snapshot of what's going on in the population so that when you are off, you're not off by much.

So imagine that we had sampled 10 individuals from the group instead of five. Here, we were off by one from what we expected. And that changed it to a 40% value. If we had sampled 10, we would expect two college students. If we were off by one, it would go from 20 to 30 instead of 20 to 40.

Now, by contrast, systematic errors are mistakes. Systematic errors are due to flaws in the design of your study. So suppose the school board wants to estimate how many students are eligible for free or reduced lunch.

If you have undercoverage bias, or we also call that selection bias, possibly you have people from a poorer neighborhood that didn't respond to some kind of a questionnaire that was sent out. They may underestimate the true number of students requiring free reduced lunch. And this type of error you can't remedy by increasing the sample size.

There's no rescuing something like this. This is biased data. This is a systematic error in the way that you collected your data. And there's no rescuing it.

Here's another example of systematic errors. Suppose that you have a child with a growth chart in his room, something like this. And he asks his parents to put it up. And instead of placing the 24 inch mark at the 24 inch level, maybe his parents mistakenly placed it at 22 and 1/2 inches.

This is going to result in the child thinking that he's one and a half inches taller than he really is. And every time he measures himself on this growth chart, his answer will be 1.5 inches higher than his real height. His answers will systematically be wrong.

So to recap, random errors are when the sample that you got doesn't match up with the population. And these are just things that happen. You can't control it. But you can take a larger sample to lessen the effect.

Conversely, systematic errors result from the wrong answers or wrong values that you got in your sample due to some kind of bias or some kind of error with your measurement. And you can't help that by increasing the sample size. When systematic error occurs, you might as well just throw away and start over, because there's no rescuing poorly collected data.

And so the terms that we used were random error and systematic error. Good luck. And we'll see you next time.