Scope of inference: generalization and causation

About this lesson

Statistics (AP-aligned) › Collecting data

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Scope of inference: generalization and causation

Warm-up

Three quick questions from earlier lessons.

Discover

A randomized experiment on 50 volunteer athletes shows a supplement improves sprint times. Can you say it helps all adults?

  1. No, only for these volunteers
  2. Yes, it was a randomized experiment

Key idea

Two kinds of randomness, two kinds of conclusions.

Random sampling → results can be generalized to the population. Random assignment → differences can be attributed to the treatment (cause and effect). Both → causal conclusions about the population. Blinding (single or double) and placebos keep expectations from affecting the results.

Worked example

Four studies.

Volunteers, no assignment: association in these people only
Neither.
Random sample, no assignment: association in the population
Sampling only.
Volunteers, random assignment: cause, in these subjects
Assignment only.

Your turn, guided

Your turn: how many of the four combinations (sampling yes/no × assignment yes/no) allow a causal conclusion about the whole population?

11
Only both random sampling and random assignment.

Practice ★

  1. A random sample of 493 adults in a city shows that those who walk to work report less stress. No treatment was assigned. What can be concluded?
    1. The association can be generalized to adults in the city, but not cause and effect
    2. Walking causes less stress for adults in the city
    3. Nothing beyond the 493 people sampled
  1. 147 volunteers are randomly assigned to a new or old teaching method; the new method scores higher. What can be concluded?
    1. The method caused the difference for these volunteers; generalizing beyond them is risky
    2. The new method works better for all students
    3. Nothing, because there was no random sample

Watch out!

Practice ★★

  1. In a drug trial with 64 patients, neither the patients nor the doctors who assess them know who receives the drug. What is this called?
    1. A double-blind experiment
    2. A placebo
    3. Blocking

Exit ticket

Three questions to check you have got it.

  1. A random sample of 493 adults in a city shows that those who walk to work report less stress. No treatment was assigned. What can be concluded?
    1. The association can be generalized to adults in the city, but not cause and effect
    2. Walking causes less stress for adults in the city
    3. Nothing beyond the 493 people sampled
  2. A random sample of 530 adults in a city shows that those who walk to work report less stress. No treatment was assigned. What can be concluded?
    1. The association can be generalized to adults in the city, but not cause and effect
    2. Walking causes less stress for adults in the city
    3. Nothing beyond the 530 people sampled
  3. A random sample of 712 adults in a city shows that those who walk to work report less stress. No treatment was assigned. What can be concluded?
    1. The association can be generalized to adults in the city, but not cause and effect
    2. Walking causes less stress for adults in the city
    3. Nothing beyond the 712 people sampled

Summary card

Scope of inference

  • Random sampling → generalize.
  • Random assignment → cause.

Watch out: you need both for a causal claim about a population.

End of the lesson

Back to the chapter

Answers: Scope of inference: generalization and causation

A

  1. The association can be generalized to adults in the city, but not cause and effect

B

  1. The method caused the difference for these volunteers; generalizing beyond them is risky

C

  1. A double-blind experiment

D

  1. The association can be generalized to adults in the city, but not cause and effect
  2. The association can be generalized to adults in the city, but not cause and effect
  3. The association can be generalized to adults in the city, but not cause and effect

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