Now again, here we've got our overall population.

And we could do a simple random sample.

We don't need to worry about anything else other than randomization.

No, except that we know that we want to stratify.

We want to group them in such a way.

That we can control the distribution of the sample across dimensions of variables.

That we know about in advance in our sample selection stratification.

Suppose that what we could do is take our 10th grade students and

divide them into two groups.

Those that have potentially lower incomes and those that have potentially higher.

Except the way we're going to do this is use identification for

each of the students.

About whether or not their school has programs for free or

reduced priced lunches.

Whether there's a high fraction of the students in their school who receive

free or reduced price lunches.

Those schools that have higher fractions of their children receiving free or

reduced price lunches, subsidized lunches if you will.

Tend to have students who come from lower socioeconomic status.

And those that have low proportions, those tend to have students coming from higher.

So we're going to have to keep our highs and lows mixed together.

A high proportion means lower income.

A low proportion means higher income.

And that's what we're doing in this particular case.

And we can stratify our population as shown here.

Now we've added two rows.

We've filled in the table.

The high row, about 20% of our students come

from schools with higher fractions of free or reduced price lunches.

And the low, the 3.2 million, the 80%,

they are coming from schools that have higher incomes among the students.

But there's a sample size now that we draw from each of these.

Our 12,000 are now divided up across these two groups, stratified sampling.

In this particular case what we're doing.

Is doing stratified proportionally allocated sampling.

We're using the saved sampling rate in each of these.

And if we apply that overall sampling rate to each of the two groups,

the 800,000 and the 3.2 million.

We get the sample size that's shown here, 2,400 and 9,600.

Or if we prefer 2,400 is 20% of the 12,000.

That's a proportionate representation in terms of our miniaturization of

our population.

But nonetheless, the weight within each of the groups is the same,

it's the inverse of that sampling fraction.

And we can go with that weight or a reduced value for it.

It's all going to cancel,

it's all going to wash out in the estimation in the end anyway.

All right, so that sample size allocation is a proportionate allocation,

2,400 from high, 9,600 from low.

2,400 from lower income schools that have a higher proportion of

children with lower incomes, 9,600 from those with higher.