Random sampling and random assignment are different things, and they buy different rights. Choosing subjects at random from the population lets you generalize to it. Assigning treatments at random lets you claim the treatment caused the difference. An observational study can only report association.
Step 1: Let's Learn
Read it, or press Listen and follow the words.
Random sampling
A simple random sample gives every member of the population an equal chance. Stratified sampling randomizes within groups. Both let the sample stand for the population. A convenience or voluntary sample does not, however large.
Random assignment
Take the subjects you have and let a coin decide who gets the treatment. Known and unknown differences between people are then spread evenly across the groups, so a difference in outcome can be pinned on the treatment.
Four combinations
Random sample and random assignment: generalize and claim cause. Random sample only: generalize, association only. Random assignment only: cause, for these subjects only. Neither: describe these people, nothing more.
Why observation is not enough
A lurking variable may explain the association entirely. Stress could cause both the coffee and the poor sleep. No amount of data removes that possibility; only assignment does.
Bias
Undercoverage leaves part of the population out. Nonresponse loses those who decline. Voluntary response attracts strong opinions. Wording can lead. A bigger biased sample is a more precise wrong answer.
One question
Was anybody assigned a treatment? If yes, and at random, cause may be claimed. If no, association is the most that may be said. That settles what a study can claim.
Step 2: Try It Yourself
Tap and try it out.
Three studies: (a) 200 volunteers randomly assigned to a new diet or their usual one; (b) a random sample of 1000 adults asked about exercise and mood; (c) 50 gym members compared with 50 non-members on blood pressure. What may each claim?
- Answer(a) random assignment, volunteers: cause, for people like these volunteersno random sample, so no generalizing to everyone
Step 0 of 3
Treatment
Control
There are 11 in all.
Treatment has the most. It has 3 more than Control.
Step 3: In Real Life
A coffee-and-health headline
A study finds coffee drinkers live longer. It is observational, so it cannot say coffee is the cause: maybe coffee drinkers are wealthier. Only an experiment could claim more.
Step 4: Watch an Example
One step at a time.
Watch Rosa Reject a Causal Claim
A survey finds coffee drinkers sleep less, and the headline says coffee causes poor sleep.
- Step 1
Nobody was assigned to drink coffee; they chose. So this is an observational study.
Step 5: Your Turn
Practice makes it stick.
The Right to Generalize
Problem 1 of 2
Which gives the right to generalize to a population?
The Right to Claim Cause
Problem 2 of 2
Which gives the right to claim causation?
What May Be Claimed
1 of 8
Sort each study by what it can support.
Tap something to move it.
- Empty
- Empty
2 of 8
A voluntary online poll. Is it likely biased?
3 of 8
Does a larger biased sample fix the bias?
4 of 8
A lurking variable explains an association. Was the study observational?
5 of 8
Match each design feature to what it protects against.
Tap a card on the left to start.
6 of 8
A census surveys what fraction of the population? Give it as a decimal.
7 of 8
Convenience sampling. Is it random?
8 of 8
An experiment with random assignment but volunteer subjects. Can it claim cause?
Step 6: Quick Check
Show what you know.
Question 1 of 1
Which is required to claim causation?
What You Learned
- Random sampling earns the right to generalize; random assignment earns the right to claim cause.
- An observational study reports association, whatever its size.
- A bigger biased sample is a more precise wrong answer.
- Ask of any study: was anybody assigned a treatment?