This tutorial will define and discuss the following topic:
Random errors are things that just happen and aren't really your fault.
When a sample is taken from a larger population, the results are unknown, meaning, it’s unclear if the results will accurately represent exactly what the population looks like.
Suppose that there were 100 individuals (considered the population). Twenty of them were college students, and you took 5 of them for a sample. What would you expect to happen? Twenty percent of the population is a college student, which is one out of every 5 people. You would probably expect one individual within your sample to be a college student.
However, that doesn't always happen. You might not get any college students or all five of them may be college students. Just because you expect to get one doesn't mean that will actually happen.Why not?Let’s say that the individuals with numbers 1 - 20 be the college students and their numbers are pink. Number 21 - 100 are individuals not in college. Using a random number generator, you might get a simple random sample that looks like this:
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 100 individuals in the population. That’s 40%. What went wrong? Nothing went wrong, it’s just that random errors happen sometimes.
Random error occurs when the sample, just by chance, doesn't match up perfectly with the population.Random error is not a mistake. While it can’t be corrected or avoided completely, the impact can be minimized by increasing the sample size. The larger the group, the better the chances are that a representative group will be obtained.
Imaging that ten individuals from the group of 100 were chosen instead of five. Two college students would be expected to make it into the sample. So if the sample was off by one, it’s not as impactful since at least one college student would be represented.
Now, by contrast, systematic errors are mistakes. Systematic errors are due to flaws in the design.
Suppose a school board wants to estimate how many students are eligible for free or reduced lunch. If you have under-coverage bias, also called “selection bias”, you can possibly have people from a poorer neighborhood that didn't respond to a questionnaire that was sent out. Maybe their parents were working nights and didn’t have time to complete the survey. The board may underestimate the true number of students requiring free reduced lunch. This type of error cannot be remedied by increasing the sample size.
A child has a growth chart in his room and his parents mistakenly put it up above the baseboard - an extra 2 inches from the floor. This is going to result in the child thinking he’s 2 inches shorter than he actually is, which is systematically wrong.
Random errors are when the sample that you got doesn't match up with the population. It cannot be controlled, but using a larger sample will 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.Increasing the sample size will not fix the issue. When systematic error occurs, you might as well just throw away and start over, because there's no rescuing poorly collected data.
Source: This work is adapted from Sophia author jonathan Osters.
A mistake in the measurements taken in the study. This is a systematic 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.
A bias that occurs when certain groups are systematically left out of the sample. This is a 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.