Step by step
The question
Question: 90 people from a city signed up for the study.
Half of them were chosen at random to take a vitamin.
The vitamin group had fewer colds.
What can the study say?
1 Two questions
To judge a study, we ask two questions.
How were the people picked?
And how were the groups made?
2 How they were picked
The story says the people signed up.
They chose to join.
So: no, not at random.
People who join by themselves can be different from the others.
Careful!
A big group is not enough.
Volunteers may be different from the rest of the city.
So what we find is true only for people like these, not for the whole city.
3 How the groups were made
The people were chosen at random to take a vitamin.
So: yes.
Chance made the groups, not the people.
So the two groups are alike, except for the vitamin.
So the difference comes from the vitamin: the vitamin causes it.
4 What the study can say
So the study can say: the vitamin causes this, but only for people like these.
5 Check
Let's check with the story.
The first sentence says: signed up.
That matches.
The second sentence says: chosen at random to take a vitamin.
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.