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Random and Systematic Errors

Random and Systematic Errors

Author: Ryan Backman
Description:

Differentiate between random errors and systematic errors.

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Hi. This tutorial covers random and systematic errors. So let's start with definitions of both of those two types of errors. So a random error is an error that results when a sample differs in some important way in its average characteristics than the population.

Random errors are less likely when the sample size increases. So random errors are just generally due to just sampling error. So you end up just getting a weird sample that's a little bit different in characteristic than the population.

A systematic error now is an error that results from biases arising from the design of the study. Increasing the sample size does not eliminate systematic errors. So random errors are less likely when the sample size increases. Systematic errors are no less likely to occur if you increase that sample size.

So let's take a look at two examples and see what sort of errors would possibly result here. So example number one, a sample of workers might randomly include 15% left-handers when the total percent of left-handed workers in a population is 8%. So this is what's going to be called a random error because your sample differs in characteristic than your population.

And since this was a random sample, this is going to be a random sampling error just because we just simply got a weird sample. This random error would probably be eliminated if a larger sample would be selected. So if you increase that sample size, chances are this 15% is going to be a lot closer to that 8%. So this is an example of when a random error might occur.

So now, let's take a look at an example where a systematic error might occur. So from a sample of residents, the average yearly income was $55,000 when the income level from the population was $42,000. So we can see a pretty big difference between the average for the sample and the average for the population. This systematic error occurred only because homeowners were included in the sample.

Since renters were not included, the average income was systematically high. So because we didn't include any of the lower income people in the study, this number was quite a bit larger than the population number. So simply increasing the number of homeowners sampled would not eliminate this error.

So if we just sampled more and more homeowners, chances are this number is not going to approach this number. So since this was a systematic error, since the error arose because of the design of our study, increasing that sample size won't affect-- won't change the error. So that is the tutorial on random and systematic errors. Thanks for watching.

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.