Steply

What a study can say

Random samples and random groups · Statistics · 20 problems, easy to harder

▶ Watch the first one solved

How we do it

  1. Two questions
  2. How they were picked
  3. How the groups were made
  4. What the study can say
  5. Check

The steps for 200 people were chosen at random from a city. Half of them were…. Every solution names its steps, so you always know what comes next.

Worked examples

200 people were chosen at random from a city. Half of them were… Easy

The question

Question: 200 people were chosen at random from a city.

Half of them were chosen at random to drink green tea each day.

The tea group slept longer.

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 were chosen at random from the city.

So: yes.

At random means all the people in the city had the same chance to be picked.

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

random: all people in the city had the same chance

So what we find can be used for the whole city: true for all people in the city.

3 How the groups were made

The people were chosen at random to drink green tea each day.

So: yes.

Chance made the groups, not the people.

So the two groups are alike, except for the tea.

random groups: alike, except for the tea

So the difference comes from the tea: the tea causes it.

Careful!

Only for the city they were picked from.

Not for all people everywhere.

Careful: not true for all people everywhere ✗

4 What the study can say

So the study can say: for all people in the city, the tea causes this.

= causes it, for the whole city

5 Check

Let's check with the story.

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

That matches.

"chosen at random from" → all the city

The second sentence says: chosen at random to drink green tea each day.

That matches too.

So the answer is right!

"chosen at random to" → causes

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.

Answer
= causes it, for the whole city

▶ Watch it solved

50 dogs were picked at random from a shelter. Half of them were… Medium

The question

Question: 50 dogs were picked at random from a shelter.

Half of them were picked at random to get a new food.

The new food group gained more weight.

What can the study say?

1 Two questions

To judge a study, we ask two questions.

How were the dogs picked?

And how were the groups made?

2 How they were picked

The story says the dogs were chosen at random from the shelter.

So: yes.

At random means all the dogs in the shelter had the same chance to be picked.

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

random: all dogs in the shelter had the same chance

So what we find can be used for the whole shelter: true for all dogs in the shelter.

3 How the groups were made

The dogs were chosen at random to get a new food.

So: yes.

Chance made the groups, not the dogs.

So the two groups are alike, except for the new food.

random groups: alike, except for the new food

So the difference comes from the new food: the new food causes it.

Careful!

Only for the shelter they were picked from.

Not for all dogs everywhere.

Careful: not true for all dogs everywhere ✗

4 What the study can say

So the study can say: for all dogs in the shelter, the new food causes this.

= causes it, for the whole shelter

5 Check

Let's check with the story.

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

That matches.

"chosen at random from" → all the shelter

The second sentence says: chosen at random to get a new food.

That matches too.

So the answer is right!

"chosen at random to" → causes

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.

Answer
= causes it, for the whole shelter

▶ Watch it solved

320 adults were picked at random from a city. Half of them chose to… Harder

The question

Question: 320 adults were picked at random from a city.

Half of them chose to drink coffee every morning.

The coffee group worked faster.

What can the study say?

1 Two questions

To judge a study, we ask two questions.

How were the adults picked?

And how were the groups made?

2 How they were picked

The story says the adults were chosen at random from the city.

So: yes.

At random means all the adults in the city had the same chance to be picked.

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

random: all adults in the city had the same chance

So what we find can be used for the whole city: true for all adults in the city.

3 How the groups were made

The adults chose for themselves.

So: no, not at random.

People who choose to drink coffee every morning may be different in other ways too.

they chose: the groups may differ in other ways

Careful!

Doing better does not prove the coffee caused it.

Something else may make the difference.

Careful: not the coffee group did better → causes ✗

So the coffee and the better result go together.

But maybe the coffee did not cause it.

4 What the study can say

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

= linked in the city, maybe not caused

5 Check

Let's check with the story.

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

That matches.

"chosen at random from" → all the city

The second sentence says: they chose.

That matches too.

So the answer is right!

"chose" → maybe not caused

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.

Answer
= linked in the city, maybe not caused

▶ Watch it solved

Practice

Try each one, then open the answer. Stuck? Open the problem to watch every step.

Easy

  1. 200 people were chosen at random from a city. Half of them were chosen at random to drink green tea each day. The tea group slept longer. What can the study say?
    Answer
    = causes it, for the whole city
  2. 100 students were chosen at random from a school. Half of them were chosen at random to use a math app. The app group got better marks. What can the study say?
    Answer
    = causes it, for the whole school
  3. 60 plants were chosen at random from a farm. Half of them were chosen at random to get a new plant food. The plant food group grew taller. What can the study say?
    Answer
    = causes it, for the whole farm
  4. 80 students from a school volunteered for the study. Half of them chose to use a study app. The app group got better marks. What can the study say?
    Answer
    = linked, for people like these
  5. 150 adults were chosen at random from a town. Half of them chose to walk every morning. The walking group felt less tired. What can the study say?
    Answer
    = linked in the town, maybe not caused
  6. 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?
    Answer
    = causes it, for people like these
  7. 120 workers were chosen at random from a company. Half of them were chosen at random to take a short break each hour. The break group made fewer mistakes. What can the study say?
    Answer
    = causes it, for the whole company
  8. 300 teens from a town volunteered for the study. They chose for themselves whether to read before bed. The reading group slept longer. What can the study say?
    Answer
    = linked, for people like these

Medium

  1. 50 dogs were picked at random from a shelter. Half of them were picked at random to get a new food. The new food group gained more weight. What can the study say?
    Answer
    = causes it, for the whole shelter
  2. 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?
    Answer
    = linked in the mall, maybe not caused
  3. 70 runners from a club signed up for the study. Half of them were chosen at random to stretch before each run. The stretching group had fewer injuries. What can the study say?
    Answer
    = causes it, for people like these
  4. 250 drivers from a city volunteered for the study. Half of them chose to listen to music while driving. The music group felt calmer. What can the study say?
    Answer
    = linked, for people like these
  5. 180 children were chosen at random from a town. Half of them were chosen at random to play outside after school. The outdoor play group slept longer. What can the study say?
    Answer
    = causes it, for the whole town
  6. 60 patients from a hospital volunteered for the study. Half of them were chosen at random to take a new medicine. The medicine group got better faster. What can the study say?
    Answer
    = causes it, for people like these
  7. 140 students were chosen at random from a college. They chose for themselves whether to eat breakfast every day. The breakfast group had more energy. What can the study say?
    Answer
    = linked in the college, maybe not caused
  8. 90 cows were chosen at random from a farm. Half of them were picked at random to eat a new grass. The grass group gave more milk. What can the study say?
    Answer
    = causes it, for the whole farm

Harder

  1. 320 adults were picked at random from a city. Half of them chose to drink coffee every morning. The coffee group worked faster. What can the study say?
    Answer
    = linked in the city, maybe not caused
  2. 40 teachers from a school signed up for the study. They chose for themselves whether to use a new reading plan. The plan group saw more progress. What can the study say?
    Answer
    = linked, for people like these
  3. 500 voters were chosen at random from a state. Half of them were chosen at random to read a short fact sheet. The fact sheet group knew more. What can the study say?
    Answer
    = causes it, for the whole state
  4. 110 swimmers from a club volunteered for the study. Half of them were chosen at random to train in the morning. The morning training group swam faster. What can the study say?
    Answer
    = causes it, for people like these