Well we've discussed sampling techniques such as simple random sampling, or

stratified random sampling, or cluster sampling.

We made a point of talking about how to calculate standard errors,

within that framework in which we talked about.

Seven steps of the process.

Going from population to frame to sample and

estimates and the sampling distribution.

And then standard errors estimated from the data and constant intervals built

around those standard errors to give us uncertainty statements.

We should do the same thing here for systematic samples,

except that what happens with systematic samples, when we start talking about that

uncertainty estimation, is that the approach is built on the others.

It's built on the others in two ways.

In one of those, it is built on the others in terms of thinking about the sampling

distribution and replicating in our sample the sampling distribution.

We're going to refer to that as multiple random starts.

So I'll tell you more about that in a moment.

But then we also saw that systematic sample is applied to lists with

certain orders gave us, effectively, certain kinds of samples.

So if the list order were simple random,

that we had effectively then, a simple random sample when we got done.

That will allow us to use simple random sampling as a variation technique under

the assumption of random ordering.

Similarly, stratified random ordering could lead to

a stratified random variance estimate.

There's a couple of other modifications though,

I'm only going to mention one of them, something called a pair difference which

is quite widely used in these kinds of circumstances.

Especially when the selection units are not just elements but

happen to be clusters, and

we'll talk a little bit more about that when we talk about paired differences.

And then we'll go through a simple illustration just to put the calculations

in context and make sure that we know how numbers would actually fit into certain

kinds of calculations.

So this is more about taking a conceptual framework and model, and

then applying it to our systematic sampling context, for the purposes

of variance estimation, standard error estimation, cost interval construction.

But we're not going to go through the full thing,

just highlight these particular topics.

And we'll rely on referring back to previous units as a basis for

getting more detail about how they work.