Random sampling and random assignment are different things, and they buy different rights.
Step 1: Let's Learn
Read it, or press Listen and follow the words.
Random sampling
Choosing subjects at random from the population lets you generalise to that population.
Random assignment
Assigning treatments at random lets you claim the treatment caused the difference.
Why observation is not enough
An observational study can only report association. A lurking variable may explain it entirely.
Randomness is what makes inference possible
A random sample is one where every member of the population has a known chance of selection. Randomness is not carelessness — it is the mechanism that makes the sampling distribution calculable.
Bias comes from the method
Voluntary response, convenience sampling and undercoverage all produce systematic error. No sample size fixes bias: a large biased sample is simply a precise wrong answer.
Observational study against experiment
An observational study records what happens; an experiment imposes a treatment. Only a randomised experiment supports a causal conclusion, and stating which design was used is required before any conclusion.
Two separate questions
Random sampling licenses generalising to the population. Random assignment licenses concluding causation. They are independent conditions, and a study can satisfy one without the other.
Step 2: Try It Yourself
Tap and try it out.
Treatment
Control
There are 11 in all.
Treatment has the most. It has 3 more than Control.
Step 3: 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.
Step 4: Your Turn
Practice makes it stick.
The Right to Generalise
Problem 1 of 2
Which gives the right to generalise to a population? 1 for random sampling, 2 for random assignment.
The Right to Claim Cause
Problem 2 of 2
Which gives the right to claim causation? 1 for random sampling, 2 for random assignment.
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? 1 for yes, 0 for no.
3 of 8
Does a larger biased sample fix the bias? 1 for yes, 0 for no.
4 of 8
A lurking variable explains an association. Was the study observational? 1 for yes, 0 for no.
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? 1 for yes, 0 for no.
8 of 8
An experiment with random assignment but volunteer subjects. Can it claim cause? 1 for yes, 0 for no.
Step 5: Quick Check
Show what you know.
Question 1 of 1
Which is required to claim causation? 1 for random sampling, 2 for random assignment.
What You Learned
- Random sampling earns the right to generalise; 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.