Element 17, 27, 37,

et cetera, are only chosen if seven is chosen as the starting point.

This is not a real problem.

It just requires a little more statistical work to determine things like

the margin of error.

The real problem with systematic sampling is that it only results in a truly random

sample if there's absolutely no pattern to the list of elements.

What if the assembly line alternately produces cat food made with fish and

cat food made with beef?

Let's say all odd-numbered elements are made with fish.

In our example, we would never sample the quality of cat food made with beef.

Of course, this an exaggerated example, but

it illustrates that systematic sampling can be dangerous.

A preexisting list or ordering of elements can always contain a pattern that

were unaware of, resulting in a biased sample.

So, systematic sampling only results in a truly random sample if

it's absolutely certain that the list of elements is ordered randomly.

We can make sure of this by randomly reordering the entire list.

We can generate a sequence of random numbers of the same size as the list and

then select elements from this list using systematic sampling.

Of course, this is equivalent to random selection directly from

the original list using random numbers.