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Random and Systematic Errors

Random and Systematic Errors

Author: Katherine Williams

Differentiate between random errors and systematic errors.

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This tutorial covers random and systematic errors. Errors can be classified in two ways. They can be done randomly or they can be done systematically.

Random errors are the less concerning of the two. They're inevitable. They're going to happen. A random error just explains the difference between your sample and the population. If you take a larger sample size or if you repeat your selection, you're going to decrease the amount of random error. Let's look at a quick example.

Let's say your company has 50% of the people who like green and 50% of the people who like blue-- green, green, green, green, and blue, blue, blue, blue. If you're taking a small sample, if you're taking a sample of two people, you would expect that it should be 50%. If it's going to reflect the population, it would have to be 50%. You'd have to select a green and a blue.

But sometimes, that's not going to happen. Sometimes, you're going to select two greens, or you can select two blues, or you could get that green and blue. So all of the time that you're taking your small samples, it doesn't match the population exactly. Sometimes it's off. If we were to take larger samples and, say, take groups of four, then you'd be more likely to get 50/50 split or to get closer to that 50/50 split that's in the population.

Now, another kind of error is systematic error. Systematic error comes from the way the survey is designed, or rather, the study is designed. It can't be eliminated just by taking a larger sample or by repeating because every time you are repeating or when you take the larger sample, your survey and your study still have the same flaws. So it can be eliminated. But when you want to eliminate it, you'd need to redesign your study to reflect those changes.

Some examples of systematic errors are most of the types of bias we've already seen. Measurement bias is a new one. It involves inaccurate measurements. So if you're using the wrong units or you're not considering that little part of the ruler that's blank, you're going to end up with an accurate measurements.

Another type is selection bias. Selection bias happens when you're inappropriately selecting the people to be part of your sample. This issue isn't going to be corrected if you take a larger sample or do it many times. You'd have to redesign how you're selecting the sample in order to get rid of the selection bias. We'll go through a few examples.

Behind me is a list of potential ways of having an error. We're going to decide whether it's a random error or a systematic error. The first one says a sample of students has 15% left handers when the student body has 8%. This type of error is a random error. It's simply describing the difference between our sample and the actual population. It's not describing any sort of error in the design. That would be a systematic error.

Another example is a phone survey during the day. This doesn't say anything about the difference between our population and our sample, so it's a systematic error. If you're doing a phone survey during the day, you're only able to reach the people who are at home who aren't working, and those people are going to have different opinions than those who are. So because we're inappropriately selecting our sample, we're getting selection bias, which is a systematic error.

The final example is measuring without accounting for the blank part of the ruler. This is also a systematic error. It's a type of management bias. In case you don't know what I'm talking about, I'm going to slide a ruler out now. So on this ruler, there is this part right here before the 0. When you're doing your measurements, you need to be starting from zero. So if you accidentally start from the bottom end of the ruler, you're not measuring things correctly. While on a small ruler, like a foot-long ruler, this isn't going to count for much difference. But sometimes, it does.

For example, my high school was measuring everyone for their cap and gown, and they needed to know how tall the students were so they could order the proper length rope. They accidentally forgot to include this chunk. Now, because the rulers they happened to use had quite a sizeable blank part at the beginning, all of the seniors' robes were off by almost 2 inches, and so everyone's were too short.

So measurement bias can happen anytime you're inappropriately doing the measurement, and it's a type of systematic error. Doing more samples or getting a larger sample isn't going to correct for it. You need to go back and make the correction to the actual design. You'd need to measure from 0 or use a different type of ruler. This has been your tutorial on random errors and systematic errors.

Terms to Know
Measurement Bias

A mistake in the measurements taken in the study. This is a systematic error.

Random Error

When the resulting value obtained from the sample does not match the value from the population simply by chance. This is not a mistake, but is inherent in the variability in sampling.

Selection Bias

A bias that occurs when certain groups are systematically left out of the sample. This is a systematic error.

Systematic Error

When the resulting value obtained from the sample does not match the value from the population as a result of an incorrect measurement or bias. This is a mistake made by the researcher.