6 <strong>Topic VI. Correlation and Causation</strong>
Topic VI. Correlation and Causation
- An introduction to the scientific approach to determining causal relationships.
- In casual conversations, we use the word “causation” in many ways. Sometimes when we say “x causes y,” we’re pointing out who are what or who is responsible for y. Sometimes we’re pointing out something about the causal mechanism or process that leads to y. In this class, the focus is on yet a third reason we use causal language: to identify the “levers” in the world that we can push or pull to bring things about. If we want to generate good policies, for example, it’s important to know what some intervention will bring about, and it’s this sense of causation that is more relevant here. Moreover, science often proceeds by identifying causal relationships in the sense defined below well before the mechanism by which it does so is understood. It is therefore valuable to have a definition of causation that captures this aspect of scientific advance.
- In this class, we will examine causal relationships using variables, interventions,and randomized controlled trials.
- Addressing the Question: How do we find out how things work?
- Correlation vs. Causation
- Randomized Controlled Trials
TOPIC RESOURCES
EXAMPLES
- Exemplary Quotes
- “Let’s think causally here. There are lots of words and concepts that we’re getting confused by here, but let’s remember that right now all we care about is what is causing what.”
- “What if causation goes the other way, or there’s a common cause? We’re getting all upset about the violence on television causing the violence in the streets because they seem to go up and down together in prevalence, but how do we know that it isn’t the other way around, or that they aren’t both being caused by some third factor. Maybe we can look at the timing of one with respect to the other? Or could we possibly control one of the factors by itself and see what happens?”
- “Even if we don’t know how, this seems to work. I know it seems crazy that you can fix this educational problem of delayed reading simply by feeding cereal to the kids every morning, but this was a pretty impressive randomized controlled trial so it’s hard to come up with another explanation.”
- Cautionary Quotes: Mistakes, Misconceptions, & Misunderstandings
- Misconceptions of Induction
- "Aspirin is no better than a placebo. I used to give my sister bread pills when she asked me to get her aspirin, and she always said how much better they made her feel and never noticed the difference."
- "Our analyses of 833 diverse middle schoolers found that most of them learned better with hands-on activities. But we can't conclude anything about children who weren't in our study, because we didn't collect any data about them."
- "Eighty percent of people who took the drug got better. But the drug didn't really work, because a quarter of people who took the placebo got better even though they didn't take the drug, and twenty percent of people who took the drug didn't get any better at all."
- "RCTs cannot give sufficient evidence for causation that salt causes heart disease, because there might be other factors at play."
- Misconceptions of Control Condition
- "We should give the experimental drug to all eight hundred people in a study, instead of giving it to just half of them, because we want to maximize our sample size."
- "If you give a drug to 500 people with a disease, and 80% of them get better, then we know the drug works."
- Students incorrectly assumed that confounding variables cannot be accounted for and did not consider that randomized assignment with a sufficient sample size can cancel out statistical biases.
- "It’s impossible to know if lack of sunlight causes myopia because there are just too many other things that could be interacting with eyesight, such as genetics, to be able to know for sure it’s connected to sunlight."#jc
- "It’s impossible to know… because you’d have to test someone as a baby before their eyes have been exposed to sunlight." Related: "You’d have to test them throughout their whole life to find out how lack of sunlight impacted their vision."#jc
- Misconceptions of Randomization
LEARNING GOALS
- A. ATTITUDES
- B. CONCEPT ACQUISITION
- Correlation is insufficient to demonstrate causation because there are other causal structures that lead to correlation:
- a. A causes B (direct causation);
- b. B causes A (reverse causation);
- c. A and B are both caused by C
- d. A causes B and B causes A (bidirectional or cyclic causation);
- e. There is no connection between A and B; the correlation is a coincidence.
- f. The effect of A on B depends on C
- Randomized Controlled Trial (RCT): An attempt to identify causal relations by randomly assigning subjects into two groups and then performing an experimental intervention on the subjects in one of the groups.
- a. Experimental Intervention: The act of an experimenter changing one variable in a possible causal network.
- b. Randomized Assignment: Given sufficient sample size, randomized assignment rules out confounds by distributing variation randomly between the two groups, thereby avoiding systematic differences except as the result of the intended intervention.
- c. Control Condition: Comparison of an experimental to a control condition is necessary in order to distinguish effect of intervention from changes that would have occurred without the intervention.
- d. Sampling: A study of a well-chosen sample can tell you something about the population (through induction), especially if it was selected in such a way as to avoid any systematic differences between the sample and the rest of the population. It is often difficult or even impossible to capture a perfectly representative sample, so scientists do the best they can. For example, many psychology studies are done with college students because they are accessible, but such samples differ systematically from the general population. Inferences from samples to a larger population need to take such differences into account.
- Causation: X causes Y if and only if X and Y are correlated under interventions on X.
- a. This is a technical notion, which overlaps with but is slightly different from everyday usage. For example, everyday usage of the word “cause” can be influenced by moral considerations, the complexity of a causal mechanism, and/or the nature of the mechanism. We typically don’t say that the big bang "caused" this sequence of letters, or that the presence of oxygen caused the forest fire, etc, but scientifically they are part of the causal history of those phenomena.
- b. There can be other evidence for causation, even when actually performing an intervention is not feasible. However, saying something is a cause implies that there is in principle a relationship under an intervention.
- C. CONCEPT APPLICATION
- State some of the basic problems in establishing causation.
- Recognize some of the basic problems in establishing causation and use them to identify situations in which claims of causation are and are not warranted.
- Explain why a randomized controlled trial can help rule out spurious correlations.
- Identify the flaw in an argument in which correlation is inappropriately being substituted for causation.
- Address the argument, “Science can only establish correlations; it can’t determine causality.”
- Use the definition of causation to identify situations in which claims of causation are and are not warranted.
- Design RCTs for sample problems.
- Identify flaws in experimental designs aimed at testing causality and explain how the flaws could be addressed.
CLASS ELEMENTS
- Suggested Readings & Reading Questions
- Clicker Questions
- Suppose there’s an epidemic of Lyn’s disease and a new drug is proposed as a treatment. 100 (or 10,000) patients with the disease are given the drug, and 79 (or 8,700) of them recover. Does this result:
- A. Give no info about the presence or absence of a causal link
- B. Establish that the treatment makes no difference.
- C. Tentatively confirm the efficacy of the treatment, though more evidence may be needed.
- D. Demonstrate conclusively the existence of an effect.
- Discussion Questions
- Why are humans so interested in the causal structure of the world? Hint: It's essential for controlling one's environment.
- Why are false beliefs about causality so common? E.g. most superstitions are about causality, like astrology, spells, curses, the feeling that you can sometimes will a traffic light to change, etc.
- Why does randomized assignment to conditions matter in an RCT?
- Why do RCTs need control conditions?
- Class Exercises
- Online Exercise: Causality Lab
- Online Exercise: Try five practice rounds at Guess the Correlation. Then refresh and test your average error based on the next five rounds. http://guessthecorrelation.com/
- Homework Question
- Try guessing correlations at http://guessthecorrelation.com/ (Links to an external site.). Once you guess one within .10 of the right answer, screenshot it and upload it.
- If, among our population of zoo animals, the frequency of ear infections has a -.8 correlation with size, can we infer that ear infections cause creatures to get smaller? Why or why not?
- Practice Problems
- Suppose you want to find out whether pumpkins grow bigger when they are given mineral-rich water from a special well. Describe all essential features of a randomized controlled trial that would allow you to determine with reasonable confidence whether or not this is the case.