400 shoppers were chosen at random from a mall. Half of them chose…

Step by step

The question

Question: 400 shoppers were chosen at random from a mall.

Half of them chose to use a coupon.

The coupon group spent more.

What can the study say?

1 Two questions

To judge a study, we ask two questions.

How were the shoppers picked?

And how were the groups made?

2 How they were picked

The story says the shoppers were chosen at random from the mall.

So: yes.

At random means all the shoppers in the mall had the same chance to be picked.

So the group is a fair small copy of the whole mall.

So what we find can be used for the whole mall: true for all shoppers in the mall.

3 How the groups were made

The shoppers chose for themselves.

So: no, not at random.

People who choose to use a coupon may be different in other ways too.

Careful!

Doing better does not prove the coupon caused it.

Something else may make the difference.

So the coupon and the better result go together.

But maybe the coupon did not cause it.

4 What the study can say

So the study can say: in the mall, the coupon and the result go together, but maybe the coupon is not the cause.

5 Check

Let's check with the story.

The first sentence says: chosen at random from the mall.

That matches.

The second sentence says: they chose.

That matches too.

So the answer is right!

Let's look back.

First: two questions.

Then: how they were picked.

Then: how the groups were made.

Then: what the study can say.

Last: check.